Запишите основные идеи и подсказки на карточках. Выражайте уверенность при помощи зрительного контакта, жестов и осанки. Тренируйтесь произносить речь перед зеркалом или другом. Старайтесь уложиться в отведенное время.

Given the above summary, write a detailed text in English for it.

Memorizing the introduction, key points, and conclusion word-for-word is wise. However, unless your teacher requires it, don’t feel like you have to memorize the entire speech verbatim. Reciting a completely memorized speech can feel stiff, so just commit the content to memory well enough that you can explain your ideas clearly and consistently.  While it’s generally okay to use slightly different phrasing, try to stick to your complete outline as best you can. If you veer off too much or insert too many additional words, you could end up exceeding your time limit. Keep in mind your speaking outline will help you stay focused. As for quotes and statistics, feel free to write them on your notecards for quick reference. Use hand gestures to emphasize key words and ideas, and make natural eye contact to engage the audience. Be sure to switch your gaze every 5 or 10 seconds instead of staring blankly in a single direction. Instead of slouching, stand up tall with your shoulders back. In addition to projecting confidence, good posture will help you breathe deeply to support your voice. Once you’ve committed the speech to memory, work on making your delivery as engaging as possible. Watch yourself in a mirror or record yourself to make sure you appear confident and natural. Get a second opinion and ask a friend or relative to watch you and offer feedback. Have them point out any spots that dragged or seemed disorganized. Ask if your tone was engaging, if you used body language effectively, and if your volume, pitch, and pacing need any tweaks. Use a stopwatch or cell phone app to time yourself when you practice your speech. Speak clearly and avoid rushing, but work on keeping your speech under the time limit, if your instructor set one.  If you keep exceeding the time limit, review your complete sentence outline. Cut any fluff and simplify complicated phrases. If your speech isn’t long enough, look for areas that could use more detail or consider adding another section to the body. Just make sure any content you...


Запишите основные события в хронологическом порядке. Решите, кто будет основными действующими лицами. Запишите лучшие моменты. Пишите так, как это сделали бы только вы. Рассказывайте о себе откровенно. Опишите дух времени.

Given the above summary, write a detailed text in English for it.

Start writing your autobiography by conducting research on your own life. Creating a timeline of your life is a good way to make sure you include all the most important dates and events, and it gives you a structure to build upon. You can consider this the "brainstorming" phase, so don't hesitate to write down everything you can remember, even if you don't think the memory will make it into the final version of the book.  Your autobiography doesn't have to begin with your birth. You may want to include some family history as well. Write down information about your ancestry, your grandparents' lives, your parents' lives, and so on. Having information about your family history will help readers get a sense of how you became the person you are. What happened when you were a teenager? What led you to make the decisions you made? Did you go to college? Write about those transitory years, too. Write about your career, your relationships, your children, and any big life-altering events that occurred. Every good story has interesting characters, friends and foes who help move the plot along. Who are the characters in your life? It's a given that your parents will play a role, along with your spouse and other close family members. Think beyond your immediate family to others who have affected your life and should play a role in your autobiography.  Teachers, coaches, mentors, and bosses are extremely influential in people's lives. Decide whether someone who has been a role model (or the opposite) for you will figure into your story. Ex-boyfriends and girlfriends might co-star in some interesting stories. What enemies have you had in life? Your story will be boring if you don't include some conflicts. Offbeat characters such as animals, celebrities you've never met, and even cities are often points of interest in an autobiography. The story of your entire life would start to get pretty long-winded, so you'll have to make some decisions about what anecdotes you're going to include. Begin drafting your manuscript by...


Запишите основные тезисы. Выберите подходящее время. Не осуждайте. Задавайте вопросы. Внимательно слушайте.

Given the above summary, write a detailed text in English for it.

Maybe you have recently discovered that your husband looks at porn. Or perhaps this has been an ongoing issue in your relationship. Either way, its time to have an honest conversation about your feelings.  Prepare to have an open conversation about the problem. Your first step is to figure out your feelings. Ask yourself why you object to his watching porn. Is it a religious issue for you? Or is it against your moral code? Choose some words that describe how you are feeling. Be descriptive with words such as "frustrated", "worried" or "nervous". Make a list of the things you want to say. This will help you to stay on track during the conversation and make sure that you make your points clear. Talking to your husband about his porn habit is an important conversation. You want to make sure that you allow yourselves time to deal with this tough topic. Take care to choose an appropriate time to have this talk.  Try to avoid having this conversation late at night or early in the morning. You two will not be at your emotional best if you are tired. Give him a heads up. Try saying, "I have something important to talk to you about. When is a good time for you?" Don't rush the conversation. Choose a time when you know neither or you will be rushing out the door to work or being interrupted by the kids. You might have a serious aversion to porn. Those are your feelings, and that is okay. However, try not to base your talk with your husband purely on judgement.  Try to use "I" statements. For example, you can say, "I feel very uncomfortable when you watch porn in our home." These types of statements are more effective than "you" statements. Your husband will likely be defensive if you say something such as "When you watch porn, you make me mad." Avoid eraser words. For example, try not to say, "I love you, but your porn habit is disgusting." Eraser words like "but" negate everything that was said before "but". It is important that you let your husband know how you are feeling. However, don't forget that effective...


Запишите остаток. Если вы не хотите записывать ответ с остатком, то можно найти ответ в виде десятичной дроби. Теперь у вас есть цифры (только нули), которые можно опускать и тем самым продолжать вычисления. Остановитесь и округлите ответ. В ответе укажите единицы измерения (метры, граммы, градусы и так далее).

Given the above summary, write a detailed text in English for it.

Depending on what you're using this division for, you may want to finish up with a quotient that's a whole number, with a remainder, i.e. an indication of how much is left over after you've completed your division.  In the example, the remainder would be 4, because 6 cannot go into four, and there are no more digits to bring down. Place your remainder after the quotient with a letter "r" before it. In the example, the answer would be expressed as "41 r4." You would stop here if you were trying to calculate something that would not make sense to express in partial units, for example, if you were trying to determine how many cars were needed to move a certain number of people. In a case such as this, it would not be useful think about things in terms of partial cars or partial people. If you plan to calculate a decimal, you can skip this step. If you are planning to calculate a precise answer rather than one with a remainder, you'll now need to move beyond whole numbers. When you've reached a point at which you are left with a number smaller than your divisor, add a decimal point to both the quotient and the dividend. In the example, since 250 is a whole number, every digit after the decimal will be 0, making it 250.000. Now you have more digits that can be brought down (all of them zeroes). Bring down a zero and continue as before, determining how many times the divisor can go into the new number. In the example, determine how many times 6 can go into 40. Add that number (6) to the quotient above the dividend and after the decimal point. Then multiply 6 by 6, and subtract the result from 40. You should end up with 4 again. In some cases, you will find that when you start to solve for the decimal, the answer repeats over and over. At this point, it's time to stop and round your answer up (if the repeating number is 5 or greater) or down (if it is 4 or less).  In the example, you could keep getting 4 out of 40-36 forever, and add 6's to your quotient indefinitely. Instead of doing this, stop the problem and...


Запишите отличительные физические черты, свойственные представителям этой расы. Опишите верования вашей расы. Идентифицируйте сильные и слабые стороны расы. Идентифицируйте остальные расы. Объясните историю расы.

Given the above summary, write a detailed text in English for it.

Do they commonly have bright green skin or hazel eyes? Are there reasons behind these physical traits? Be creative. This is your race and your creation, so you have complete control - maybe add on a tail or extra arms if that is what you want. There are no limits to what you could create! Choose a theme: Is your race an elegant, peaceful race, or are they brutal monsters? This doesn't have to be religious beliefs. Do they have free or strict gender roles? Do they believe their rulers are the descendant of some divine being? The things they believe in will greatly shape the mentality of the race. There's no such thing as an entire race being all evil or all good. You can however make it so that another species believes they are all evil because of certain events in the past which created this stereotype. Are they exceptional fighters? Can they use certain types of magic?  Are they always bad tempered, etc.? How can they be killed? This is essential to identify, especially if your race will be at war with another race at any point in your story. Does your race have any close relatives? Was there interbreeding that caused a mixture of races? Is one race descended from another? How did they come to be as they are? Were there any defining aspects of their history that have shaped the way they are now? Build a culture for your race. How did they make their weapons? What do their homes look like? What did they do for entertainment?


Запишите первые две цифры значения емкости. Воспользуйтесь третьей цифрой в качестве множитель нуля. Определите единицы измерения Определите значение допуска керамических конденсаторов. Определите значение допуска, когда маркировка имеет вид «буква-цифра-буква». Определите значение напряжения Интерпретация других маркировок.

Given the above summary, write a detailed text in English for it.

Older capacitors are less predictable, but almost all modern examples use the EIA standard code when the capacitor is too small to write out the capacitance in full. To start, write down the first two digits, then decide what to do next based on your code:  If your code starts with exactly two digits followed by a letter (e.g. 44M), the first two digits are the full capacitance code. Skip down to finding units. If one of the first two characters is a letter, skip down to letter systems. If the first three characters are all numbers, continue to the next step. The three-digit capacitance code works as follows:  If the third digit is 0 through 6, add that many zeroes to the end of the number. (For example, 453 → 45 x 103 → 45,000.) If the third digit is 8, multiply by 0.01. (e.g. 278 → 27 x 0.01 → 0.27) If the third digit is 9, multiply by 0.1. (e.g. 309 → 30 x 0.1 → 3.0) . The smallest capacitors (made from ceramic, film, or tantalum) use units of picofarads (pF), equal to 10-12 farads. Larger capacitors (the cylindrical aluminum electrolyte type or the double-layer type) use units of microfarads (uF or µF), equal to 10-6 farads. A capacitor may overrule this by adding a unit after it (p for picofarad, n for nanofarad, or u for microfarad). However, if there is only one letter after the code, this is usually the tolerance code, not the unit. (P and N are uncommon tolerance codes, but they do exist.) Ceramic capacitors, which are usually tiny "pancakes" with two pins, typically list the tolerance value as one letter immediately after the three-digit capacitance value. This letter represents the tolerance of the capacitor, meaning how close the actual value of the capacitor can be expected to be to the indicated value of the capacitor. If precision is important in your circuit, translate this code as follows:     B = ± 0.1 pF. C = ± 0.25 pF. D = ± 0.5 pF  for capacitors rated below 10 pF, or ± 0.5% for capacitors above 10 pF. F = ± 1 pF or ± 1% (same system as D above). G = ± 2 pF or ± 2% (see above). J = ± 5%....


Запишите пример. Для дробных функций с переменной в знаменателе надо приравнять знаменатель к нулю. Запишите область определения:

Given the above summary, write a detailed text in English for it.

Let's say you're working with the following problem: f(x) = 2x/(x2 - 4) When finding the domain of a fractional function, you must exclude all the x-values that make the denominator equal to zero, because you can never divide by zero. So, write the denominator as an equation and set it equal to 0. Here's how you do it:  f(x) = 2x/(x2 - 4) x2 - 4 = 0 (x - 2 )(x + 2) = 0 x ≠ (2, - 2) Here's how you do it: x = all real numbers except 2 and -2


Запишите пример. Задайте подкоренное выражение больше или равным 0. Выделите переменную. Запишите область определения. Найдите область определения функции с корнем, когда есть несколько решений.

Given the above summary, write a detailed text in English for it.

Let's say you're working with the following problem: Y =√(x-7) You cannot take the square root of a negative number, though you can take the square root of 0. So, set the terms inside the radicand to be greater than or equal to 0. Note that this applies not just to square roots, but to all even-numbered roots. It does not, however, apply to odd-numbered roots, because it is perfectly fine to have negatives under odd roots. Here's how: x-7 ≧ 0 Now, to isolate x on the left side of the equation, just add 7 to both sides, so you're left with the following: x ≧ 7 Here is how you would write it: D = [7,∞) Let's say you're working with the following function: Y = 1/√( ̅x2 -4). When you factor the denominator and set it equal to zero, you'll get x ≠ (2, - 2). Here's where you go from there:  Now, check the area below -2 (by plugging in -3, for example), to see if the numbers below -2 can be plugged into the denominator to yield a number higher than 0. They do. (-3)2 - 4 = 5  Now, check the area between -2 and 2. Pick 0, for example. 02 - 4 = -4, so you know the numbers between -2 and 2 don't work.  Now try a number above 2, such as +3. 32 - 4 = 5, so the numbers over 2 do work.  Write the domain when you're done. Here is how you would write the domain: D = (-∞, -2) U (2, ∞)


Запишите пример. Сложите цифры в правой колонке. Перенесите десятку влево. Сложите следующую колонку цифр. Повторяйте до конца строчки. Запишите ответ.

Given the above summary, write a detailed text in English for it.

For this method, you'll need to write out the problem as any other addition problem. Write the number twice, placing a plus sign in between.  Example: Find the double of 357. Write the problem as you would write out any other addition problem: 357 + 357 Add the right-hand digits of both written values together. Essentially, you are simply doubling the right-hand digit.  Example: For 357 + 357, the number on the right is 7. 7 + 7 = 14 If the sum of the right-hand digits is 10 or greater, you will need to carry the value in the “tens” place position over to the next set of digits. Only write the number in the “ones” place position as part of your answer.  Example: In this problem, 14 is greater than 10, so the you must carry the 1 over to the next place setting. The 4 will be the right-most digit in your answer. Add the next set of digits together, moving to the left. If you carried over a “1” from the previous place setting, you should add that to the two digits, as well.  Example: For 357 + 357, the next digit to the left is 5.  Since you carried over 1 from the previous place setting, you must also add it to the doubled value of this place setting. 5 + 5 + 1 = 11 Continue through the rest of the number in the same manner, working from right to left, until you reach the final set of digits on the left-hand side of the total value.  Example: Since 11 is greater than 10, you will need to carry the extra 1 over to the next place setting. The right-hand 1 will be the middle digit in your answer.  There is only one place setting left to deal with in this answer. You will need to add the values of this place setting together along with the 1 you carried over: 3 + 3 + 1 = 7 This 7 will be the left-most digit in your answer. If you haven't done so already, write the calculated sums from each place position side-by-side. This answer should be the doubled amount of your original number.  Example: The left-most digit is 7. The middle digit is 1. The right-most digit is 4. When written together, the answer is '714....


Запишите причины, по которым родители могут отказать вам. Попробуйте самостоятельно решить эти проблемы. Найдите информацию о правильном уходе за кошкой. Найдите способы выделить время для своего питомца. Заранее отрепетируйте фразы, которые собираетесь сказать родителям.

Given the above summary, write a detailed text in English for it.

" Think about why your parents may not want you to get a cat. Extra cost and responsibility may be concerns. If you can find solutions to problems, you can get a "Yes" answer.  Parents may worry about a cat clawing at furniture or making messes. Your parents may also worry about cost. A new animal needs new toys, bedding, and so on. Your parents are likely very busy, so they may worry about caring for the animal. Pets need a lot of time and attention. One of them may be allergic to cats. Don't let this dissuade you, however; there are some hypoallergenic cats! Be proactive and think of some solutions for potential issues. This way, if your parents raise concerns, you can quickly address their worries. Write these down right next to or right under your concerns, answering them. For example:  If your parents are worried about a cat harming furniture, suggest claw caps. They fit over a cat's claws, preventing it from scratching. Never declaw a cat. If your parents are worried about cost, offer to save up your allowance or get a job to pay for new supplies for your cat. If time is an issue, promise your parents you'll care for the cat yourself. Remind them that cats are independent animals and don't require as much attention as dogs. If one of your parents is allergic to cats, suggest hypoallergenic breeds, such as the Balinese, Bengal, Burmese, Cornish Rex, Siamese, Siberian, or Sphynx. The more you know, the more impressed your parents will be. Research a cat's basic needs in terms of food, attention, and grooming. If your parents see you can care for a cat, they're more likely to let you have one.  Tell your parents you'll provide your cat with a clean bed and keep the litter box in your room or garage. Tell your parents you'll feed your cat healthy cat food, and even suggest a few brands you found while researching. Vet visits can get expensive. Offer to help pay for the visits, and mention that you are willing to find a job to help earn money. Your parents want to make sure your cat is loved. Tell your...


Запишите простые множители для числителя и для знаменателя. Запишите исходное число как перемножение простых чисел. Избавьтесь от одинаковых множителей.

Given the above summary, write a detailed text in English for it.

A "prime" number is a number that cannot be divided by any other number and stay whole (apart from itself and 1, of course). 2, 3, 5, 7, and 11 are examples of prime numbers.  Start with the numerator. From 24, branch off into 2 and 12. Since 2 is a prime number already, you're done with that branch! Then take 12 into two more numbers: 2 and 6. 2 is a prime number -- great! Now divide 6 into two numbers: 2 and 3. You now have 2, 2, 2, and 3 as your prime numbers. Move onto the denominator. From 60, branch off your tree to 2 and 30. 30 will then split into 2 and 15. Then split 15 into 3 and 5,both prime. You now have 2, 2, 3 and 5 as your prime numbers. Take the list of prime numbers you have for each number and write them out to be multiplied. You don't actually have to do the math -- this just makes it easier to see.  So, for 24, you have 2 x 2 x 2 x 3 = 24. For 60, you have 2 x 2 x 3 x 5 = 60 Any numbers that you see that are part of both numbers can be eliminated. In this case, what we have in common is a pair of twos and a 3. Goodbye!  What we are left with is 2 and 5 -- or 2/5! The same answer we got with the above method. if both numerator and denominator are even numbers, just think of splitting the number in half.  keep on doing it to both until they are to small to split any more.


Запишите разряд каждой цифры двоичного числа. Умножьте каждую цифру двоичного числа на соответствующий разряд. Сложите полученные результаты.

Given the above summary, write a detailed text in English for it.

When you learned decimal counting, you learned about the "place values": the ones place, tens place, and so on. Since binary has two symbols, the place values multiply by two each time you move to the left:   1 is the ones place  10 is the twos place  100 is the fours place  1000 is the eights place Start with the ones place on the far right, and multiply that digit (0 or 1) by one. On a separate line, move to the twos place, and multiply that digit by two. Repeat this pattern until you've multiplied each digit by its place value. Here's an example:  What is the binary number 10011 in decimal? The rightmost digit is 1. This is in the ones place, so multiply by one: 1 x 1 = 1. The next digit is also 1. Multiply this by two: 1 x 2 = 2. The next digit is 0. Multiply this by four: 0 x 4 = 0. The next digit is also 0. Multiply this by eight: 0 x 8 = 0. The leftmost digit is 1. Multiply this by sixteen (eight times two): 1 x 16 = 16. Now you've converted each digit into its decimal value. To find the value of the full number, just add all the decimal values together. Here's the rest of your example:  1 + 2 + 16 = 19. The binary number 10011 is the same as the decimal number 19.


Запишите свое определение голода. Ешьте сидя. Ешьте не спеша.

Given the above summary, write a detailed text in English for it.

It can be difficult to maintain small portions or not snack when you feel hungry.  However, it's also important to understand and define what true physical hunger is.  You may feel "hungry" when you're bored, stressed or angry and be tempted to eat.  Physical hunger comes on gradually.  In addition your stomach may feel empty or growl or make noises.  Physical hunger also goes away after even a small portion of food.  If it's been several hours since your last meal or snack, you may be physically hungry.  Eat your planned snack or meal. If you notice that you're feeling "hungry" without the signs of physical hunger, consider the other reasons you may be craving foods. Remember, feeling hungry is OK.  You should feel hungry before your meal and you might feel hungry at bedtime.  This is normal and expected. It can be easy to eat in the car, during a work meeting or while watching TV.  Sitting down to eat will draw your attention to your meal.  This can help you stick to a smaller portion.  Take this a step further and disconnect from all technology.  Turn off the TV, computers and phones so you can fully pay attention to your meal. Set a rule that you only eat when you're sitting down at a table or desk.  This will help curb unnecessary eating or snacking. Take about 20 minutes or more to eat your meal.  This is about the time it takes for your brain and stomach to communicate that you've had enough to eat and you're satisfied.  Promote an environment that is solely used to eat. Avoid snacking while working or watching TV. Sit down to a meal and don't get up until it's done. Really savor your food and dedicate a specific meal time to you. You will appreciate your meal more and feel more full as you enjoy each bite. Set a timer or a stop watch to give you an idea of how much longer it should take you to eat. Put your fork down in between each bite, take a sip of water between each bite or chat with friends or family as you eat. Take small bites and chew each bite at least 20 times to slow you down.


Запишите свои идеи. Придумайте тему для игры. Разработайте сначала механику игры (как альтернативный вариант). Определитесь с возрастными рамками игры. Определите количество игроков, игровое время и предельные размеры своей игры. Решите, каким образом будет определяться победа в игре. Запишите основные правила игры.

Given the above summary, write a detailed text in English for it.

You never know when the perfect inspiration is going to hit. You may find that combining two different ideas makes a neat new game concept. Keep a log of ideas in a notebook, on your computer, or in a note taking app on your phone.  It might be particularly useful for you to keep your note-taking tools handy when you’re at game night. Playing games might spark the perfect idea for your own game. When using store-bought games for inspiration, ask yourself, “What would I do to improve this game?” This question can often lead you to interesting innovations. Themes are the “feel” of a game and can also be referred to as the game’s “genre.” Games like Sorry! have a simple "race to the end" theme. Complex wargames have conflicts, player politics, and game piece placement strategy.  You might find inspiration for the theme of your game in your favorite novel, comic book, or TV series. Mythology and legends are often used when developing themes. Common elements include vampires, witches, wizards, dragons, angels, demons, gnomes, and more. Mechanics are the ways players interact with the game and each other. In Monopoly, the mechanics are centered around dice-rolling, buying/selling property, and making money. The mechanics of Axis & Allies involve moving pieces across a large board and resolving player conflicts with dice rolls.  Some people come up with a mechanic and then create a theme around it, while others come up with a great theme and then tailor the mechanics to match that theme. Experiment to find what works best for you. Common mechanics you might be interested in using include turns, dice rolling, movement, card drawing, tile laying, auctioning, and more. The age range of your players will influence the complexity of your game board and its rules. If you are designing the game for children, it’s better for your game to be simple, easy-to-understand, and fun. For adults, you could create something more competitive, exciting, and complex. Keep your theme in mind when you’re deciding the age range. A zombie...


Запишите свои качества, которыми вы гордитесь. Записывайте цели. Помогайте другим. Позвольте себе жить дальше. Создавайте новую реальность без бывшего парня.

Given the above summary, write a detailed text in English for it.

This will help you to focus on the positive rather than the negative. You’ll also notice which of your strengths you value, rather than what someone else does or doesn't like about you. Once your viewpoint is no longer clouded by negativity you'll be able to uncover your true self.  Were you always proud of your ability to write thoughtful poems, but he didn't appreciate you for it? Put this one at the top of your list. Alternately make a list of obstacles you’ve overcome and hardships you’ve persevered through. Recognizing how resilient you’ve been in the past, reminds you that you can do it in the present. Make a list of realistic steps and a timeline to help you focus on anything but your break up and your ex. A sense of accomplishment will boost your self-esteem and remind you of your worth. Working hard towards something for the future will mean you’re less focused on the day-to-day and more determined on the overall big picture.  Writing down your goals, rather than simply imagining them, will help them seem real and make you more likely to hold yourself accountable. Your goals can be anything from working towards a promotion at your job to simply flossing your teeth everyday. The idea is to feel good about yourself and your accomplishments. Focusing on another person, and acting as their support system, will give you a purpose and shift your thoughts away from your break up. Think of it as rechanneling the love and energy you previously put into your relationship. Others will naturally be drawn to you and want to spend time with you, making you feel less lonely and rejected.Volunteer at a local soup kitchen or perform acts of kindness towards a friend who has experienced a death in the family.  Giving back and showing kindness towards others has been proven to relieve symptoms of depression.  People will be more likely to help and support you in your time of need. It may be hard to believe that you’ll find love again, but remember that unless you put yourself out there and take risks, you won’t reap...


Запишите свои мысли. Проявляйте эмпатию. Откажитесь от любых ожиданий. Говорите за себя. Выслушайте точку зрения человека.

Given the above summary, write a detailed text in English for it.

If you're unable to get over a disappointment, it's important you talk things out with the other person. Having a conversation about how someone hurt or disappointed you can be stressful. You should try writing your emotions out ahead of time. This way, you'll have your thoughts somewhat organized going into the conversation.  Try to write down what you're feeling. After spilling your thoughts out onto the page, consider how you can best articulate them. Reword your thoughts a bit, trying to phrase them in a way that would make sense to another person.  Also, keep in mind what you want to accomplish. Do you want an apology? Do you want the person to explain his or her actions? Do you want this person's behavior to change in the future? The answers to these questions can help guide your writing. If you're going to have a difficult conversation with someone, enter the conversation with empathy. This will prevent you from coming off as combative during a discussion. Try to consider the other person's perspective as much as you can. Be open to listening to their side and genuinely considering it. Remember, the point of a conversation is to resolve a dispute and not to win it. There are two sides to every story and it's important to be open to the other person's side. You should abandon any expectations you may have going into the conversation. If you expect things to go a certain way, you may feel disappointed or frustrated when they turn out differently. Allow the discussion to unfold naturally. Remember, you don't know how the other person will feel. It's unproductive to make assumptions ahead of time. "I"-statements are statements phrased in such a way to emphasize personal feeling over objective truth. When you use an "I"-statement, you make your feelings the main point of a sentence. You are not blaming or judging a person for his or her actions. You are simply stating how those actions made you feel and why.  "I" statements have three parts. They begin with "I feel," followed by the emotion you're feeling....


Запишите свои мысли. Решите, с кем вы хотите поделиться. Решите, насколько подробным будет рассказ. Соберите информацию для друзей. Скажите, какую помощь вы желаете получить. Уясните, что вы не надоедаете друзьям.

Given the above summary, write a detailed text in English for it.

Since telling your friends about anxiety may cause you anxiety, you should help yourself by getting your thoughts together beforehand. If you get anxious and upset while talking to your friends, you may not be able to get words out. Make a list of points you want to make, things you want to say, or ideas you want to address when you talk to your friends. After you write down your thoughts, you should start a new list. Carefully decide who you want to tell about your anxiety disorder. Consider who the person is to you. Ask yourself why you want to tell this person. You should also decide if you feel comfortable with this person knowing.  Figure out if you believe the person you want to tell is supportive. How has this person reacted when you’ve shared things with him or her before? You also should think about whether you want help from the person or if you simply just want them to know. For example, you may want to tell your immediate family, your partner, and your best friends about your anxiety disorder because you spend the most time with them. However, you may also want to tell the person you share your office with about your anxiety disorder in case you face anxiety while at work. Depending on who you tell, the amount of information you share with that person may change. You should consider how much about your disorder you feel comfortable sharing.  For example, you may decide to be completely honest with your parents, spouse, or best friend. But you may limit how much detail you give your co-worker. Figure out how much you feel comfortable sharing with your friends. You should also consider why they need to know certain details. Some people may not need to know about medication or some of the ways anxiety keeps you from certain activities. Unless your friends know someone else with an anxiety disorder, they may have no experience with it. They may also not have any knowledge about anxiety, anxiety disorders, panic disorders, or mental health issues. Put together some resources for them so they can learn...


Запишите свои мысли. Теперь воплотите ожидания в жизнь. Используйте «Я-утверждения», они помогут уменьшить вину. Попросите извинений.

Given the above summary, write a detailed text in English for it.

Sometimes, letting someone know why and how they hurt you can make you feel like you got back at them. If possible, let your ex know you want to talk.  A productive confrontation may make you feel better. Prior to the conversation, try to write down your thoughts.  Write down how you feel and why. Try to find the best way to articulate how you were hurt. Focus on what you expect to get out of the situation. Do you want an apology? Do you want your ex to understand how he hurt you and feel bad? Expectations can skew how you behave. When you're hurt and angry, it can be especially difficult to control your emotions. If you go into the conversation expecting your ex to react a particular way, you may find yourself becoming angry or frustrated if things unfold differently.  You want the conversation to flow naturally. You do not want to react with surprise or frustration if things unfold slightly different than you imagined. Go into the conversation acknowledging you're uncertain what will occur. This way, you'll be better equipped to handle unexpected turns. "I"-statements are statements phrased in a way to reduce blame. They put focus on your feelings over an outside judgement of the situation. An "I"-statement has three parts. It begins with, "If feel..." after which you immediately state your feeling. From there, you state the action that led to that feeling. Lastly, you explain why you felt the way you did.  For example, you may be inclined to say something like, "It was incredibly hurtful that you lied to me about needing time to yourself. You immediately started dating someone else. You could have just told me you weren't interested in me romantically." Rephrase the above sentiment using an "I"-statement. For example, "I felt incredibly hurt when you told me you didn't want to be in a relationship and then had a new girlfriend in a week because I wish you have been honest with me." An apology can really help make you feel better. It lessens the need for revenge and helps you forgive someone who hurt you....


Запишите свои негативные качества. Определите свои основные ценности. Ваше самоопределение должно быть позитивным.

Given the above summary, write a detailed text in English for it.

Recording them and paying attention to them will help you let go of them. Getting them out in the open can help to take away some of their hold on your mind and self. Don't limit yourself in negative ways. Definition of the self determines the action. So, for instance, if you're defining yourself as someone who has bad romantic relationships, you've already lost the potential for a good romantic relationship. It is a story that you tell yourself, and then because you believe the story, you will already be behaving in ways that make the story true. You don't want to define yourself based on outside forces, because outside forces are volatile and subject to constant change. By basing your self-definition on core values, you will have a better chance of having a stable self-definition.  You won't lose your self identity if you base it on values you hold at your core, like compassion, courage, integrity. Write down a list of these values and consciously and mindfully act them out in your daily life. Therefore, if courage is one of your core values, stand up for someone being harassed at the bus stop, or if honesty is a core value, fess up to having lost your father's favorite watch. If compassion is on that list, spend time volunteering at a homeless shelter. This doesn't mean that you don't acknowledge the negative events and actions that have happened in your life. They are as much a part of you as the positive, but they do not define you.  This means don't let outside circumstances rule your identity. That comes from within in, from the core values that you have already identified as being important to your identity. Understand that the negative experiences in your life have offered knowledge. For example, if you have had negative experiences with romance, learn from those experiences. What have they taught you about the kind of person you want to be?


Запишите свои оценки. Рядом с каждым предметом запишите полученную числовую оценку. Запишите, сколько времени (в неделю) отводилось на каждый предмет. Вычислите, сколько баллов вы получили за каждый предмет. Вычислите среднюю оценку (GPA) за семестр.

Given the above summary, write a detailed text in English for it.

Write down a list of what classes you took during the term. Next to each class, write down the grade you earned. Don't worry about writing down a percentage, just note the letter grade that you got. For example, your list may look something like this:  Biology: B Calculus: A History: A Spanish: C Use your school's grading scale to determine how many points each letter grade earns. The scale should be available from the registrar or the registrar’s website. Be sure to take into account any pluses or minuses, if applicable. These may or may not change the number of points assigned to each grade letter, depending on your school’s policy. For example, you'd build on your list like this:  Biology: B (3 points) Calculus: A (4 points) History: A (4 points) Spanish: C+ (2 points) Once you've made your list, look in your school's course catalog to determine how many credits each course is worth. Sometimes, seminars or labs may be worth fewer credits so it's important to calculate how many credits you took in a term. Write down how many credits each course is worth. For example, your list may now look something like this:  Biology: B (3 credit points) at 3 hours Calculus: A (4 credit points) at 4 hours History: A (4 credit points) at 3 hours Spanish: C (2 credit points) at 3 hours For each course on your list, multiply the credit for your grade by the number of hours the course was worth. Once you've done this for each course, you can add up all of the grade points (credit points) to calculate your total grade points (credit points) for the term. Your list may look like this:  Biology: B (3 credit points) at 3 hours = 9 credit points Calculus: A (4 credit points) at 4 hours = 16 credit points History: A (4 credit points) at 3 hours = 12 credit points Spanish: C (2 credit points) at 3 hours = 6 credit points Total = 43 credit points Take your total credit points and divide this number by the number of credit hours you took. Remember not to count any classes you withdrew from. For example, you would divide 43 (credit...


Запишите свои сильные стороны, достижения, и все то, что вам в себе нравится. Заботьтесь о себе. Займитесь тем, что вам нравится делать. Устанавливайте перед собой новые цели и задачи. Проводите время с людьми, которые вызывают у вас положительные чувства и заставляют гордиться собой. Подумайте о том, за что вы благодарны. Учитесь всегда чувствовать себя важным.

Given the above summary, write a detailed text in English for it.

Grab a pen and paper and start making three detailed lists about yourself.  Make one list each for your strengths, achievements, and things that you value about yourself.  This will help you focus on the positive aspects about yourself.  You can also read the lists anytime for a quick self-esteem boost.  Have a friend or family member help you. Read over your lists regularly to help remind you of how important you are. Remind yourself that you are valued and important by taking excellent care of yourself.  Caring for your health and personal needs can help you to have a healthy amount of self-esteem and self-worth.  Get enough sleep at night. Eat a healthy diet, getting plenty of fruits and vegetables while avoiding foods with high levels of fat and sugar. Exercise regularly to help you feel your best and stay strong and healthy. At least once a day, set aside time for an activity that you love doing.  Whatever that activity may be, you can show yourself that you are important and deserve the freedom to do what interests you. Select a new hobby or activity that has always interested you and start doing it.  Set goals to improve your skills in this new hobby and start working to meet them.  This will allow you to remind yourself that you are capable and confident when meeting a challenge.  Try learning how to play a musical instrument. Learn a new language that you find interesting. Try taking up a new sport or exercise program. A large part of our self-esteem comes from the people we surround ourselves with.  Being around negative or critical people can cause self-doubt to arise.  However, surrounding yourself with positive and energizing people can help make you feel important and valued. Gratefulness can remind you of what is important to you, your life, and the people who matter to you. Think about all of the people, whether it's friends or family, who hold you in high regard. Remembering gratefulness can help you remember that you are important. Work on building your self-esteem enough to realize how much...


Запишите свой отзыв. Резюмируйте суть речи. В своем отзыве сосредоточьтесь на содержании выступления. Всегда нужно находить повод  для похвалы. Постарайтесь основать свой отзыв на пересмотре выступления. Постарайтесь указывать не более трех советов для усовершенствования речи.

Given the above summary, write a detailed text in English for it.

Whatever the occasion and the reason you're giving feedback, for school or informally, it's better to write down your criticisms, praise, and comments, so the speaker will have some document of your feedback. If you have some suggestions, it'll be too easy for the speaker to forget, especially immediately following the speech. It's best to write a short note, no more than 250 or 300 words, to accompany your evaluation of the speech. For some speech classes, you may have to fill out a rubric or assign a grade to a speech. Follow the specific class instructions regarding this and assign a grade appropriate. Starting feedback with a summary of what you took from the speech is the most helpful way of letting the speaker know whether or not what they were trying to say was communicated accurately. Don't worry about whether or not your summary is perfectly accurate or not. If you were listening closely and trying your best to follow it, any failure on your part should be instructive for the speaker. That's something they need to make more clear in the speech.  Try to start your response with things like, “What I heard you saying is…” or “What I got from this speech was…” A good summary should be several sentences in the evaluation, perhaps slightly less than half of your feedback. Identify the main idea and the main supporting points of the speech. The summary should focus on content only. Not everyone can or should be Martin Luther King Jr. Focusing your feedback primarily on the oratorical skills of the speaker isn’t usually going to be that helpful, especially if we’re talking about a class speech, a wedding speech, or some kind of business presentation. If the speaker is mostly a wet blanket, focus on how the content could better match the speaking style and how the tone might be changed to match. These are changeable things. Telling a speaker to be "more dynamic" or "funny" isn't good feedback. Even if you just watched your best friend struggle through the lamest best-man speech of all time, it’s important to...


Запишите свою мысль (мысли). Представьте себе эту ситуацию. Теперь поставьте эту мысль на паузу! Тренируйтесь.

Given the above summary, write a detailed text in English for it.

Your thoughts are distracting you from your daily activities and causing you unhappiness, anxiety or worry, so the first thing you must do is put them on paper.  Write down all your upsetting thoughts in order of the most stressful to the least stressful.  For example, if you keep thinking you might lose your job, your list could look something like this:  1. How will I be able to pay my bills and take care of my child?  2. What if I can't find a new job?  3. I'll be so embarrassed if I'm escorted by security out of the office with my belongings in a box. You're going to begin your practice with the least-stressful thought. Sit or lie down in a private place.  Close your eyes. Imagine a situation in which you might have this stressful thought. Set a timer, watch or other alarm for three minutes. Then focus on your unwanted thought. When the timer or alarm goes off, shout "Stop!" That's your cue to empty your mind of that thought. Think of one intentional thought (the beach, etc.) and keep your mind fixed on that image or thought for 30 seconds. If the upsetting thought comes back during that time, shout "Stop!" again. Practicing meditation or yoga may help calm and clear your mind.  You can stand up when you say "Stop" if you'd like or snap your fingers or clap your hands. These actions reinforce the "Stop" command and further interrupt your thought. Instead of using a timer, you can tape-record yourself shouting "Stop!" at one-, two- and three-minute intervals and use the recording to do the thought-stopping exercise. When you hear your recorded voice say "Stop," empty your mind for 30 seconds. Repeat this exercise until the thought goes away on command. Then try the exercise again and interrupt the thought by saying "Stop" in a normal voice rather than a shout.  Once your normal voice is able to stop the thought, try whispering "Stop." Over time, you can just imagine hearing "Stop" inside your mind. At this point, you should be able to  stop the thought whenever and wherever it occurs.  Once you've achieved...


Запишите свою проблему. Поговорите о проблеме. Примите свои чувства. Обратитесь к психологу.

Given the above summary, write a detailed text in English for it.

Put your problem on paper with pen. This will help the problem seem more tangible and will make you more likely to try to solve it when it is written down and staring you in the face.  For example, if your problem is that you don't have enough money, you could write that down. You could also write down the implications of that problem to drive home the point and motivate you to solve it. An implication of not having enough money might be that you are stressed out and that you can't enjoy the kinds of things that you would like to. If the problem isn't something private, put the list somewhere you see it so you don't forget to act on it. For example, you might put it on your fridge. Share all the relevant details of your problem with someone that you trust with the information, such as a friend, family member, teacher, or parent. At the least it can help to reduce stress. . In addition, she or he may be able to offer you advice that you hadn't thought of before. If you’re going to talk to someone else who has the same problem, you will need to be tactful. Let her know that you just want to learn so you can solve it, too. Your feelings can act as guides that let you know how your problem solving is going. Feelings are important, even the negative ones. If you feel very frustrated or angry, for example, rather than trying to brush those feelings under the rug, acknowledge them and assess their cause. By finding the source, you may also find solutions to your problem.  It’s okay to feel upset, angry, worried so long as you know that being upset, angry or worried won’t help solve the problem. You will have to take action to solve the problem. Still, these emotions can help you realize you have a problem, as well as suggest its source. Some ways to calm down when you're feeling upset include: focusing on your breathing, count to 10 (or higher if you need to), gently talk yourself down (tell yourself "it's going to be alright," or "take it easy."). Try going for a walk or run or listening to calming music. If your...


Запишите свою речь. Отрепетируйте свою речь. Решите, кому сказать об этом в первую очередь. Выберите подходящее время. Проанализируйте свои чувства. Поставьте точку. Скажите родителям, что вы готовы встречаться с парнем. Будьте готовы вести переговоры. Расскажите о вашем парне. Не пытайтесь утаивать информацию.

Given the above summary, write a detailed text in English for it.

If you're afraid you'll get flustered, it's perfectly fine to write out what you think you'll say. This can help you process what you want to say so that you can present your new relationship in the best way possible. That way, when the time comes, you'll be able to get it out without stopping. As you write out what you might say, you may try to anticipate your parents' responses. That way you can answer their concerns as you tell them about your boyfriend. It's normal to feel apprehensive about telling your parents about your new relationship. Practicing what you'll say to them can make it easier. Use a friend or understanding relative for practice.   You can also practice in front of a mirror.  Ask someone you trust to help, not someone who may reveal your news before you're ready. For example, choose a cousin you're close to rather than an older sibling, who might feel obligated to tell your parents. You might have a parent you feel closer to or maybe one of your parents tends to be more lenient than the other. Oftentimes, breaking the news to a parent who is easier to talk to can clear the way for talking to the other parent.  For instance, if you grew up as a "daddy's girl," meaning you can now wrap him around your little finger, you might start with your dad. On the other hand, if your dad tends to be overprotective, you might start with your mother instead. This approach can be an especially helpful idea if you are a teenager with your first boyfriend. On the other hand, if you think both of your parents will take it equally well (or badly), just rip off the bandaid and tell them both at the same time. You don't want to tell your parents when they are busy with something else or when they aren't in a good mood. If you want, you can ask them when a good time to talk would be. Try to choose a time when the house is calm, and your parents are not stressed or distracted by something else. However, don't use picking a good time as a way to continually put off telling them. You will need to tell them...


Запишите себя на диктофон. Читайте вслух. Слушайте подкасты, радио и новости. Слушайте музыку. Смотрите телевидение и фильмы. Думайте вслух.

Given the above summary, write a detailed text in English for it.

When you're by your lonesome, you have no reason to be nervous. You can let your brain flow freely -- so record yourself now! Your English is going to be at its best. Find a book on tape or a clip online that you can mimic. Does your English sound the same? Or record yourself reading from a book. You'll be able to actually hear yourself (which we surprisingly have trouble with in real time) and be able to pinpoint the quirks in your English and where you slow down and have trouble. Then rerecord it and see how you've improved! If your hands are full or you don't have a recording device, simply read aloud -- ideally, every day for at least 15 or 20 minutes. You'll get used to speaking for longer periods of time and forming long sentences won't phase you. And you'll run into words you can add to your vocabulary. It's best to choose books with lots of dialogue. The language is generally more real and a bit simpler; after all, dialogue is conversation. Being able to read poetry is great but conversations are a much more practical skill, you know? We live in such a digital age; even if you think you don't have native speakers at your disposal, you actually do. Scientific American, CBC, BBC and Australia's ABC Radio are great mp3s to get started with, but there's also a million podcasts out there and handfuls of news stations, too. And the best part is that these people generally speak clearly and have pretty generic accents. Another bonus? You'll have interesting things to talk about in English! You'll be up on all the news - even if you're just repeating what you've heard (not like anyone will know!). You're improving your English by expanding your knowledge. Two birds with one stone, really. Alright, so it's not as good as listening to spoken news/podcasts/etc., but it is good. If you can concentrate on one song a day or so, even better. Just make sure you actively try to understand it. Google the lyrics and sing along! It's best to stick to ballads -- songs that go a bit more slowly. Pick one a day until you...


Запишите серийный номер вашего телефона. Зарегистрируйте телефон на специализированном онлайн-сервисе. Храните вещи на своих местах. Примите меры во избежание утери телефона в будущем.

Given the above summary, write a detailed text in English for it.

Every cell phone is equipped with an electronic serial number. Depending on the type and model of cell phone you use, your phone's unique number may be called an IMEI (International Mobile Equipment Identity), MEID (Mobile Equipment Identifier), or ESN (Electronic Serial Number). It's often located on a sticker under the battery, though its location will vary depending on your phone.  Find your cell phone's serial/identification number when you first purchase it. Write the number down and keep it in a safe place at home. If you ever lose your phone, you can report your serial/identification number to the police and to your wireless provider. Some online services, such as MissingPhones.org, allow you to register your cell phone with the website. This can help you in the future, should your phone become lost or stolen down the line. In order to register your phone, you'll need the serial number from your device. If you're prone to losing things, you may want to work on reducing the frequency of those losses, no matter what the item may be. Try getting into a habit of leaving things in particular places, which can help you know where to look next time.  If you tend to lose your phone at home, try to keep it on a nightstand or coffee table whenever it's not on your person. When your phone is on your person, give it a designated pocket and always check that you have everything when you get up to leave. For example, you might tap your pockets to confirm in a particular order that you've got your keys, wallet, and cell phone. There are certain precautions you can take to assist your efforts in the future, should you lose or misplace your phone again. You can register your phone for a GPS tracking service, either through your wireless provider or through an independent service like AccuTracking or Belon.gs. You can also keep a written record of your phone's serial/identification number in your wallet or at home.


Запишите скрипичный ключ в нотном стане. Напишите музыкальный размер (такт). Определите тональность. Изучите различные виды нот, которые вы будете использовать. Читайте ноты. Выберите свой состав инструментов.

Given the above summary, write a detailed text in English for it.

A page of sheet music is made up of notes and rests printed on five parallel lines and the spaces in between them, which is called the staff. The lines and spaces are counted from the bottom to the top, meaning the higher-pitched notes will be higher up on the staff. The staff can be in either bass or treble clef, which will be marked at the left-most point on each line of the staff. The clef marker will tell you which line corresponds to which set of notes:   In the treble clef, also known as "G clef," you'll notice a sign a bit like the ampersand (&), printed on the left side of each staff. This is the most common clef for sheet music. Guitar, trumpet, saxophone and most higher-register instruments will be printed on treble clef. The notes, starting on the bottom line and going to the top line, are E, G, B, D, and F. The notes in the spaces between the lines, starting with the space between the first and second, are F, A, C, and E.  In the bass clef you'll notice a sign that looks a bit like a curved number "7" to the left of each line of the staff. The bass clef is used for instruments in the lower register, like trombone, bass guitar, and tuba. Starting with the bottom, or first line, the notes ascend G, B, D, F, and A. In the spaces are A, C, E, and G, from the bottom to the top.  The tenor clef is used for choral works. It looks like the treble clef but with a little number 8 under it. It reads just like the treble clef but sounds an octave lower. The time signatures reforest to the number of notes and beats in each measure on the staff. On the staff, measures will be separated by periodic vertical lines, separating the staff into little chunks of notes. Just to the right of the clef will be two numbers, one over the other, like a fraction. The top number represents the number of beats in each measure on the staff, while the bottom number represents the value of each beat in the measure. In western music, the most common time signature is 4/4 time, which means there are four beats in each measure, and...


Запишите сюжет, который вы придумали, и решите, интересен он вам или нет. Определите возрастную группу, для которой вы пишете свой рассказ. Придумайте персонажей. Начните придумывать свой рассказ. Напечатайте ваш рассказ или запишите его.

Given the above summary, write a detailed text in English for it.

Or you could pick a common topic that's regularly associated with the public, like "mean" cliques in middle school or a "Cinderella" like story, and add a twist to it. Just make sure that people will not be annoyed by that. Another method that works is to pick a few key words of the theme your story will be and write them down. For example, a few words of the theme of your story could be "scary", "horror", and "terrifying". It's basically the mood of your story, the theme of it and what "feeling" it sets off to your readers. If you want to base your story towards younger people, write about youthful topics. If your age group is based towards older people, it is better to write about more mature topics. Don't write about callow topics if you're basing your story towards older people. However, keep in mind, some older people do like younger story topics. Make sure the characters relate to your story and try to mix it up a little. Like you could have a bizarre character be in a professional business. You can write a whole profile for your characters, or you could just keep it simple by just writing their name, age, and maybe a small description. Give them a unique name. Give them an unexpected personality. Just don't overdo it or readers will be confused. This plot could be anything, from talking zebras to upwards gravity, anything. Make it interesting and unique. Make up a topic that was never used before. That may sound hard, but it's really not. Pick a random scene with a unique topic and plot. It's really important to make sure it interests you.


Запишите теорему Пифагора. В формулу подставьте значения сторон. Длину и ширину возведите в квадрат, а затем сложите полученные результаты. Извлеките квадратный корень из обеих сторон уравнения.

Given the above summary, write a detailed text in English for it.

The formula is a2+b2=c2{\displaystyle a^{2}+b^{2}=c^{2}}, where a{\displaystyle a} and b{\displaystyle b} equal the side lengths of a right triangle, and c{\displaystyle c} equals the length of a right triangle’s hypotenuse. You use the Pythagorean Theorem because a diagonal of a rectangle cuts the rectangle into two congruent right triangles. The length and width of the rectangle are the side lengths of the triangle; the diagonal is the hypotenuse of the triangle. These should be given, or you should be able to measure them. Make sure you are substituting for a{\displaystyle a} and b{\displaystyle b}. For example, if the width of a rectangle is 3 cm, and the length is 4 cm, your formula will look like this: 32+42=c2{\displaystyle 3^{2}+4^{2}=c^{2}}. Remember, squaring a number means to multiply the number by itself. For example:32+42=c2{\displaystyle 3^{2}+4^{2}=c^{2}}9+16=c2{\displaystyle 9+16=c^{2}}25=c2{\displaystyle 25=c^{2}} The easiest way to find a square root is to use a calculator. You can use an online calculator if you do not have a scientific calculator. This will give you the value of c{\displaystyle c}, which is the hypotenuse of the triangle, and the diagonal of the rectangle. For example:25=c2{\displaystyle 25=c^{2}}25=c2{\displaystyle {\sqrt {25}}={\sqrt {c^{2}}}}5=c{\displaystyle 5=c}So, the diagonal of a rectangle with a width of 3 cm and a length of 4 cm is 5 cm.


Запишите уравнение Клапейрона-Клаузиуса, которое используется для расчета давления пара при его изменении с течением времени. Подставьте в уравнение Клапейрона-Клаузиуса данные вам значения величин. Подставьте константы. Решите уравнение при помощи алгебраических операций.

Given the above summary, write a detailed text in English for it.

The formula used for calculating vapor pressure given a change in the vapor pressure over time is known as the Clausius-Clapeyron equation (named for physicists Rudolf Clausius and Benoît Paul Émile Clapeyron). This is the formula you'll use to solve the most common sorts of vapor pressure problems you'll find in physics and chemistry classes. The formula looks like this: ln(P1/P2) = (ΔHvap/R)((1/T2) - (1/T1)). In this formula, the variables refer to:   ΔHvap: The enthalpy of vaporization of the liquid. This can usually be found in a table at the back of chemistry textbooks.  R: The real gas constant, or 8.314 J/(K × Mol).  T1: The temperature at which the vapor pressure is known (or the starting temperature.)  T2: The temperature at which the vapor pressure is to be found (or the final temperature.)  P1 and P2: The vapor pressures at the temperatures T1 and T2, respectively. The Clausius-Clapeyron equation looks tricky because it has so many different variables, but it's actually not very difficult when you have the right information. The most basic vapor pressure problems will give you two temperature values and a pressure value or two pressure values and a temperature value — once you have these, solving is a piece of cake.  For example, let's say that we're told that we have a container full of liquid at 295 K whose vapor pressure is 1 atmosphere (atm). Our question is: What is the vapor pressure at 393 K? We have two temperature values and a pressure, so we can solve for the other pressure value with the Clausius-Clapeyron equation. Plugging in our variables, we get ln(1/P2) = (ΔHvap/R)((1/393) - (1/295)). Note that, for Clausius-Clapeyron equations, you must always use Kelvin temperature values. You can use any pressure values as long as they are the same for both P1 and P2. The Clausius-Clapeyron equation contains two constants: R and ΔHvap. R is always equal to 8.314 J/(K × Mol). ΔHvap (the enthalpy of vaporization), however, depends on the substance whose vapor pressure you are examining. As noted...


Запишите уравнение в стандартной форме. Упростите уравнение (если можно). Проверьте, можно ли решить уравнение.

Given the above summary, write a detailed text in English for it.

A linear equation is one that has no exponents greater than 1 on any variables. To solve a linear equation in this style, you need to begin by writing it in what is called “standard form.” The standard form of a linear equation looks like Ax+By=C{\displaystyle Ax+By=C}, where A,B{\displaystyle A,B} and C{\displaystyle C} are integers. If the equation is not already in standard form, you need to use the basic rules of algebra to rearrange or combine the terms to create the standard form. For example, if you begin with 23x+4y−7x=−3y+15{\displaystyle 23x+4y-7x=-3y+15}, you can combine similar terms to reduce the equation to 16x+7y=15{\displaystyle 16x+7y=15}. When the equation is in standard form, check all three terms A,B{\displaystyle A,B} and C{\displaystyle C}. If there is a common factor in all three terms, then reduce the equation by dividing all terms by that factor. If you reduce evenly across all three terms, then any solution you find for the reduced equation will also be a solution for the original equation. For example, if all three terms are even, you can at least divide by 2, as follows:   42x+36y=48{\displaystyle 42x+36y=48}  (all terms are divisible by 2)  21x+18y=24{\displaystyle 21x+18y=24}  (all terms now are divisible by 3)  7x+6y=8{\displaystyle 7x+6y=8}  (this equation is as reduced as possible) In some cases, you may be able to tell immediately if there is no solution to your problem. If you see a common factor on the left side of the equation that is not shared on the right side, then there can be no solution to the problem. For example, if both A{\displaystyle A} and B{\displaystyle B} are even, then the sum of the left side of the equation would have to be even. But if C{\displaystyle C} is odd, then there will be no integer solution to the problem.   2x+4y=21{\displaystyle 2x+4y=21} will have no integer solution.  5x+10y=17{\displaystyle 5x+10y=17} can have no integer solution, because the left side of the equation is divisible by 5, but the right side is not.


Запишите уравнение для вычисления энергии связи. Запишите химическое уравнение и обозначьте все связи между отдельными элементами. Изучите правила подсчета разорванных и образовавшихся связей. Определите, какие связи разрываются в левой части уравнения. Подсчитайте количество образовавшихся связей в правой части уравнения.

Given the above summary, write a detailed text in English for it.

Bond energy is defined by the sum of all of the bonds broken minus the sum of all of the bonds formed: ΔH = ∑H(bonds broken) - ∑H(bonds formed). ΔH is the change in bond energy, also referred to as the bond enthalpy and ∑H is the sum of the bond energies for each side of the equation.  This equation is a form of Hess’s Law. The unit for bond energy is kilojoules per mol or kJ/mol. When given a reaction equation simply written with chemical symbols and numbers, it is helpful to draw this equation out, illustrating all of the bonds formed between the various elements and molecules. This visual representation will allow you to easily count all of the bonds that break and form on the reactant and product sides of the equation.  Remember, the left side of the equation is all of the reactants and the right side is all of the products. Single, double, and triple bonds have different bond energies, so be sure to draw your diagram with the correct bonds between elements.  For example, if you were to draw out the following equation for a reaction between 2 hydrogen and 2 bromine: H2(g) + Br2(g) ---> 2 HBr(g), you would get: H-H + Br-Br ---> 2 H-Br. The hyphens represent single bonds between the elements in the reactants and the products. In most cases, the bond energies you will be using for these calculations will be averages. The same bond can have a slightly different bond energy based on the molecule it is formed in; therefore, average bond energies are generally used..  A single, double, and triple bond are all treated as 1 break. They all have different bond energies, but count as only a single break. The same is true for the formation of a single, double, or triple bond. It will be counted as single formation. For our example, all of the bonds are single bonds. The left side contains the reactants. These will represent all of the broken bonds in the equation. This is an endothermic process that requires the absorption of energy to break the bonds. For our example, the left side has 1 H-H bond and 1 Br-Br bond....


Запишите уравнение каждой прямой, обособив переменную «у» на левой стороне уравнения. Приравняйте выражения, расположенные с правой стороны каждого уравнения. Найдите значение переменной «х» Используйте найденное значение переменной «х» для вычисления значения переменной «у». Проверьте ответ. Запишите координаты (х,у). Вычисления в особых случаях.

Given the above summary, write a detailed text in English for it.

If necessary, rearrange the equation so y{\displaystyle y} is alone on one side of the equal sign. If the equation uses f(x){\displaystyle f(x)} or g(x){\displaystyle g(x)} instead of y{\displaystyle y}, separate this term instead. Remember, you can cancel out terms by performing the same action to both sides.  If you do not know the equations, find them based on the information you have.  Example: Your two lines are y=x+3{\displaystyle y=x+3} and y−12=−2x{\displaystyle y-12=-2x}. To get y{\displaystyle y} alone in the second equation, add 12 to each side: y=12−2x{\displaystyle y=12-2x} We're looking for a point where the two lines have the same x{\displaystyle x} and y{\displaystyle y} values; this is where the lines cross. Both equations have just y{\displaystyle y} on the left side, so we know the right sides are equal to each other. Write a new equation that represents this.  Example: We know y=x+3{\displaystyle y=x+3} and y=12−2x{\displaystyle y=12-2x}, therefore x+3=12−2x{\displaystyle x+3=12-2x}. . The new equation only has one variable, x{\displaystyle x}. Solve this using algebra, by performing the same operation on both sides. Get the x{\displaystyle x} terms on one side of the equation, then put it in the form x=??{\displaystyle x=??}. (If this is impossible, skip down to the end of this section.)   Example: x+3=12−2x{\displaystyle x+3=12-2x}  Add 2x{\displaystyle 2x} to each side: 3x+3=12{\displaystyle 3x+3=12} Subtract 3 from each side: 3x=9{\displaystyle 3x=9} Divide each side by 3:  x=3{\displaystyle x=3}. Choose the equation for either line. Replace every x{\displaystyle x} in the equation with the answer you found. Do the arithmetic to solve for y{\displaystyle y}.   Example: x=3{\displaystyle x=3} and y=x+3{\displaystyle y=x+3}  y=3+3{\displaystyle y=3+3} y=6{\displaystyle y=6} It's a good idea to plug your x{\displaystyle x}-value into the other equation and see if you get the same result. If you get a different solution for y{\displaystyle y}, go back and check your work for mistakes.  ...


Запишите уравнение прямой. Вместо «х» подставьте 0. Найдите «у». Проверьте ответ, построив график (если хотите). Найдите точку пересечения в случае квадратного уравнения.

Given the above summary, write a detailed text in English for it.

If you already have the equation of the line, you can find the y-intercept with a little algebra.   Example 3: What is the y-intercept of the line x + 4y = 16? Note: Example 3 is a straight line. See the end of this section for an example of a quadratic equation (with a variable raised to the power of 2). The y-axis is a vertical line along x = 0. This means any point on the y-axis has an x-coordinate of 0, including the y-intercept of the line. Plug in 0 for x in the line equation.  Example 3 (cont.): x + 4y = 16x = 00 + 4y = 164y = 16 The answer is the y-intercept of the line.  Example 3 (cont.): 4y = 164y4=164{\displaystyle {\frac {4y}{4}}={\frac {16}{4}}}y = 4.The y-intercept of the line is 4. . To check your answer, graph the equation as neatly as you can. The point where the line crosses the y-axis is the y-intercept. A quadratic equation includes a variable (x or y) raised to the power of 2. You can solve for y with the same substitution, but since the quadratic describes a curve, it could intercept the y-axis at 0, 1, or 2 points. This means you may end up with 0, 1, or 2 answers.  Example 4: To find the y-intercept of y2=x+1{\displaystyle y^{2}=x+1}, substitute x = 0 and solve the quadratic equation.In this case, we can solve y2=0+1{\displaystyle y^{2}=0+1} by taking the square root of both sides. Remember, when taking a square root, you must account for two answers: a negative and a positive.y2=1{\displaystyle {\sqrt {y^{2}}}={\sqrt {1}}}y = 1 or y = -1. These are both y-intercepts of this curve.


Запишите уравнение, характеризующее отношение сторон. Запишите формулу для вычисления площади прямоугольника. В формулу подставьте значение площади прямоугольника. В формулу подставьте выражение, характеризующее отношение сторон. Запишите квадратное уравнение. Разложите квадратное уравнение на множители. Найдите w{\displaystyle w}. Подставьте найденное значение ширины (или длины) в уравнение, характеризующее отношение сторон. Запишите теорему Пифагора. В формулу подставьте значения длины и ширины. Длину и ширину возведите в квадрат, а затем сложите полученные результаты. Извлеките квадратный корень из обеих сторон уравнения.

Given the above summary, write a detailed text in English for it.

You can isolate the length (l{\displaystyle l}) or the width (w{\displaystyle w}). Set this formula aside. You will plug it into the area formula later. For example, if you know the width of a rectangle is 2 cm more than the length, you can write a formula for w{\displaystyle w}: w=l+2{\displaystyle w=l+2}. The formula is A=lw{\displaystyle A=lw}, where A{\displaystyle A} equals the area of the rectangle, l{\displaystyle l} equals the length of the rectangle, and w{\displaystyle w} equals the width of the rectangle. You can use this method if you know the perimeter of the rectangle, except you would now set up the perimeter formula instead of the area formula. The formula for the perimeter of a rectangle is P=2(w+l){\displaystyle P=2(w+l)}, where w{\displaystyle w} equals the width of the rectangle, and l{\displaystyle l} equals the length of the rectangle. Make sure you substitute for the variable A{\displaystyle A}. For example, if the area of the rectangle is 35 square centimeters, your formula will look like this: 35=lw{\displaystyle 35=lw}. Since you are working with a rectangle, it doesn’t matter whether you work with the l{\displaystyle l} or w{\displaystyle w} variable. For example, if you found that w=l+2{\displaystyle w=l+2}, then you would substitute this relationship for w{\displaystyle w} in the area formula:35=lw{\displaystyle 35=lw}35=l(l+2){\displaystyle 35=l(l+2)} To do this, use the distributive property to multiply the terms in parentheses, then set the equation to 0. For example:35=l(l+2){\displaystyle 35=l(l+2)}35=l2+2l{\displaystyle 35=l^{2}+2l}0=l2+2l−35{\displaystyle 0=l^{2}+2l-35} For complete instructions on how to do this, read Solve Quadratic Equations. For example, the equation 0=l2+2l−35{\displaystyle 0=l^{2}+2l-35} can be factored as 0=(l+7)(l−5){\displaystyle 0=(l+7)(l-5)}. To do this, set each term to zero and solve for the variable. You will find two solutions, or roots, to the equation. For example:0=(l+7){\displaystyle 0=(l+7)}−7=l{\displaystyle...


Запишите уравнение. Вынесите за скобки коэффициент при первых двух членах. Делим на 2 второй член и возводим его в квадрат. Прибавьте и вычтите полученную величину к/из уравнения. Вынесите за скобку новый член со знаком минус. Преобразуйте слагаемые в скобках в полный квадрат. Сложите свободные члены. Запишите уравнение в вершинной форме.

Given the above summary, write a detailed text in English for it.

Let's say you're working with the following equation: 3x2 - 4x + 5. To factor out a three from the first two terms, simply pull out a 3 and place it around a set of parenthesis around both terms, while dividing each term by 3. 3x2 divided by 3 is simply x2 and 4x divided by 3 is 4/3x. So, the new equation should look like this: 3(x2 - 4/3x) + 5. The 5 will remain outside of the equation because you did not divide it by 3. The second term, also known as the b term in the equation, is 4/3. Halve the second term, or divide it by 2 first. 4/3 ÷ 2, or 4/3 x 1/2, is equal to 2/3. Now, square this term by squaring both the numerator and denominator of the fraction. (2/3)2 = 4/9. Write this term down. You'll need this "extra" term to turn the first three terms in this equation into a perfect square. But you have to remember that you added it by subtracting it from the equation as well. Though obviously, it won't do you much good to simply combine the terms -- you'll be back where you started. The new equation should look like this: 3( x2 - 4/3 x + 4/9 - 4/9) + 5. Since you're working with a coefficient of 3 outside the parentheses, you can't just pull out the -4/9. You'll have to multiply it by 3 first. -4/9 x 3 = -12/9, or -4/3. If you're not working with an equation with a coefficient other than 1 over the x2 term, then you could skip this step. Right now, you're left with 3(x2 -4/3x +4/9) within the parentheses. You worked backwards to get the 4/9, which was really another way of finding the term that would complete the square. So, you can rewrite those terms like this: 3(x - 2/3)2. All you had to do was halve the second term and remove the third. You can check that this works by multiplying it out to see that it gives you the first three terms of the equation.  3(x - 2/3)2 = 3(x - 2/3)(x -2/3) = 3[(x2 -2/3x -2/3x + 4/9)] 3(x2 - 4/3x + 4/9) You're left with two constant terms, or terms that aren't attached to a variable. Right now, you're left with 3(x - 2/3)2 - 4/3 + 5. All you have to do is add up -4/3 and 5 to...


Запишите уравнение. Определите угловой коэффициент данной (первой) прямой. В представленное уравнение подставьте координаты точки, которая лежит на второй прямой. Запишите уравнение второй прямой. Упростите уравнение.

Given the above summary, write a detailed text in English for it.

Point-slope form allows you to write the equation of a line when you know its slope and have an (x, y) coordinate. You would use this formula when you want to define a second parallel line to an already given line with a defined slope. The formula is y – y1= m(x – x1) where m is the slope of the line, x1 is the x coordinate of a point given on the line and y1 is the y coordinate of that point. As in the slope-intercept equation, x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation. The following steps will work through this example: Write the equation of a line parallel to the line y = -4x + 3 that goes through point (1, -2). When writing the equation of a new line, you must first identify the slope of the line you want to draw yours parallel to. Make sure the equation of the original line is in slope-intercept form and then you know the slope (m). The line we want to draw parallel to is y = -4x + 3. In this equation, -4 represents the variable m and therefore, is the slope of the line. This equation only works if you have a coordinate that passes through the new line. Make sure you don’t choose a coordinate that is on the original line. If your final equations have the same y-intercept, they are not parallel, but the same line. In our example, we will use the coordinate (1, -2). Remember the formula is y – y1= m(x – x1). Plug in the slope and coordinates of your point to write the equation of your new line that is parallel to the first. Using our example with slope (m) -4 and (x, y) coordinate (1, -2): y – (-2) = -4(x – 1) After you have plugged in the numbers, the equation can be simplified into the more common slope-intercept form. This equation's line, if graphed on a coordinate plane, would be parallel to the given equation.  For example: y – (-2) = -4(x – 1) Two negatives make a positive: y + 2 = -4(x -1)  Distribute the -4 to x and -1: y + 2 = -4x + 4. Subtract -2 from both side: y + 2 – 2 = -4x + 4 – 2 Simplified equation: y = -4x + 2


Запишите уравнение. Перенесите все члены уравнения на одну сторону и приравняйте его к 0. Вынесите за скобку коэффициент при переменной высшего порядка. Избавьтесь от множителя перед скобкой. Делим на 2 второй член и возводим его в квадрат. Переместите свободный член (из исходного уравнения) с левой стороны уравнения в правую. Запишите левую часть уравнения в виде квадрата: Возьмите квадратный корень из обеих сторон уравнение. Выделите переменную.

Given the above summary, write a detailed text in English for it.

Let's say you're working with the following equation: 3x2 + 4x + 5 = 6 The constant terms are any terms that aren't attached to a variable. In this case, you have 5 on the left side and 6 on the right side. You want to move 6 over to the left, so you'll have to subtract 6 from both sides of the equation. That will leave you with 0 on the right side (6-6) and -1 on the left side (5-6). The equation should now read: 3x2 + 4x - 1 = 0. In this case, 3 is the coefficient of the x2 term. To factor out a 3, just pull out a 3, place the remaining terms in parentheses, and divide each term by 3. So, 3x2 ÷ 3 = x2, 4x ÷ 3 = 4/3x, and 1 ÷ 3 = 1/3. The equation should now read: 3(x2 + 4/3x - 1/3) = 0. This means that you can get rid of that pesky 3 term outside the parentheses for good. Since you divided every term by 3, it can be removed without impacting the equation. Now you have x2 + 4/3x - 1/3 = 0 Next, take the second term, 4/3, also known as the b term, and find half of it. 4/3 ÷ 2 or 4/3 x 1/2, is 4/6, or 2/3. And 2/3 squared is 4/9. When you're done, you'll have to write it on the left and the right side of the equation, since you're essentially adding a new term. You'll need it on both sides of the equation to keep it balanced. The equation should now read x2 + 4/3 x + 2/32 - 1/3 = 2/32 Move the original constant term, -1/3, over to the right side to make it 1/3. Add it to the term you just placed there, 4/9, or 2/32. Find a common denominator to combine 1/3 and 4/9 by multiplying both the top and bottom of 1/3 by 3. 1/3 x 3/3 = 3/9. Now, add up 3/9 and 4/9 to get 7/9 on the right side of the equation. This yields: x2 + 4/3 x + 2/32 = 4/9 + 1/3 and then x2 + 4/3 x + 2/32 = 7/9. Since you've already used a formula to find the missing term, the hard part is already over. All you have to do is place x and half of the second coefficient in parentheses and square them, like so:(x + 2/3)2. Note that factoring that perfect square will give you the three terms: x2 + 4/3 x + 4/9. The equation should now read: (x + 2/3)2...


Запишите уравнение. Разделите каждый коэффициент на коэффициент при x2. Перенесите постоянную в правую часть уравнения. Дополните до полного квадрата левую часть уравнения. Упрощаем левую часть уравнения. Используйте его для нахождения координат x и y.

Given the above summary, write a detailed text in English for it.

Completing the square is another way to find the vertex of a quadratic equation. For this method, when you get to the end, you'll be able to find your x and y coordinates right away, instead of plugging the x coordinate back in to the original equation. Let's say you're working with the following quadratic equation: x2+4x+1=0{\displaystyle x^{2}+4x+1=0}. In this case, the coefficient of the x2{\displaystyle x^{2}}  term is 1, so you can skip this step. Dividing each term by 1 would not change anything. Dividing each term by 0, however, will change everything. The constant term is the term without a coefficient. In this case, it is 1. Move 1 to the other side of the equation by subtracting 1 from both sides. Here's how you do it:  x2+4x+1=0{\displaystyle x^{2}+4x+1=0} x2+4x+1−1=0−1{\displaystyle x^{2}+4x+1-1=0-1} x2+4x=−1{\displaystyle x^{2}+4x=-1} To do this, simply find (b2)2{\displaystyle ({\frac {b}{2}})^{2}} and add the result to both sides of the equation. Plug in 4 for b{\displaystyle b}, since4x{\displaystyle 4x} is the b-term of this equation.  (42)2=22=4{\displaystyle ({\frac {4}{2}})^{2}=2^{2}=4}. Now, add 4 to both sides of the equation to get the following:  x2+4x+4=−1+4{\displaystyle x^{2}+4x+4=-1+4} x2+4x+4=3{\displaystyle x^{2}+4x+4=3} Now you will see that x2+4x+4{\displaystyle x^{2}+4x+4} is a perfect square. It can be rewritten as (x+2)2=3{\displaystyle (x+2)^{2}=3} You can find your x{\displaystyle x} coordinate by simply setting (x+2)2{\displaystyle (x+2)^{2}} equal to zero. So when (x+2)2=0{\displaystyle (x+2)^{2}=0}, what would x{\displaystyle x} have to be? The variable x{\displaystyle x} would have to be -2 to balance out the +2, so your x{\displaystyle x} coordinate is -2. Your y-coordinate is simply the constant term on the other side of the equation. So, y=3{\displaystyle y=3}. You can also do a shortcut and just take the opposite sign of the number in parentheses to get the x-coordinate. So the vertex of the equation x2+4x+1=(−2,−3){\displaystyle x^{2}+4x+1=(-2,-3)}.


Запишите формулу для вычисления диагонали прямоугольника. В формулу подставьте данные значения диагонали и длины. Обе стороны уравнения возведите в квадрат. Обособьте w{\displaystyle w}. Найдите w{\displaystyle w}. Запишите окончательный ответ.

Given the above summary, write a detailed text in English for it.

The formula is D=w2+l2{\displaystyle D={\sqrt {w^{2}+l^{2}}}}, where D{\displaystyle D} equals the length of the rectangle’s diagonal, l{\displaystyle l} equals the length of the rectangle, and w{\displaystyle w} equals the width of the rectangle.  This method will only work if you are given the length of the diagonal and the length of the side of the rectangle. You might also see the formula written as D=w2+h2{\displaystyle D={\sqrt {w^{2}+h^{2}}}}, where h{\displaystyle h} equals the height of the rectangle and is used instead of length. The variables l{\displaystyle l} and h{\displaystyle h} refer to the same measurement. Make sure you substitute for the correct variables. For example, if you are trying to find the width of a rectangle that has a diagonal length of 5 centimeters, and a side length of 4 centimeters, your formula will look like this: 5=w2+42{\displaystyle 5={\sqrt {w^{2}+4^{2}}}} You need to do this to get rid of the square root sign, which makes isolating the width variable easier. For example:5=w2+42{\displaystyle 5={\sqrt {w^{2}+4^{2}}}}52=w2+42{\displaystyle 5^{2}=w^{2}+4^{2}}25=w2+16{\displaystyle 25=w^{2}+16} To do this, you need to subtract the squared length from each side of the equation. For example, in the equation 25=16+w2{\displaystyle 25=16+w^{2}}, you would subtract 16 from each side.25=16+w2{\displaystyle 25=16+w^{2}}9=w2{\displaystyle 9=w^{2}} To do this, you need to find the square root of each side of the equation. For example:9=w2{\displaystyle {\sqrt {9}}={\sqrt {w^{2}}}}3=w{\displaystyle 3=w} Don’t forget to include the unit of measurement. For example, for a rectangle with a diagonal length of 5cm{\displaystyle 5cm} and a side length of 4cm{\displaystyle 4cm}, the width would be 3cm{\displaystyle 3cm}.


Запишите формулу для вычисления длины дуги. В формулу подставьте радиус окружности. В формулу подставьте центральный угол. Радиус умножьте на 2π{\displaystyle 2\pi }. Разделите центральный угол на 360. Перемножьте два числа.

Given the above summary, write a detailed text in English for it.

The formula is arc length=2π(r)(θ360){\displaystyle {\text{arc length}}=2\pi (r)({\frac {\theta }{360}})}, where r{\displaystyle r} equals the radius of the circle and θ{\displaystyle \theta } equals the measurement of the arc’s central angle, in degrees. This information should be given, or you should be able to measure it. Make sure you substitute this value for the variable r{\displaystyle r}. For example, if the circle’s radius is 10 cm, your formula will look like this: arc length=2π(10)(θ360){\displaystyle {\text{arc length}}=2\pi (10)({\frac {\theta }{360}})}. This information should be given, or you should be able to measure it. Make sure you are working with degrees, and not radians, when using this formula. Substitute the central angle’s measurement for θ{\displaystyle \theta } in the formula. For example, if the arc’s central angle is 135 degrees, your formula will look like this: arc length=2π(10)(135360){\displaystyle {\text{arc length}}=2\pi (10)({\frac {135}{360}})}. If you are not using a calculator, you can use the approximation π=3.14{\displaystyle \pi =3.14} for your calculations. Rewrite the formula using this new value, which represents the circle’s circumference. For example:2π(10)(135360){\displaystyle 2\pi (10)({\frac {135}{360}})}2(3.14)(10)(135360){\displaystyle 2(3.14)(10)({\frac {135}{360}})}(62.8)(135360){\displaystyle (62.8)({\frac {135}{360}})} Since a circle has 360 degrees total, completing this calculation gives you what portion of the entire circle the sector represents. Using this information, you can find what portion of the circumference the arc length represents. For example:(62.8)(135360){\displaystyle (62.8)({\frac {135}{360}})}(62.8)(.375){\displaystyle (62.8)(.375)} This will give you the length of the arc. For example:(62.8)(.375){\displaystyle (62.8)(.375)}23.55{\displaystyle 23.55}So, the length of an arc of a circle with a radius of 10 cm, having a central angle of 135 degrees, is about 23.55 cm.


Запишите формулу для вычисления длины дуги. В формулу подставьте радиус окружности. В формулу подставьте центральный угол. Умножьте радиус на центральный угол (измеренный в радианах).

Given the above summary, write a detailed text in English for it.

The formula is arc length=θ(r){\displaystyle {\text{arc length}}=\theta (r)}, where θ{\displaystyle \theta } equals the measurement of the arc’s central angle in radians, and r{\displaystyle r} equals the length of the circle’s radius. You need to know the length of the radius to use this method. Make sure you substitute the length of the radius for the variable r{\displaystyle r}. For example, if the circle’s radius is 10 cm, your formula will look like this: arc length=θ(10){\displaystyle {\text{arc length}}=\theta (10)}. You should have this information in radians. If you know the angle measurement in degrees, you cannot use this method. For example, if the arc’s central angle is 2.36 radians, your formula will look like this: arc length=2.36(10){\displaystyle {\text{arc length}}=2.36(10)}. The product will be the length of the arc. For example:2.36(10){\displaystyle 2.36(10)}=23.6{\displaystyle =23.6}So, the length of an arc of a circle with a radius of 10 cm, having a central angle of 23.6 radians, is about 23.6 cm.


Запишите формулу для вычисления длины окружности через диаметр. Подставьте данные вам значения в формулу и найдите длину окружности.

Given the above summary, write a detailed text in English for it.

The formula is simply this: C = πd. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its numerical value, which is a closer approximation of 3.14 or 22/7. Example problem:  You have a circle tub with a diameter of 8 feet, and you want to build a white fence that creates a 6-foot wide space around the tub. To find the circumference of the fence that has to be created, you should first find the diameter of the tub and the fence which will be 8 feet + 6 feet + 6 feet, which will account for the entire diameter of the tub and fence. The diameter is 8 + 6 + 6, or 20 feet. Now plug it into the formula, plug π into your calculator for its numerical value, and solve for the circumference: C = πd C = π x 20 C = 62.8 feet


Запишите формулу для вычисления длины окружности через радиус. Подставьте данные вам значения в формулу и найдите длину окружности.

Given the above summary, write a detailed text in English for it.

The radius is half as long as the diameter, so the diameter can be thought of as 2r. Keeping this in mind, you can write down the formula for finding the circumference of a circle given the radius: C = 2πr. In this formula, "r" represents the radius of the circle. Again, you can plug π into your calculator to get its numeral value, which is a closer approximation of 3.14. For this example, let's say you're cutting out a decorative strip of paper to wrap around the edge of a pie you've just made. The radius of the pie is 5 inches. To find the circumference that you need, just plug the radius into the equation:  C = 2πr C = 2π x 5 C = 10π C = 31.4 inches


Запишите формулу для вычисления длины. Найдите координаты точек отрезка. Подставьте координаты в формулу.

Given the above summary, write a detailed text in English for it.

The formula states that d=(x2−x1)2+(y2−y1)2{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}, where d{\displaystyle d} equals the distance of the line, (x1,y1){\displaystyle (x_{1},y_{1})} equal the coordinates of the first endpoint of the line segment, and (x2,y2){\displaystyle (x_{2},y_{2})} equal the coordinates of the second endpoint of the line segment. These might already be given. If not, count along the x-axis and y-axis to find the coordinates.  The x-axis is the horizontal axis; the y-axis is the vertical axis. The coordinates of a point are written as (x,y){\displaystyle (x,y)}. For example, a line segment might have an endpoint at (2,1){\displaystyle (2,1)} and another at (6,4){\displaystyle (6,4)}. Be careful to substitute the values for the correct variables. The two x{\displaystyle x} coordinates should be inside the first set of parentheses, and the two y{\displaystyle y} coordinates should be inside the second set of parentheses. For example, for points (2,1){\displaystyle (2,1)} and (6,4){\displaystyle (6,4)}, your formula would look like this: d=(6−2)2+(4−1)2{\displaystyle d={\sqrt {(6-2)^{2}+(4-1)^{2}}}}


Запишите формулу для вычисления объема призмы. В формулу подставьте объем. Вычислите площадь основания. Подставьте площадь основания в формулу для вычисления объема призмы. Найдите h{\displaystyle h}.

Given the above summary, write a detailed text in English for it.

The volume for any prism can be found by using the formula V=Ah{\displaystyle V=Ah}, where V{\displaystyle V} equals the volume of the prism, A{\displaystyle A} equals the area of one base, and h{\displaystyle h} equals the height of the prism. The base of a prism is one of its congruent sides. Since all opposite sides of a rectangular prism are congruent, any side can be used as the base, as long as you are consistent in your calculations. If you do not know the volume, you cannot use this method. For example, if you know the volume of the prism is 64 cubic meters (m3{\displaystyle m^{3}}), then your formula will look like this:64=Ah{\displaystyle 64=Ah} To find the area, you need to know the length and width of the base (or of one side, if the base is a square). Use the formula A=lw{\displaystyle A=lw}. To find the area of a rectangle. For example, if the base is a rectangle with a length of 8 meters and a width of 2 meters, to find the area you would calculate:A=(8)(2){\displaystyle A=(8)(2)}A=16m2{\displaystyle A=16m^{2}} Make sure you are substituting for the variable A{\displaystyle A}. For example, if you found the area of the base to be 16 square meters, then your formula will look like this:64=16h{\displaystyle 64=16h} This will give you the height of your prism. For example, if your equation is 64=16h{\displaystyle 64=16h}, you would need to divide each side by 16 to find h{\displaystyle h}.Thus:6416=16h16{\displaystyle {\frac {64}{16}}={\frac {16h}{16}}}4=h{\displaystyle 4=h}So, the height of your rectangular prism would be 4 meters.


The volume for any prism can be found by using the formula V=Ah{\displaystyle V=Ah},  where V{\displaystyle V} equals the volume of the prism, A{\displaystyle A} equals the area of one base, and h{\displaystyle h} equals the height of the prism. The base of a prism is one of its congruent sides. The base of a triangular prism will be a triangle. The sides will be rectangles. If you do not know the volume, you cannot use this method. For example, if you know the volume of the prism is 840 cubic meters (m3{\displaystyle m^{3}}), then your formula will look like this:840=Ah{\displaystyle 840=Ah} To find the area, you need to know the length of the triangle’s base and the height of the triangle. Use the formula A=12(b)(h){\displaystyle A={\frac {1}{2}}(b)(h)} to find the area of a triangle.  Alternatively, if you know the length of all three sides of a triangle, you can find the area using Heron’s formula.  Read Calculate the Area of a Triangle for complete instructions. For example, if the base of the triangle is 12 meters, and the height of the triangle is 7 meters, to find the area you would calculate:A=12(12)(7){\displaystyle A={\frac {1}{2}}(12)(7)}A=12(84){\displaystyle A={\frac {1}{2}}(84)}A=42{\displaystyle A=42} Make sure you are substituting for the variable A{\displaystyle A}. For example, if you found the area of the base to be 42 square meters, then your formula will look like this:840=42h{\displaystyle 840=42h} This will give you the height of your prism.  For example, if your equation is 840=42h{\displaystyle 840=42h}, you would need to divide each side by 42 to find h{\displaystyle h}.Thus:84042=42h42{\displaystyle {\frac {840}{42}}={\frac {42h}{42}}}20=h{\displaystyle 20=h}  So, the height of your triangular prism would be 20 meters.