The first three days after you decide to quit will be extremely hard on your physical body. Your body takes 72 hours to pass nicotine out of your system.  Drink lots of water during this stage.     Channel your anger into some activity, whether it is working out, journaling your experience, or making art.    While the worst of the physical ailments will be over by this point because the nicotine has passed through your system, you will begin to have to develop mental will-power. Your body has to figure out how to operate without nicotine.  During this stage, you may encounter cravings, irritability, insomnia, fatigue, inability to focus, headache, sore throat, tongue, and/or gums, constipation, gas, stomach pain, and dry mouth. Focus on your mental stamina and health during the second stage. Avoid triggers. Triggers are certain behaviors that bring up the desire to dip. These may be places where you usually dip, people you usually dip with, or activities you usually complete with a dip in. By day 50 or so, you should be experiencing less symptoms and be slowly transitioning to a normal routine. Sores may form in your mouth, but don't be alarmed, this is your mouth healing small ulcers that may have developed from dipping.  Visit your dentist if the sores become painful, discolored, or seem to be infected. You should be sleeping better by this stage. If you are not, think about visiting a doctor who can evaluate your body's progress. During this stage, some people suffer from anxiety attacks as a result of the inability to use tobacco to calm themselves down.  If your anxiety attacks are really bad and physically alarming, contact your doctor. S/he may prescribe an anxiety medication or an anti-depressant of some sort. Think about talking with a therapist or joining a community of ex-dippers to quell stress by talking about your anxieties. Expect to feel sluggish, unclear, and experience scattered cravings at this stage. Some people experience just a few days of feeling like they just started the process, but...

TL;DR in Russian:

Бросайте сразу. С 4 по 20 день наступает стадия умственной борьбы. Наблюдайте за вашими симптомами, которые должны ослабеть через полтора месяца. Подготовьтесь к возможным приступам тревоги, которые могут возникнуть в течение двух месяцев. В первые три месяца вы можете испытать разочарование. Отпразднуйте свой 100-ый день!


The first three years of life are known as a "critical period" in child development, since a baby's brain is constantly growing and learning, storing information that he will use for the rest of his life.  Baby behaviors that might seem like stubbornness or even naughtiness are actually their natural processes of learning about cause and effect. For example, if you are in the habit of just saying "no" or making an angry face every time your baby does an unwanted behavior, it is possible that the baby is simply repeating the behavior to see if your reaction stays the same. By varying your response to the behavior, your child will see that he cannot always get the response he wants and he will try different behaviors. If your baby is stubbornly touching the same breakable item every day or refuses to stay out of the kitchen cabinets, instead of punishing or disciplining the child, rearrange the home to make it safe and accessible for her. After all, it is her home too, and she learns best when she can explore it.  Babies learn by exploring, and are not trying to be naughty by getting into things. Move your breakables and "babyproof" your home rather than trying to squelch normal learning behaviors. Check out this helpful wikiHow article for advice on babyproofing your home. As your baby grows, you will discover new areas that need to be made safe for her. This is all part of structuring her environment so that she is safe and has the most potential to learn and play without risk. You should begin babyproofing your home before your child is mobile (usually around nine or 10 months old). " Most babies and toddlers spend their days hearing "no" after "no," and rarely engaging in the behaviors they choose. After you have changed your home environment to make it safe, make it your goal to say "yes" as often as it is safe and possible to do so. Saying "yes" will let your child take charge of his learning experiences and explore things that are interesting to him. Let your child spend time outside, doing arts and...

TL;DR in Russian:

Попробуйте понять малышей, только начинающих ходить. Измените обстановку. Говорите ребенку «да». Научитесь перенаправлять внимание ребенка. Обучите ребенка «обходительности».


The first thyroid test that is generally taken by physicians is the TSH. TSH stands for "Thyroid Stimulating Hormone," which is created by the pituitary gland and stimulates the thyroid to create and release hormones T4 and T3.  TSH can be thought of as the metaphorical "engine" of the thyroid gland, in that it determines the amount of thyroid hormone that is synthesized and then released from the thyroid into the body. A normal value for TSH is between 0.4 – 4.0 mIU/L.  If your TSH is in this range, that is a good sign; however, a normal TSH value does not completely rule out thyroid problems. TSH values on the high end of normal can indicate potential thyroid problems that are evolving. Most thyroid problems require two or more tests to detect and diagnose, given the complex interplay of the various hormones that contribute to thyroid function. Your doctor may order more tests, even if your TSH is normal, if he still suspects that you may have a thyroid problem. TSH tells the thyroid to produce more T4 and T3, which are the hormones released from the thyroid (at the command of TSH) to act throughout the body. If your thyroid is underactive, then it is not releasing enough much T4 and T3, and so your pituitary gland will release more TSH to try and compensate.   Thus, a high TSH may be a sign of hypothyroidism (a condition in which your thyroid gland is producing insufficient amounts of hormones). You will need further testing, however, to further investigate and to confirm such a diagnosis. In addition to a high TSH reading, hypothyroidism also presents with many clinical indications. Tell your doctor if you are experiencing any of the following signs or symptoms, which may be suspicious for hypothyroidism:  Increased cold sensitivity Fatigue Unexplained weight gain Unusually dry skin Constipation Muscle aches and stiffness Joint pain and swelling Depression and/or other mood changes A slower than normal heart rate Thinning hair Changes to your menstrual cycle Slowed thinking or speaking On the other hand,...

TL;DR in Russian:

Проверьте, соответствует ли ваш уровень тиреотропного гормона (ТТГ) норме. Изучите возможные причины повышения уровня ТТГ. Поищите у себя признаки гипотиреоза. Узнайте, что могут означать сниженные показатели уровня ТТГ. Поищите у себя признаки гипертиреоза. Опирайтесь на результаты анализов на ТТГ, чтобы отслеживать свое состояние во время лечения.


The first time you read through an article, you should simply try to understand the overall argument that the author is making. Note the author's thesis. It is sometimes helpful to use a red pen to make your markings stand out. Ask yourself questions like these as you read through a second time:  What is the author's thesis/argument? What is the author's purpose in arguing said thesis? Who is the intended audience? Does the article effectively reach this audience? Does the author have ample and valid evidence? Are there any holes in the author's argument? Did the author misrepresent evidence or add bias to evidence? Does the author reach a conclusive point? Create a unique symbol to differentiate between parts of the text that might be confusing, important, or inconsistent.  For example, you could underline important passages, circle confusing ones, and star inconsistencies. Creating a legend with assigned symbols allows you to quickly mark up an article. Though it may take a little bit of time to recognize your own symbols, they will quickly become ingrained in your mind and allow you to breeze through an article much quicker than without a symbol legend. In addition to a legend, it is helpful to take notes when expanded thoughts come to you as you read. For instance, if you realize that an author's claim can be refuted by noting a scientific study that you previously read, make a note of it in the margins, on a separate piece of paper, or on a computer so that you can come back to your idea.  Don't be foolish enough to think that you will remember your idea when it comes time to write your critique. Spend the necessary time writing down your observations as you read. You will be glad you did when it comes time to put your observations into a complete analytical paper. Form a vague opinion of the piece in question. Evaluate the author's overall argument after you have read the article through two or three times. Record your initial reactions to the text. Make a list of possible sources of evidence for your...

TL;DR in Russian:

Прочитайте статью, чтобы уловить ключевую идею. Перечитайте текст и делайте пометки. Придумайте условные обозначения для пометок. Делайте расширенные записи при последующих прочтениях. Обдумайте предварительное содержание будущей рецензии.


The first time you read through your text, take notes on things that stand out, such as the main conflict, the characters' motivations, the tone, and the setting.   Mark pieces of the text that seem interesting or noteworthy. Does the author seem to be making a major statement in one section? Are they suddenly being more philosophical? Highlight or make a note about that section. For instance, one of the main quotes you see repeated from George Orwell's novel 1984 is "War is peace. Freedom is slavery. Ignorance is strength." As it's the Party's (the country's only political party) main slogan, that keys you into the fact that it's going to be important to the story. It's a good idea to use a certain color highlighter to mark this statement every time it's made. This makes it easier to spot the statement so you can analyze where, when, and why Orwell is repeating the line. Literary devices are things the author uses to tell the story or make a point. They could include alliteration, imagery, metaphors, allusions, allegories, repetition, flashback, foreshadowing, or any number of other devices the author employs to write the story or poem.  For instance, imagery is how the author uses vivid language to help create mental pictures. It can set the tone of the work. Take this example from George Orwell's novel 1984, which is presented as the fourth paragraph in the novel: "Outside, even through the shut window-pane, the world looked cold. Down in the street little eddies of wind were whirling dust and torn paper into spirals, and though the sun was shining and the sky a harsh blue, there seemed to be no colour in anything, except the posters that were plastered everywhere."  Just from this short text, you get a sense of the harshness of the world, drained of color and very cold. Themes are the major ideas the author seems to be repeating throughout the text. They can be things like religion, government, good versus evil, authority, social structure, coming-of-age, war, education, or human rights, to name a few....

TL;DR in Russian:

Записывайте идеи, когда читаете текст. Замечайте литературные приемы. Сосредоточьтесь на ключевых темах. Обратите внимание на форму произведения. Учитывайте исторический контекст. Определите цель автора. Обдумайте, как автор демонстрирует свою главную цель. Сосредоточьтесь на теме, чтобы определиться с аргументами.


The first time you use the peroxide treatment, your hair may get just a little lighter. If you want to lighten your hair more, then you'll have to repeat the treatment one or more times.  Your hair will become much lighter if you repeat this process in smaller doses every day for a week than if you use a whole bottle of hydrogen peroxide on your hair one night. The final color also depends on what color your hair was to start out with. If your hair is very dark, your peroxide-saturated hair might seem a bit more orange at first. Keep continuing the treatment and your hair should seem blonder. Using a hair dryer on a low setting to gently heat your hair can help to speed up the lightening process. Turn on your hair dryer to a low heat setting and move it from root to strand all over your head. Do this until your hair reaches the desired lightness. It is best to use heat if you have bleached your hair with peroxide before and have a good idea of how it will turn out. If you are not sure, then avoid using a hair dryer.  Go slow instead and see how the peroxide affects your hair as it air dries. Don't wash your hair every day. Washing your hair daily strips out natural oils that protect your hair from breaking. Try shampooing your hair only once or twice per week and use a dry shampoo (a powder you comb into your hair) to keep it looking fresh between washes. This will control any yellow tones in your hair. You can buy a violet conditioner at a grocery store or beauty store. Don't blow dry or straighten your hair too much. These heating tools can exacerbate the damage caused by the peroxide, so only use them once a week or less. Try using heat free styling methods, or use a hair dryer on a lower setting. Let your hair air dry as often as possible, and don't wring it out or rub it with a towel after showering. Just give your hair a gentle squeeze with the towel, and then leave it be for a while. Also, make sure that when you brush your hair, you start from the ends and go slow to avoid breaking your strands.

TL;DR in Russian:

Повторите обработку перекисью, чтобы сильнее осветлить волосы. Чтобы ускорить осветление, воспользуйтесь феном. Начните реже мыть голову. Раз или два в неделю используйте фиолетовый кондиционер для волос. Ограничьте термообработку волос. Аккуратно обращайтесь со своими волосами.


The first way to start halter training the horse is to get it used to having your hands near his head, ears, and neck. Do this slowly. Stay within the horse's eyesight so you don't startle it. Reach out slowly. If you reach out too fast, it may misinterpret your action. Continue doing this until you can touch the horse. Make sure to give the horse release when it allows more touch. The horse will know your touch does not hurt and it does not need to shake you off since you will back away on your own. Start by letting the horse see and smell the halter in your hands. For the first few days, simply allow it to see and smell the halter as you rub it on the horse as you pull it away. Then, start slowly placing the halter over the nose and onto the head. At first, you may want to leave it on without buckling. When the horse gets used to that, then you can buckle the halter behind the ears.  This may take multiple attempts. Be patient and calm, trying to make a little bit of progress each day. Try using food to motivate your horse, such as by luring your horse into its muzzle with a carrot. Take the halter off immediately once it is on so it will not get anxious and allow it more easily the next time. Remember, you are teaching it these things are not scary and go away on their own so your horse does not feel the need to fight. Start by introducing the bridle to the horse along with the halter. Rub the bridle all over the horse's face gently. Try to get the horse to open its mouth for the bit. Be very gentle. In addition to halter breaking the horse, you will also have to break the horse into using the bit. Slowly introduce the bit into the horses' mouth. At first, only do this for a few minutes. Slowly build up to having the bit in the mouth for longer. Adding a layer of molasses to the bit can help encourage the horse to put it in its mouth and make it more enjoyable. Once the bit is in the horse's mouth without the horse fighting you, put the ear pieces over the ears. Do not fasten the straps yet. Gradually work...

TL;DR in Russian:

Дайте лошади привыкнуть к вашим рукам. Дайте лошади привыкнуть к узде. Познакомьте с уздечкой. Добавьте удила. Наденьте заушники.


The first, most basic step in giving good advice (or any at all really) is to not judge the other person. No one should be thought of as less or as bad for a single decision that they made. We're all playing with a different set of cards and what you have in your hand and what you managed to do with it doesn't have anything to do with what someone else has. Keep a straight face and remember what your mother taught you: if you don't have anything nice to say, don't say anything at all. We of course all have our own opinions on what is and isn't right or what someone should do, but when you give advice, the idea is to give someone the tools to make their own decision, not make the decision for them. Try to remove your own opinions from the conversation and just focus on helping them come to their own conclusion.  For example, if your friend is considering an abortion but you don't believe in it, don't spend the whole time telling her how bad it is. Instead, talk her through the arguments that you know of for and against it, in equal balance. Only when someone asks you "What would you do?" should you let your own personal opinion shine through. Just make sure that you give the reasons why you have the opinion that you do, so that they can understand your logic. Let them know if you're not an expert. You don't have to be a lot of the time, since all they really need is a sounding board. But it's important that you don't give them the impression that you're an authority when you're not. It's okay to not say "I know how you feel", too. Instead, say something like "You're right to be upset about that" or "I can see how that would make me feel neglected". Sometimes all someone needs to make the right decision is to know that someone believes in them and that someone thinks that they can do the right thing. Be that person for them, especially if no one else can be. Tell them something like, "This is a really tough decision, but I know you want to do the right thing. And I know you will do the right thing. You just...

TL;DR in Russian:

Не осуждайте. Не нажимайте. Будьте честны. Выразите уверенность. Знайте, когда необходимо вмешательство и когда оно неуместно.


The first, most obvious thing you can do to volumize hair is to use a volumizing shampoo and conditioner. These have a lighter formula than most other shampoos and conditioners, meaning that they won't weigh hair down, causing it to lie flat against the scalp. They will effectively clean and moisturize hair, while also leaving it light and bouncy. There is a volumizing shampoo and conditioner combo available for every budget, from drugstore favorites to fancy salon brands.  When shampooing, use enough product to create a lather. Make sure to massage the shampoo into the scalp, as this will help provide volume once the hair is dry. Rinse your hair thoroughly, then shampoo again if necessary. Apply conditioner from the mid-lengths of the hair to the tips, using any leftover product near the roots. Applying too much conditioner to the roots may make it look greasy and flat. While the conditioner is still in your hair, comb out any tangles with a wide-tooth combing, starting at the bottom and working your way up. This will help to prevent breakage, which can make hair look thin. Most shampoos and conditioners contain plastic-type substances such as silicon and polymers which stick to the hair shaft and weigh the hair down, making it flat and lifeless. Clarifying shampoos remove these built-up chemicals and other deposits, making your hair lighter and more voluminous. Most people should use a clarifying shampoo once a week, for best results.  As well as shampoos, hair care products such as mousses, waxes and sprays  contain chemicals which build up in the hair, causing it to lose volume. In addition, things like hard water and chlorine from swimming pools can leave deposits in the hair. People who swim frequently are more likely to have built-up deposits in their hair, so they should use a clarifying shampoo more frequently, perhaps 2 to 3 times a week. If you have colored hair, choose a sulfate-free clarifying shampoo that is safer for colored hair. You can find them at your local beauty supply store, salon, or...

TL;DR in Russian:

Используйте шампунь и кондиционер для объема. Мойте голову очищающим шампунем раз в неделю.


The five stages of grief are denial, anger, bargaining, depression, and acceptance. In that order. However, know that no two people grieve the same. However you need to do it, whether it's balled up in the corner with a teddy bear or running until the backs of shins hurt, do it. You'll be better in the long run.  Anyone else's preconceptions as to what grieving is can be shoved you know where. How you feel compelled to handle it is how you should handle it. As long as you're treating yourself and others with care (read: not turning to drugs, alcohol, and the like), it's okay. Right now, you and the loved ones around you need to join together. Sometimes, when you grieve with others, it feels a lot less like grieving. The combined efforts of everyone can make the time pass a lot quicker.  If you feel like you're the only one going through this and no one else is grieving, just the company of others can help. Having someone hold your hand can let you know that you're not alone. That things will be okay. Seek support in those around you, whoever they are. At one point or another, there was a you that existed outside, independently of this relationship. And it still does. It's just a matter of finding your old you once more. With a little brushing off, they'll be good as new.  Reconnect with people and things from your past. What used to fill you with zest? What made you come alive? What is something that you always wish you had the time or energy to take part in? And the last, most important question: What better time than now? The only reason it isn't bright is because you're wearing shades. The future holds just as many promises as it did six weeks, six months, or six years ago. It's just a matter of what you make from it. Instead of dwelling on the past, think of tomorrow. What might it bring? When you hold onto the past, you have no room to hold onto the future. You could be missing out on an entire world out there. Would your loved one want that? In order to find love, you have to give and receive it. You...

TL;DR in Russian:

Позвольте себе горевать. Не горюйте в одиночестве. Откройте себя заново. Смотрите в будущее. Напишите официальное письмо расставания. Помните о том, что наступит момент, когда вы отпустите человека.


The flat side of a chisel should be as reflective as a mirror once it's properly sharpened. Start by working it back and forth lengthwise over the course grit on your stone. Use both hands to keep it steady as you slide it back and forth. Your movements should be smooth and steady, rather than jerky. When the entire flat surface shows the intricate scratches of the stone's course grit, do the same thing with the medium grit, and again with the fine. The flat side is finished when it's as reflective as a mirror.  Do not move the chisel from side to side, or rock it back and forth.     Use the entire surface of the stone for a more even finish.     Clean the blade and your hands between grits so the powder doesn't obscure your view of the chisel's surface.    It's possible to sharpen a bevel by freehanding it against the stone, but it's very difficult to make sure you get the exact angle you want without using a honing guide. Fit the chisel into the honing guide and tighten the screws on either side to hold it in place. Depending on the type of chisel you have and what you'll be using it for, you'll want to set the guide to create an angle somewhere between 20 and 35 degrees.  For a paring chisel, set it at 20 degrees. Standard chisels work well at 25 degrees. If you don't want to buy a honing guide, it's common to make one out of wood. You'll need to saw a wooden wedge to the angle you want, superglue two strips on either side to act as rails (the chisel rests between these), then screw another strip of wood over the rails so you can tighten the chisel in place. Place the bevel flat against the coarsest grit on the stone. Using both hands to hold the guide, move the chisel back and forth over the stone in a very thin, stretched figure 8 pattern. When you can see the grit's scratches on the bevel, switch to the medium grit, then the fine grit, wiping the blade in between grits.  Use the entire surface of the stone as you sharpen. If you use the same area too much, a hollow will develop there, and it won't...

TL;DR in Russian:

Начинайте с плоской стороны. Используйте инструмент для заточки, чтобы установить угол наклона. Заточите фаску.


The fleas are most likely in your carpet because they came from your pet. In order to prevent the fleas from getting into your carpet, you will need to check your pet to see if he or she has fleas. If your pet is constantly scratching him or herself, he or she probably has fleas. Purchase a flea comb from a pet store and brush your pet with it. The flea comb has small, tight bristles that will catch the tiny pests in your pet's fur. It will also remove any loose fur, thus preventing shedding. Consider keeping a small bowl filled with water and a few drops of dish soap. You can dip the comb into the soapy water to drown the fleas and get them off the comb while you are brushing your pet's fur. The water will drown the fleas, and the soap will kill any larva. Consider using a special soap for killing off fleas. Keep in mind, however, that this may not work very well if you have a cat. Most cats hate water and will become aggressive if forced into water. If you wish to give your cat a bath, make sure that you are wearing thick gloves and long sleeves to protect your skin. Take your pet to a vet and ask what sort of flea medication would be the best for your pet. Your vet will then prescribe or recommend a medication type (cat or dog) and a dosage. If you wish to prescribe the medication yourself, make sure that you read the label—it will tell you whether it is for a cat or a dog, what age range it is for, and what weight it is for. If you do not do this, you will risk overdosing your pet and get tragic results.  Depending on the type, flea medication can be given orally or topically. If it is given topically, it is usually applied on the base of your pet's neck, right between the shoulder blades. Refer to the instructions on the label to find out how you should give the medication to your pet. Watch your pet for any signs of discomfort or allergic reactions. Sometimes, a cat or dog may be allergic to flea medication. Never give dog flea medication to a cat and vice versa. Always use the recommended dosage, and...

TL;DR in Russian:

Проверьте, есть ли блохи у вашего домашнего питомца. Регулярно расчесывайте ваших питомцев. Выкупайте питомца. Дайте животному лекарство против блох. Купите блошиный ошейник. Не используйте чеснок или пивные дрожжи. Повлияйте на блох с помощью эфирных масел. Отпугивайте блох растениями.


The floor might be wet as well as your feet so you need to be extra careful to prevent yourself from falling. Also, your blood pressure might be slowed down and you could get a head rush when you stand up. Pull the plug and pour cold water in to gradually bring your core temperature down then slowly stand. If you can, hold on to something stable as you stand up. If you have dry skin, you may want to rinse off with clean water from the faucet to get off any soap residue from your bath. You can do this by filling up a cup and repeatedly pouring water over your body. You can also turn on the shower to have a quick rinse. If you decide to use the shower, wait until at least half of the bath water drains out so water doesn't splash on the floor and the tub won't over flow. Put a towel around yourself to soak up the water left on your skin. To keep your head warm and dry your hair, take another towel and wrap it around your head. This will help prevent additional water from dripping on the floor that you could slip on. Pat yourself dry and apply lotion or cream to your body and face to help moisturize your skin(optional). Just unplug the bath tub, put everything back and wipe up any spills or footprints. You can also spray an after shower cleaner that doesn't involve any wiping and will help keep your tub clean. Natural cleaning products that don't use chemicals are safe to use and better for the environment.

TL;DR in Russian:

Выходите из ванны неспешно. Ополоснитесь чистой водой. Обмотайте полотенцем волосы и тело. Не забудьте вымыть ванну.


The flowchart map allows you to examine a process and see the multiple options for getting it done. The flowchart can be linear and can just flow from one concept to the next, but it can also have multiple elements for examining a variety of outcomes. The starting point can be a process or a problem that needs a solution. Let's use the starting point, "Lamp doesn't turn on". For the problem, "Lamp doesn't turn on," the most typical solution is that the lamp is not plugged in. Just write, "Lamp plugged in?" and connect it with an arrow to "Lamp doesn't turn on". Write a line from "Lamp plugged in?" that says "no" and another that says "yes." If you follow the line that says "no", then the response would be "Plug in lamp". Connect this response to "no" with a line. You've completed one flow of the concept, starting with "Lamp doesn't turn on" to "Plug in lamp". If you follow this "flow," then it should solve the problem. But if the lamp is plugged in, you'll follow "yes" to another option: "Bulb burned out?" This is the next logical solution. From the question, "Bulb burned out?" you'll need to branch out two terms: "yes" and "no" If the answer to "Bulb burned out" is "yes," then you'll need to connect this word to the solution, "Replace bulb", You've completed another flow of the concept, because this should fix the broken lamp. But if it turns out that the bulb is not burned out, you'll have to follow "no" to the last option: "Repair lamp". You have now completed a flowchart for the problem of a broken lamp, which will lead you to one of three solutions: plugging it in, replacing the bulb, or repairing the lamp.

TL;DR in Russian:

Выберите отправную точку или проблему. Напишите простейший способ решения проблемы. Напишите два результата решения. Запишите выводы для следующего решения.


The flying side kick is an advanced technique that is often used for demonstration purposes. If they are done correctly in a fight, they can also be very effective.  This is a longer range technique than a regular side kick. The run-up to the kick provides a lot of momentum, making this a very powerful kick. A common fighting position is to stand with your left foot in front and right foot in back with your body turned almost all the way to the side. Your right fist will be by your chin with your left 12-16 inches (30-40 cm) from your left shoulder. If you are kicking a target then you can take one or two steps only but if you are trying to jump over a target then you may need to get a running start for more speed and power. Plant your non-kicking foot (the front foot) solidly on the ground and push off of it to get into the air. As you push off turn your body to the side to swing your kicking foot into the front. You should also bring your non-kicking foot up so that your opponent cannot sweep it away from you. While swinging your kicking foot into place be sure to bend your knee up the same as you would do for a normal side kick. This bend of your knee creates a lot of extra power when it is straightened, so keeping your leg straight will lead to a much weaker kick.  The farther you bring your knee to your chest, the stronger your kick will be. Keep your heel pointing towards your target. Straighten at the very end of the strike. Timing is very important here so you must practice often to learn how to time your kick properly. A lot of your power comes from straightening your knee at the correct time. Be sure you are the right distance from your target to straighten fully but not so far that the kick barely touches the target. The blade of your foot and heel are the strongest parts of your foot. Your heel is especially strong so if you are going for a knock-out kick then you should strike with the heel for maximum power. Striking with the blade (or outside edge) of the foot is also effective and helps your...

TL;DR in Russian:

Нанесите боковой удар в полете, чтобы произвести впечатление на своих друзей. Начните с обычной боевой стойки. Приблизьтесь к вашей цели. Оттолкнитесь опорной ногой и поднимите бьющую ногу. Поднесите колено к груди. Выпрямите колено при ударе. Нанесите удар внешним ребром стопы или пяткой. Согните колено и приземлитесь.


The focal point of the room will depend on what room you're in. In a living room, it could be a picture window, fireplace or television. In a bedroom, it should be the bed. A dining room, the table. Figure out what the focal point of the room will be, since the majority of the furniture will be around it. If you have the option to get an item of different sizes, get one that fits the space that it's in. For example, don't get a bed or dining table that is too big for the room. There should be a minimum of three feet around the large objects in a room, to make them usable. Move your focal point, if you can, to the best spot in the room. This should be a place where, when you walk in to the room, you should have the focal point facing you and very prominent. Your eye should be drawn to the object. Draw further attention to the focal point later by placing accessories in this area. For a bedroom this will mean side tables with lamps or other items, while with a couch it will mean paintings or a mirror. A TV should generally be made more prominent with shelving or bookshelves, unless it is a part of a large entertainment center.

TL;DR in Russian:

Определитесь с тем, где будет фокальная точка. Учитывайте масштабы. Передвиньте точку фокуса. Привлеките внимание к этой точке.


The following are common kinds of stucco finishes, each of you may want to try before deciding:  Use only a roller to create a stippled effect. This is not the best option if you need to cover uneven or blemished walls. Use a trowel to spread on the stucco paint in a thick, uneven pattern. This is commonly used for outside walls. This is the best option if you are trying to cover up a heavily marred surface.  Use a sponge to create a square pattern. You can dip the sponge in the paint and apply it directly to a surface, then repeat in a geometrical or random pattern. Use a stiff brush or a comb to create "draw" onto the stucco or textured paint once it has been applied. You can draw waves, stripes, cross hatches or circles. Give your stucco the best chance to adhere to your wall by prepping your surface first. Of course, how you prep your surface depends on what kind of wall you have:  For concrete, brick, or block walls: Apply a coat of concrete bonding agent onto the wall. Allow it to dry completely before moving on to the next step. For wood walls: Nail roofing felt over the wall, also called "building wraps" or "stucco wraps." Then, cover with 17-gauge metal netting, which comes in 150-foot (45 m) rolls. Nail the netting to the felt using galvanized roofing nails. The scratch coat is the first layer of stucco, usually applied to a wire mesh lath, which is then scraped. These scrapes provide teeth for the next coat of stucco to hold onto. Whether you decide on a scratch coat depends largely on how much wall you want to stucco: Doing a whole wall probably requires a scratch coat, while intermittent patches probably don't.  Shoot for the scratch coat to be about 3/8-inch thick. Score the scratch coat horizontally with a ½-inch notched trowel when the stucco is firm, but not yet dry. This scoring is what gives the scratch coat its distinctive name, and allows it to bite and hold the next layer of stucco properly. Again, try to get it so that it's about 3/8-inch thick. If working out in the sun, be sure to...

TL;DR in Russian:

Нанесите часть штукатурки на лист фанеры, чтобы поэкспериментировать с текстурой, которую вы хотели бы создать. Подготовьте стену к нанесению штукатурки. Нанесите первый слой штукатурки с помощью кельмы и сокола, если необходимо. Наложите второй слой, который называется грунтом, или выравнивающим слоем. Пройдите грунт правилом, чтобы выровнять его. Нанесите отделочное покрытие, текстуру или сделайте "затирку" по вашему усмотрению.


The following are signs that your relationship is suffering:  You are fighting more than usual. She hasn't contacted you in several days. Either one of you has totally lost interest in sex. (Remember that this could be due to a variety of factors, like a death in the family, personal insecurities, or excess stress).  She continuously cancels plans without suggesting a different date. One of you has been dating/sleeping with somebody else. One of you suggests a "break." No matter what either of you says, a break is usually just a segue into an official break-up. Either one of you has become physically abusive. If this is the case, then it's time to end the relationship and seek professional help to cope with the issue. Never make an excuse for domestic violence. The only way to fix a problem in any relationship is for both parties to first be made aware of the issue. Remember that sometimes people are totally unaware of their own behavior. Once you have talked about the issue at hand and have both voiced your views and opinions, come to an agreement about what to do next. Come up with something that both parties can get on board with and feel comfortable with.  If you can't reach an agreement, then consider couples therapy. Getting the opinion of a third party will help put things in perspective and allow you to rationally sort of the issue from an objective standpoint. Know when the relationship can't be fixed. If you or your girlfriend are chronically unhappy in the relationship, then don't force things. Making healthy compromises to keep a relationship alive is one thing, but making yourself miserable to maintain the status quo will not do either of you any good. Some issues just need a little time to blow over. If you recently had a big fight, give each other space for a day or two. Chances are that the issue will resolve itself, and being apart will remind you both how much you care for one another.

TL;DR in Russian:

Научитесь распознавать проблемы. Обсудите возникшую проблему с девушкой. Ищите компромисс. Будьте терпеливы.


The following are symptoms of potential bacterial infections that may require treatment by a physician.  Fever, especially with a severe head or neck ache or chest pain Trouble breathing or pain in the chest A cough that lasts longer than a week Rash or swelling that won’t go down Increasing pain in the urinary tract (which may be pain with urination, in the lower back, or in the lower abdomen) Pain, swelling, warmth, pus drainage or red streaks extending from a wound. The only sure way to determine what types of bacterial infection you have is to visit a doctor. If you think you have an infection, call your doctor and schedule an appointment right away. Your doctor may perform a blood test, urine culture, or swab of the infected area to determine what type of infection you have. Remember that bacterial infections can only be diagnosed by a doctor. If you think that you have an infection, note the symptoms and go to the doctor for treatment as soon as possible. Asking your doctor about the different types of antibiotics that are available will make it easier for you to understand what your doctor is prescribing.   Broad-spectrum antibiotics fight a wide variety of bacteria. Broad-spectrum antibiotics treat gram positive and negative bacteria, so your doctor may prescribe one of these types of antibiotics if he or she is unsure about what bacteria you have. Amoxicillin, Augmentin,Cephalosporins(4th and 5th Generation),Tetracycline Aminoglycosides and Fluoroquinolones (Ciprofloxacin) are examples of broad-spectrum antibiotics.   Medium-spectrum antibiotics target a group of bacteria. Penicillin and bacitracin are popular medium-spectrum antibiotics.  Narrow-spectrum antibiotics are made to treat one specific kind of bacteria. Polymyxins fall into this small category of antibiotics. Treatment is much easier and more effective when your doctor knows what kind of bacterial infection you have. Your doctor will select the type of antibiotic that works best against the specific bacteria that has caused your...

TL;DR in Russian:

Обратите внимание на свои симптомы. Запишитесь на прием к врачу. Узнайте у врача о различных типах антибиотиков. Следуйте предписаниям своего лечащего врача. Пройдите полный курс лечения, назначенный врачом.


The following instructions are written generically; for specific instructions for your graphic editor program, consult the program's help file. You can make this file whatever size you wish, although you may need to resize it to match the size of the picture file you'll apply the watermark to. Layers are essentially transparent sheets on which you can place and arrange individual components to make up a graphic image. You'll later copy this layer to the graphic files you want to add your watermark to. If you're planning to watermark pictures for your Web site, your watermark text should include a copyright notice with your name, your Web site URL or both. You may want to use a font with thick letters or bold it to make the watermark text distinct. You may also want to enhance the text appearance with beveling or embossed effects. This will let you call up the watermark another time and apply it to other graphic files.  Depending on the graphic editor you're using, you can drag and drop the layer or copy the layer to the Clipboard and then paste it into the new graphic. You may want to save this file with a different name, in case you want to retain a copy of the graphic file without the watermark.

TL;DR in Russian:

Откройте ваш графический редактор. Создайте новый графический файл. Создайте новый слой в графическом файле. Введите текст водяного знака, используя соответствующий текстовый инструмент вашего редактора. Сохраните водяной знак в виде файла. Откройте рисунок, в который вы хотите вставить водяной знак. Скопируйте слой из файла с водяным знаком в файл открытого  рисунка. Сохраните файл рисунка с добавленным водяным знаком.


The following is a quick list of things you may already have around your home. Even if you don't have these things, don't worry, the messy bun can be easily created with just your fingers and a rubber-band. It is also easy enough to find all of the following items at your local 24-hour drug store. If you are thinking of creating a messy bun for a more important event like a wedding or prom you can plan ahead and find a store that specializes in carrying hair care products and accessories.  For the quick and simple messy bun up-do, you will need about 5 minutes, your fingers, and a rubber-band. If you have more time, gather a soft brush, wide-tooth comb and an elastic ponytail holder. Preferably an elastic holder without a metal clasp to reduce the chance of hair damage. Select a light-weight mousse that will allow your hair to be easily pliable yet still appear soft and natural. For extra body, select a mousse that says it includes a volumizing agent. This will be displayed on the mousse bottle. If you have very soft and fine hair or want your messy bun up-do to last for a long time, pick out a hairspray that you like to ensure your messy bun stays intact.  For the most natural look, choose a hair spray with a micro-fine mist for minimal build up that you can apply and reapply without washing your hair. For a more extreme edgy look, choose a hair spray that offers massive volume without stiffness. If you have extremely soft or freshly washed hair, you can also experiment with dry shampoo or hair salt spray to add texture. (optional) Purchase some plain bobby pins, decorative flowers, bling gem-studded hair pins, small decorative hair clips, or similar hair items. When searching for such items remember to keep them delicate and classy. (optional)

TL;DR in Russian:

Выберите средства для укладки. Создайте более изысканный вид. Добавьте оригинальные и изысканные украшения.


The following list explains exactly what is needed (also see Things You'll Need below for the crafting items):  At least 34 diapers (newborn or early stage) 2 receiving blankets 2 bibs, a chain linked toy (appropriate for a newborn or infant) 1 pair of infant socks 1 baby bottle 1 washcloth 1 plush stuffed toy (that does not contain buttons or any items that could pose a choking hazard).

TL;DR in Russian:

Выберите цвета и стили необходимых элементов, которые, на ваш взгляд, хотела бы будущая мама.


The following terms are used in the instructions below:  Apollonian Gasket: One of several names for a type of fractal composed of a series of circles nested inside one large circle and tangent to all others nearby. These are also called "Soddy Circles" or "Kissing Circles". Radius of a circle: The distance from the center point of a circle to its edge. Usually assigned the variable r. Curvature of a circle: The positive or negative inverse of the radius, or ±1/r. Curvature is positive when dealing with the outer curvature of the circle and negative for the inner curvature. Tangent: A term applied to lines, planes, and shapes that intersect at one infinitely small point. In Apollonian Gaskets, this refers to the fact that each circle touches each nearby circle at only one point. Note that there is no intersection - tangent shapes do not overlap. Descartes's Theorem is a formula that is useful for calculating the sizes of the circles in an Apollonian Gasket. If we define the curvatures (1/r) of any three circles as a, b, and c, respectively, the Theorem states that the curvature of the circle (or circles) tangent to all three, which we will define as d, is: d = a + b + c ± 2 (sqrt (a × b + b × c + c × a )). For our purposes, we'll generally only use the answer we obtain by putting a plus sign in front of the square root ( in other words, ... + 2 (sqrt(...)). For now, it's enough to know that the subtraction form of the equation has its uses in other related tasks.

TL;DR in Russian:

Определите ключевые термины. Разберитесь в теореме Декарта.


The following terms will be used throughout the examples, and are common in problems involving algebraic fractions:   Numerator: The top part of a fraction (ie. (x+5)/(2x+3)).  Denominator: The bottom part of the fraction (ie. (x+5)/(2x+3)).  Common Denominator: This is a number that you can divide out of both the top and bottom of a fraction. For example, in the fraction 3/9, the common denominator is 3, since both numbers can be divided by 3.  Factor: One number that multiples to make another. For example, the factors of 15 are 1, 3, 5, and 15. The factors of 4 are 1, 2, and 4.  Simplified Equation: This involves removing all common factors and grouping similar variables together (5x + x = 6x) until you have the most basic form of a fraction, equation, or problem. If you cannot do anything more to the fraction, it is simplified. These are the exact same steps you will take to solve algebraic fractions.  Take the example, 15/35. In order to simplify a fraction, we need to find a common denominator. In this case, both numbers can be divided by five, so you can remove the 5 from the fraction:  15    →     5 * 335   →       5 * 7 Now you can cross out like terms. In this case you can cross out the two fives, leaving your simplified answer, 3/7. In the previous example, you could easily remove the 5 from 15, and the same principle applies to more complex expressions like, 15x – 5. Find a factor that both numbers have in common. Here, the answer is 5, since you can divide both 15x and -5 by the number five. Like before, remove the common factor and multiply it by what is “left.”15x – 5 = 5 * (3x – 1) To check your work, simply multiply the five back into the new expression – you will end up with the same numbers you started with. The same principle used in common fractions works for algebraic ones as well. This is the easiest way to simplify fractions while you work.  Take the fraction: (x+2)(x-3)(x+2)(x+10) Notice how the term (x+2) is common in both the numerator (top) and denominator (bottom). As such, you can...

TL;DR in Russian:

Освойте термины, используемые для описания алгебраических дробей. Ознакомьтесь с действиями с простыми дробями. В алгебраических выражениях общие множители выделяются точно так же, как и в обычных. Сложные члены можно выделять точно так же, как и простые.


The following treatments will have to be confirmed by a doctor before they can be employed. Some types of scoliosis do not have to be treated at all as they are caused by another ailment in the body that needs to be corrected. Consult with your doctor about the steps you can take to treat your scoliosis. Braces cannot treat scoliosis, but they can slow down the progression of the effects of scoliosis. When you first start using the brace, you will need to wear the brace each day and night. However, as your time with the braces progresses, you may be able to wear it less. Braces are particularly important because they can reduce the need for surgery. If you begin wearing a brace soon after being diagnosed with scoliosis, it may keep your back from curving further. If the curve of your back stays at 25 to 40 degrees, you will not need surgery. If your back curves more than 40 degrees, you will most likely need to get surgery to ensure that your back stops curving. If you do not get surgery, you spine may continue to curve one to two degrees each year. You will have have to consult with your doctor about the next steps you will have to take.

TL;DR in Russian:

Поговорите с врачом. Носите корсет. Сделайте операцию.


The food items listed on the kid's menu can be a great option when you're dieting. The portions are smaller, so they contain fewer calories than items on the main menu. Plus, you can often select a piece of fruit as a side option. Be aware that the meal's calorie count on the board does not include the calorie count for sodas. The average cup of soda can contain around 300 calories and 19 grams (0.67 oz) of sugar, which isn't helpful for maintaining your diet. Water is always a safe, calorie-free, and refreshing choice. Also, your body needs water to survive and function properly.  While diet soda has zero calories, the artificial sugars in the beverage can make you crave more real sugars, causing you to over indulge in other sweetened treats.  Lemonade and fruity drinks typically carry just as many calories and sugar as soda. Many meals at fast-food chains offer an order of fries as a side. While fries are certainly delicious, that can pack a calorie count that can range from 300 to even 900 calories! They don't have much nutritional value either. They are mostly just fat and calories. Ask if you can replace the order of fries with a side salad, a piece or fruit, or opt to skip the side altogether. Condiments like mayonnaise, tartar sauce, sour cream, barbecue sauce, and salad dressings can be deceivingly high in calories and sugars. Mayonnaise, for example, has about 180 calories for every 2 tablespoons or 30 milliliters (1  fl oz). Those calories can add up quickly. Ask to receive the condiments or salad dressing in a small container on the side so you can control the amount you use. Opt to use mustard or hot sauce to enhance the flavor. At about 20 calories for 2 tablespoons, mustard is a tasty, low-calorie condiment that packs a lot of flavor. Hot sauce can also kick up the flavor. There are only 3 calories for 2 tablespoons, and all you really need is a little dash! When ordering food from a fast-food restaurant, avoid ordering food that is breaded or fried. Opt for a grilled fish sandwich instead of...

TL;DR in Russian:

Сделайте заказ из детского меню. Откажитесь от сладкой газированной воды. Откажитесь от картофеля фри. Попросите подать соусы или приправы отдельно. Отдайте предпочтение блюдам на гриле, а не жареным. Отдайте предпочтение буррито на тарелке, а не его традиционному варианту. Откажитесь от булочек для гамбургеров. Попробуйте салат с постными белками. Разделите обед с другом.


The food you consume can have a profound affect on your brain power. Strive for a healthy diet, rich in brain food. A Mediterranean diet can increase your brainpower. This is a diet comprised of mainly fresh fruits and vegetables, legumes, healthy fats, and fish. Healthy fats include monounsaturated fats and are found in foods like fish, avocados, olive oil, and canola oil. Transitioning into a more Mediterranean-based dietary plan can help you increase your overall brain power.  Spinach is a powerful brain food. Eating three or more servings of spinach or other leafy greens like kale each day slows mental decline and increases overall brain function.  Simple sugars, like table sugars and brown sugars, as well as syrupy sweeteners like high fructose corn syrup, can have a detrimental effect on the brain. Saturated and trans fats, the kinds of found in red meat and dairy, have a negative effect on your mental level as well as overall health. Enriched, bleached, or refined flour, the flour found in white breads, white rices, and white pastas, also has a poor affect on the brain. Getting a solid 7 to 8 hours of sleep each night can increase brain power and promote logical thinking. To improve your sleep schedule, have a set bedtime and wake time that you do not deviate from, even on weekends. Stay away from electronic screens close to bedtime. Do not eat heavy meals late at night and work on engaging in a relaxing activity, like reading, in the hour before bed. Breathing increases brain power by increasing oxygen flow in the brain. Practice deep breathing exercises in the morning and before bed. Practice yoga, meditation, Pilates and other activities that focus on healthy breathing patterns. Physical exercise has a profound effect on cognitive abilities. In addition to being great for the body, a regular exercise routine can boost your mind's capacity for logic.  Make exercise a priority. Many people push exercise to the peripheral of their lives, not making the time necessary to go to the gym or go for a run....

TL;DR in Russian:

Употребляйте в пищу продукты, полезные для мозга. Измените режим сна. Уделяйте внимание дыханию. Регулярно занимайтесь физкультурой. Проводите время на природе. Делайте перерывы.


The force (F) required to move an object of mass (m) with an acceleration (a) is given by the formula F = m x a. So, force = mass multiplied by acceleration. The International System of Units (SI) unit of mass is the kilogram, and the SI unit of acceleration is m/s2 (meters per second squared). So when mass and acceleration are expressed in their SI units, we get the force in its SI units which is N (Newtons) As an example, if the mass of the object is given to be 3 pounds, you'll need to convert those pounds to kilograms. 3 pounds make 1.36 kg, so the mass of the object is 1.36 kg. If the weight of an object is given in N (Newtons), then divide it by 9.8 to get the equivalent mass. For example, 10 N weight is equivalent to 10/9.8 = 1.02 kg.

TL;DR in Russian:

Умножьте массу на ускорение. Переведите единицы измерения в систему СИ. Помните о том, что вес и масса – это различные понятия в физике.


The force of an object is simply the product of its mass and acceleration. This relationship can be defined by the following formula: Force = Mass x Acceleration. Here are a few other things to keep in mind as you measure force:  The standard unit for mass is kilograms (kg). The standard unit for acceleration is m/s2. The standard unit for force is the newton (N). The newton is a derived standard unit. 1N = 1 kg x 1m/s2. An object's mass is the amount of matter that it contains. The mass of an object never changes, no matter what planet it's on; while weight fluctuates depending on gravitational pull, your mass is the same on Earth and on the Moon. In the metric system, mass can be expressed in grams or kilograms. Let's say the object we're working with is a truck that has a mass of 1000 kg.  To find the mass of a given object, place it on a triple beam or a double pan balance. This will calculate the mass in kilograms or grams. In the English system, mass can be expressed in pounds. Because force can also be expressed in pounds, the term "pound-mass" has been coined to distinguish its usage. However, if you find the mass of an object using pounds in the English system, it's best to convert it to the metric system. If you know an object's mass in pounds, simply multiply it by .45 to find the mass in kilograms. In physics, acceleration is defined as a change in velocity, which is defined as speed in a given direction, per unit of time. In addition to the common definition of acceleration as speeding up, it also can mean an object is slowing down or changing direction. Just as velocity can be measured with a speedometer, acceleration is measured with an accelerometer. Let's say the acceleration of the 1000 kg truck we're working with is 3m/s2.  In the metric system, velocity is expressed in centimeters per second or meters per second, and acceleration is expressed as centimeters per second per second (centimeters per second squared) or meters per second per second (meters per second squared). In the English...

TL;DR in Russian:

Разберитесь в соотношении между силой, массой и ускорением. Измерьте массу заданного объекта Измерьте ускорение объекта. Умножьте массу объекта на ускорение.


The former material is also a good way to speed pepper growth in cool climate areas. Gardeners in warm climates will want to stick to mulch because it helps conserve moisture and protects the plants’ roots from hot temperatures. These plants benefit from an addition of slow release granular fertilizer, such as Osmocote, or organic varieties, like those made with fish meal or alfalfa. However, if one has leafy green plants and no peppers, gardeners should probably cut back on the nitrogen fertilizer. This element is known for producing lush, fruitless plants. Almost all bell peppers start off green and eventually ripen to the desired color in about two weeks, though some types can take as long as a month for the right color to develop. Tall varieties may need to be staked to support the fruit and keep the plants from falling over while the fruit grows and ripens. Wire cages wrapped with plastic were mentioned in Mother Earth News article the author read as a good way to insulate tomato seedlings against sudden drops in temperature. Another way to prevent seedling from getting too cold is to use bell jars (hot caps). These devices were originally made from glass but now are more likely to be made from leftover plastic milk or soda bottles. Pepper seeds can be saved for up to two years under ideal conditions. This means that growers will not have to purchase seed annually if they store the leftovers in a dark, dry location to keep them from sprouting prematurely. Once the first chill of winter sets in, gardeners can harvest the remaining fruit and then dig the plants up. Specimens that are not diseased are good candidates for the compost bin. Diseased plants can be bagged up and left with the trash to prevent the disease from spreading.

TL;DR in Russian:

Используйте черную укрывную пленку, спанбонд или мульчирование для защиты от сорняков. Проводите подкормку перцев. Дождитесь, когда перцы созреют, и только потом собирайте урожай. Защитите растения от внезапного понижения температуры. Сохраните семена перца для дальнейшего выращивания. Уберите растения по окончании плодоношения.


The formula for calculating kinetic energy (KE) is KE = 0.5 x mv2. Here m stands for mass, the measure of how much matter is in an object, and v stands for the velocity of the object, or the rate at which the object changes its position. Your answer should always be stated in joules (J), which is the standard unit of measurement for kinetic energy. It is equivalent to 1 kg * m2/s2. If you are solving a problem where the mass isn’t given, you will have to determine the mass yourself. This can be done by weighing the object on a balance and obtaining the mass in kilograms (kg).  Tare the balance. Before you weigh your object, you must set it to zero. Zeroing out the scale is called taring.  Place your object in the balance. Gently, place the object on the balance and record its mass in kilograms. If necessary, convert grams to kilograms. For the final calculation, the mass must be in kilograms. Oftentimes, the problem will give you the velocity of the object. If this is not the case, you can determine the velocity by using the distance an object travels and how long it takes to cover that distance. The units for velocity are meters per second (m/s).  Velocity is defined by the equation, displacement divided by time: V = d/t. Velocity is a vector quantity, meaning it has both a magnitude and a direction. Magnitude is the number value that quantifies the speed, while the direction is the direction in which the speed takes place during motion. For example, an object’s velocity can be 80 m/s or -80 m/s depending on the direction of travel. To calculate velocity, simply divide the distance the object traveled by the time it took to travel that distance.

TL;DR in Russian:

Запомните формулу для вычисления кинетической энергии. Определите массу объекта. Найдите скорость объекта.


The formula for calculating kinetic energy (KE) is KE = 0.5 x mv2. Here m stands for mass, the measure of how much matter is in an object, and v stands for velocity of the object, or the rate at which the object changes its position. Your answer should always be stated in joules (J), which is the standard unit of measurement for kinetic energy. It is equivalent to 1 kg * m2/s2. In some problems, you may know the kinetic energy and the mass or kinetic energy and velocity. The first step to solving this problem is to plug in all of the variables that are known.  Example 1: What is the velocity of an object with a mass of 30 kg and a kinetic energy of 500 J?  KE = 0.5 x mv2 500 J = 0.5 x 30 x v2   Example 2: What is the mass of an object with a kinetic energy of 100 J and a velocity of 5 m/s?  KE = 0.5 x mv2 100 J = 0.5 x m x 52 Using algebra, you can solve for the unknown variable by rearranging all of the known variables to one side of the equation.  Example 1: What is the velocity of an object with a mass of 30 kg and a kinetic energy of 500 J?  KE = 0.5 x mv2 500 J = 0.5 x 30 x v2 Multiply mass by 0.5: 0.5 x 30 = 15 Divide kinetic energy by the product: 500/15 = 33.33 Square root to find velocity: 5.77 m/s   Example 2: What is the mass of an object with a kinetic energy of 100 J and a velocity of 5 m/s?  KE = 0.5 x mv2 100 J = 0.5 x m x 52 Square the velocity: 52 = 25 Multiply by 0.5: 0.5 x 25 = 12.5 Divide kinetic energy by product: 100/12.5 = 8 kg

TL;DR in Russian:

Запишите формулу. Подставьте в формулу известные значения. Преобразуйте уравнение, чтобы найти неизвестную величину.


The formula for calculating percentage error is simple: [(|Approximate Value - Exact Value|) / Exact Value] x 100. You will use this as a reference to plug in the two values you need to know.  The approximate value is your estimated value, and the exact value is the real value. For example, if you guess that there will be 9 oranges in a bag, but there are actually 10, 9 is the approximate value, and 10 is your exact value. In the example of oranges, you will subtract 10 (the exact value) from 9 (the estimated value). In this case, the result is 9 - 10 = -1.  This difference is considered the magnitude of difference in approximate and estimated values. This begins to tell you how far off the results were from what they were expected to be. Since the formula uses the absolute value of the difference, you can discard a negative sign. In this example, -1 will become just 1.  In the oranges example, 9 - 10 = -1. The absolute value of -1, written as |-1|, is 1. If your result is positive, leave the number as it is. For example, 12 apples (approximate) - 10 apples (exact) = 2. The absolute value of 2 (|2|) is just 2. In statistics, taking the absolute value simply means you don't care which direction your guess was off (either too high—positive—or too low—negative). You just want to know how far off the estimate was from the exact value. Either with a calculator or by hand, divide the top number by the absolute value of your exact variable. In this example, the exact value is already positive, so you just need to divide 1 (from the previous step) by 10 (the exact number of oranges).  For this example, 1/|10| = 1/10. In some cases, the exact value might be a negative number to begin with. If this is the case, you want to ignore the negative (i.e. take the absolute value of the exact number).

TL;DR in Russian:

Запишите формулу для вычисления процентной погрешности. Вычтите точное значение из оценочного. Найдите абсолютное значение этой разности. Разделите найденную разность на абсолютную величину истинного значения.


The formula for the area of a triangle is  A=1/2bh.    A = Area of the triangle  b = Length of the base of the triangle  h = Height of the base of the triangle You already know the area, so assign that value to A.  You should also know the value of one side length; assign that value to "'b'".  Any side of a triangle can be the base, regardless of how the triangle is drawn. To visualize this, just imagine rotating the triangle until the known side length is at the bottom. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle!

TL;DR in Russian:

Напомним формулу для вычисления площади треугольника. Посмотрите на треугольник и подумайте, какие величины вам уже известны. Подставьте данные вам значения в формулу для вычисления площади (А = 1/2bh) и найдите высоту.


The formula for the frequency of a wave in a vacuum is almost identical to that of a wave not in a vacuum. Since there are no outside influences on the velocity of the wave, though, you would use the mathematical constant for the speed of light, which electromagnetic waves would travel at under these conditions. As such, the formula is written as: f = C / λ  In this formula, f represents frequency, C represents the velocity or speed of light, and λ represents the wavelength of the wave. Example: A particular wave of electromagnetic radiation has a wavelength of 573 nm when passing through a vacuum. What is the frequency of this electromagnetic wave? When the problem gives you the wavelength in meters, no further action is needed. If, however, the wavelength is given in micrometers, you need to convert this value into meters by dividing it by the number of micrometers in a single meter.  Note that when working with extremely small numbers or extremely large numbers, it is generally easier to write the values in scientific notation. The values will be shown in and out of their scientific notation forms for this example, but when writing your answer for homework, other schoolwork, or other formal forums, you should stick with scientific notation. Example:  λ = 573 nm 573 nm x (1 m / 10^9 nm) = 5.73 x 10^-7 m = 0.000000573 The speed of light is a constant, so even if the problem does not provide you with a value, the value remains 3.00 x 10^8 m/s. Divide this value by the wavelength converted into meters. Example: f = C / λ = 3.00 x 10^8 / 5.73 x 10^-7 = 5.24 x 10^14 With this, you should have calculated the value of the frequency of the wave. Write your answer in Hertz, Hz, the unit for frequency. Example: The frequency of this wave is 5.24 x 10^14 Hz.

TL;DR in Russian:

Формула: Преобразуйте единицы измерения длины волны в метры (если необходимо). Разделите скорость света на длину волны. Запишите ответ.


The formula for the surface area of any prism is SA=2B+Ph{\displaystyle SA=2B+Ph}, where SA{\displaystyle SA} equals the surface area, B{\displaystyle B} equals the area of the base, P{\displaystyle P} equals the perimeter of the base, and h{\displaystyle h} equals the height of the prism. In order for this method to work you must know the surface area of the prism, as well as the area of the triangular base, and the length of all three sides of the base. If you do not know the surface area, this method will not work. For example, if you know the surface area is 1460 square centimeters, your formula will look like this:1460=2B+Ph{\displaystyle 1460=2B+Ph} 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 8 centimeters, and the height of the triangle is 4 centimeters, to find the area you would calculate:A=12(8)(4){\displaystyle A={\frac {1}{2}}(8)(4)}A=12(32){\displaystyle A={\frac {1}{2}}(32)}A=16{\displaystyle A=16} Make sure you are substituting for the letter B{\displaystyle B}. For example, if you found the area of the base to be 16, your formula will look like this:1460=2(16)+Ph{\displaystyle 1460=2(16)+Ph}1460=32+Ph{\displaystyle 1460=32+Ph} To find the perimeter of a triangle, add up the length of all three sides. For example, if the base is a triangle has three sides with lengths of 8, 4, and 9 centimeters, to find the perimeter you would calculate:P=8+4+9{\displaystyle P=8+4+9}P=21{\displaystyle P=21} Make sure you are substituting for the letter P{\displaystyle P}. For example, if you found the perimeter of the base to be 21, your formula will look like this:1460=32+21h{\displaystyle 1460=32+21h} This will give you the height of...

TL;DR in Russian:

Запишите формулу для вычисления площади поверхности призмы. В формулу подставьте площадь поверхности. Вычислите площадь основания. Подставьте площадь основания в формулу для вычисления площади поверхности призмы. Найдите периметр основания. Подставьте периметр основания в формулу для вычисления площади поверхности призмы. Найдите h{\displaystyle h}.


The formula is A=(l)(w){\displaystyle A=(l)(w)}, 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.  This method will only work if you are given the area and length of the rectangle. You might also see the formula written as A=(h)(w){\displaystyle A=(h)(w)}, where h{\displaystyle h} equals the height of the rectangle and is used instead of length. These two terms 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 an area of 24 square centimeters, and a length of 8 centimeters, your formula will look like this:24=8w{\displaystyle 24=8w} To do this, you need to divide each side of the equation by the length. For example, in the equation 24=8w{\displaystyle 24=8w}, you would divide each side by 8.24=8w{\displaystyle 24=8w}248=8w8{\displaystyle {\frac {24}{8}}={\frac {8w}{8}}}3=w{\displaystyle 3=w} Don’t forget to include the unit of measurement. For example, for a rectangle with an area of 24cm2{\displaystyle 24cm^{2}} and a length of 8cm{\displaystyle 8cm}, the width would be 3cm{\displaystyle 3cm}.

TL;DR in Russian:

Запишите формулу для вычисления площади прямоугольника. В формулу подставьте данные значения площади и длины. Найдите w{\displaystyle w}. Запишите окончательный ответ.


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. 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}. To do this, divide both sides of the equation by l{\displaystyle l}. Set this value aside. You will plug it into the perimeter formula later. For example:35=lw{\displaystyle 35=lw}35l=w{\displaystyle {\frac {35}{l}}=w}. The formula 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 P{\displaystyle P}. For example, if the perimeter of a rectangle is 24 centimeters, your formula will look like this: 24=2(w+l){\displaystyle 24=2(w+l)}. This will give you the value of w+l{\displaystyle w+l}. For example:24=2(w+l){\displaystyle 24=2(w+l)}242=2(w+l)2{\displaystyle {\frac {24}{2}}={\frac {2(w+l)}{2}}}12=w+l{\displaystyle 12=w+l}. Use the value you found by rearranging the formula for area. For example, if using the area formula you found that 35l=w{\displaystyle {\frac {35}{l}}=w}, replace this value of w{\displaystyle w} into the perimeter formula:12=w+l{\displaystyle 12=w+l}12=35l+l{\displaystyle 12={\frac {35}{l}}+l} To do this, multiply both sides of the equation by l{\displaystyle l}. For example:12=35l+l{\displaystyle 12={\frac {35}{l}}+l}12×l=(35l×l)+(l×l){\displaystyle 12\times l=({\frac {35}{l}}\times l)+(l\times l)}12l=35+l2{\displaystyle 12l=35+l^{2}} To do this, subtract the first-degree term from both sides of the equation. For example:12l=35+l2{\displaystyle 12l=35+l^{2}}12l−12l=35+l2−12l{\displaystyle 12l-12l=35+l^{2}-12l}0=35+l2−12l{\displaystyle 0=35+l^{2}-12l} This means the term with the exponent will be first, followed by the term with the variable,...

TL;DR in Russian:

Запишите формулу для вычисления площади прямоугольника. В формулу подставьте значение площади прямоугольника. Перепишите формулу так, чтобы обособить w{\displaystyle w}. Запишите формулу для вычисления периметра прямоугольника. В формулу подставьте значение периметра прямоугольника. Разделите обе стороны уравнения на 2. В формулу подставьте выражение для вычисления w{\displaystyle w}. Избавьтесь от дроби. Приравняйте уравнение к 0. Упорядочьте члены уравнения. Разложите квадратное уравнение на множители. Найдите l{\displaystyle l}. 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.


The formula is A=s2{\displaystyle A=s^{2}}, where A{\displaystyle A} equals the area of the square, and s{\displaystyle s} equals the length of one side of the square.  This method only works if you are given the area of the square. To find the length of the diagonal, you have to first find the length of one side of the square, which is why you must set up the area formula and solve for s{\displaystyle s}. Make sure you are substituting for the variable A{\displaystyle A}. For example, if the area of the square is 25 square centimeters, your formula will look like this:25=s2{\displaystyle 25=s^{2}} To do this, find the square root of the area. This will give you the length of one side of the square. To find the square root, use a calculator. If you need help calculating the square root by hand, read Calculate a Square Root by Hand. For example:25=s2{\displaystyle 25=s^{2}}25=s2{\displaystyle {\sqrt {25}}={\sqrt {s^{2}}}}5=s{\displaystyle 5=s} In the formula d{\displaystyle d} equals the length of the diagonal and s{\displaystyle s} equals one side of the square. This formula is derived from the Pythagorean Theorem (a2+b2=c2){\displaystyle a^{2}+b^{2}=c^{2})}. A diagonal divides a square into two congruent right triangles, thus, you can use the side lengths of the square to find the length of the diagonal (which would be the hypotenuse of the right triangle). Make sure you are substituting for the variable s{\displaystyle s}. For example, if the square has a side length of 5 centimeters, set up the formula like this:d=52{\displaystyle d=5{\sqrt {2}}} This will give you the length of the diagonal. *It’s best to perform the calculation on a calculator, so that you can get a more precise result. If you don’t have a calculator, you can round 2{\displaystyle {\sqrt {2}}} to 1.414. For example, if you are calculating the diagonal of a 5-centimeter square, your formula will look like this:d=52{\displaystyle d=5{\sqrt {2}}}d=7.07{\displaystyle d=7.07}So, the diagonal of the square is 7.07 centimeters long.

TL;DR in Russian:

Запишите формулу для вычисления площади квадрата. В формулу подставьте значение площади квадрата. Найдите s{\displaystyle s}. Запишите формулу d=s2{\displaystyle d=s{\sqrt {2}}}. Подставьте в формулу значение длины стороны квадрата. Умножьте сторону квадрата на 2{\displaystyle {\sqrt {2}}}, чтобы найти диагональ квадрата.


The formula is Asector=θ360(π)(r2){\displaystyle A_{sector}={\frac {\theta }{360}}(\pi )(r^{2})}, where Asector{\displaystyle A_{sector}} equals the area of the sector, θ{\displaystyle \theta } equals the central angle of the sector in degrees, and r{\displaystyle r} equals the radius of the circle. This information should be given to you. Make sure you have the area of the sector, not the area for the circle. Substitute the area for the variable Asector{\displaystyle A_{sector}} and the angle for the variable θ{\displaystyle \theta }. This will tell you what fraction of the entire circle the sector represents. To do this, divide both sides of the equation by the fraction or decimal you just calculated. This will isolate the r{\displaystyle r} variable. For a more precise result, use a calculator. You can also round π{\displaystyle \pi } to 3.14. This will give you the radius of the circle.

TL;DR in Russian:

Запишите формулу для вычисления площади сектора. В формулу подставьте значения площади сектора и центрального угла. Разделите центральный угол на 360. Изолируйте (π)(r2){\displaystyle (\pi )(r^{2})}. Разделите обе части формулы на π{\displaystyle \pi }. Извлеките квадратный корень из обеих частей формулы.


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}.

TL;DR in Russian:

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.


The formula is P=2l+2w{\displaystyle P=2l+2w}, where P{\displaystyle P} equals the perimeter of the rectangle, 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 perimeter and length of the rectangle. You might also see the formula written as P=2(w+h){\displaystyle P=2(w+h)}, 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, and the distributive property dictates that these two formulas, although arranged differently, will give you the same result. Make sure you substitute for the correct variables. For example, if you are trying to find the width of a rectangle that has a perimeter of 22 centimeters, and a length of 8 centimeters, your formula will look like this:22=2(8)+2w{\displaystyle 22=2(8)+2w}22=16+2w{\displaystyle 22=16+2w} To do this, you need to subtract the length from each side of the equation, then divide by 2. For example, in the equation 22=16+2w{\displaystyle 22=16+2w}, you would subtract 16 from each side, then divide by 2.22=16+2w{\displaystyle 22=16+2w}6=2w{\displaystyle 6=2w}62=2w2{\displaystyle {\frac {6}{2}}={\frac {2w}{2}}}3=w{\displaystyle 3=w} Don’t forget to include the unit of measurement. For example, for a rectangle with a perimeter of 22cm{\displaystyle 22cm} and a length of 8cm{\displaystyle 8cm}, the width would be 3cm{\displaystyle 3cm}.

TL;DR in Russian:

Запишите формулу для вычисления периметра прямоугольника. В формулу подставьте данные значения периметра и длины. Найдите w{\displaystyle w}. Запишите окончательный ответ.


The formula is P=4s{\displaystyle P=4s}, where P{\displaystyle P} equals the perimeter of the square, and s{\displaystyle s} equals the length of one side of the square.  This method only works if you are given the perimeter of the square. To find the length of the diagonal, you must first find the length of one side of the square, so you need to set up the perimeter formula and solve for s{\displaystyle s}. Make sure you are substituting for the variable P{\displaystyle P}. For example, if the perimeter of the square is 20 centimeters, your formula will look like this:20=4s{\displaystyle 20=4s} To do this, divide each side of the equation by 4. This will give you the length of one side of the square. For example:20=4s{\displaystyle 20=4s}204=4s4{\displaystyle {\frac {20}{4}}={\frac {4s}{4}}}5=s{\displaystyle 5=s} In the formula d{\displaystyle d} equals the length of the diagonal and s{\displaystyle s} equals one side of the square. This formula is derived from the Pythagorean Theorem (a2+b2=c2){\displaystyle a^{2}+b^{2}=c^{2})}. A diagonal divides a square into two congruent right triangles, thus, you can use the side lengths of the square to find the length of the diagonal (which would be the hypotenuse of the right triangle). Make sure you are substituting for the variable s{\displaystyle s}. For example, if the square has a side length of 5 centimeters, set up the formula like this:d=52{\displaystyle d=5{\sqrt {2}}} This will give you the length of the diagonal. It’s best to perform the calculation on a calculator, so that you can get a more precise result. If you don’t have a calculator, you can round 2{\displaystyle {\sqrt {2}}} to 1.414. For example, if you are calculating the diagonal of a 5-centimeter square, your formula will look like this:d=52{\displaystyle d=5{\sqrt {2}}}d=7.07{\displaystyle d=7.07}So, the diagonal of the square is 7.07 centimeters long.

TL;DR in Russian:

Запишите формулу для вычисления периметра квадрата. Подставьте в формулу значение периметра квадрата. Найдите s{\displaystyle s}. Запишите формулу d=s2{\displaystyle d=s{\sqrt {2}}}. Подставьте в формулу значение длины стороны квадрата. Умножьте сторону квадрата на 2{\displaystyle {\sqrt {2}}}, чтобы найти диагональ квадрата.


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.

TL;DR in Russian:

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.


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.

TL;DR in Russian:

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.


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.

TL;DR in Russian:

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


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

TL;DR in Russian:

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


The formula is sum=(n−2)×180{\displaystyle sum=(n-2)\times 180}, where sum{\displaystyle sum} is the sum of the interior angles of the polygon, and n{\displaystyle n} equals the number of sides in the polygon.  The value 180 comes from how many degrees are in a triangle. The other part of the formula, n−2{\displaystyle n-2} is a way to determine how many triangles the polygon can be divided into. So, essentially the formula is calculating the degrees inside the triangles that make up the polygon.  This method will work whether you are working with a regular or irregular polygon. Regular and irregular polygons with the same number of sides will always have the same sum of interior angles, the difference only being that in a regular polygon, all interior angles have the same measurement. In an irregular polygon, some of the angles will be smaller, some of the angles will be larger, but they will still add up to the same number of degrees that are in the regular shape. Remember that a polygon must have at least three straight sides. For example, if you want to know the sum of the interior angles of a hexagon, you would count 6 sides. Remember, n{\displaystyle n} is the number of sides in your polygon. For example, if you are working with a hexagon, n=6{\displaystyle n=6}, since a hexagon has 6 sides. So, your formula should look like this:sum=(6−2)×180{\displaystyle sum=(6-2)\times 180} To do this, subtract 2 from the number of sides, and multiply the difference by 180. This will give you, in degrees, the sum of the interior angles in your polygon. For example, to find out the sum of the interior angles of a hexagon, you would calculate:sum=(6−2)×180{\displaystyle sum=(6-2)\times 180}sum=(4)×180{\displaystyle sum=(4)\times 180}sum=(4)×180=720{\displaystyle sum=(4)\times 180=720}So, the sum of the interior angles of a hexagon is 720 degrees.

TL;DR in Russian:

Запишите формулу для вычисления суммы внутренних углов многоугольника. Найдите число сторон многоугольника. Подставьте число сторон в формулу. Вычислите сумму углов.


The formula is δx=x0−xx{\displaystyle \delta x={\frac {x_{0}-x}{x}}}, where δx{\displaystyle \delta x} equals the relative error (the ratio of the absolute error to the actual value), x0{\displaystyle x_{0}} equals the measured value, and x{\displaystyle x} equals the actual value. This will likely be a decimal. Make sure you substitute it for δx{\displaystyle \delta x}. For example, if you know that the relative error is .025, your formula will look like this: .025=x0−xx{\displaystyle .025={\frac {x_{0}-x}{x}}}. This information should be given to you. Make sure you substitute this value for x{\displaystyle x}. For example, if you know that the actual value is 360 ft, your formula will look like this: .025=x0−360360{\displaystyle .025={\frac {x_{0}-360}{360}}}. This will cancel out the fraction. For example:.025=x0−360360{\displaystyle .025={\frac {x_{0}-360}{360}}}.025×360=x0−360360×360{\displaystyle .025\times 360={\frac {x_{0}-360}{360}}\times 360}9=x0−360{\displaystyle 9=x_{0}-360} This will give you the value of x0{\displaystyle x_{0}}, giving you the measured value. For example:9=x0−360{\displaystyle 9=x_{0}-360}9+360=x0−360+360{\displaystyle 9+360=x_{0}-360+360}369=x0{\displaystyle 369=x_{0}} Since absolute error is always positive, take the absolute value of this difference, ignoring any negative signs. This will give you the absolute error. For example, if the measured value is 369 ft, and the actual value is 360 feet, you would subtract 369−360=9{\displaystyle 369-360=9}. So, the absolute error is 9 feet.

TL;DR in Russian:

Запишите формулу для вычисления относительной ошибки. Подставьте в формулу относительную ошибку. Подставьте в формулу фактическое значение. Умножьте обе стороны уравнения на фактическое значение. Прибавьте фактическое значение к каждой стороне уравнения. Вычтите фактическое значение из измеренного значения.


The formula of a line in slope-intercept form is y = mx + b, where m is the slope, b is the y-intercept, and x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation. In this form, you can easily determine the slope of the line as the variable "m". For example. Rewrite 4y - 12x = 20 and y = 3x -1. The equation 4y - 12x = 20 needs to be rewritten with algebra while y = 3x -1 is already in slope-intercept form and does not need to be rearranged. Oftentimes, the formula of the line you are given will not be in slope-intercept form. It only takes a little math and rearranging of variables to get it into slope-intercept.  For example: Rewrite line 4y-12x=20 into slope-intercept form. Add 12x to both sides of the equation: 4y – 12x + 12x = 20 + 12x Divide each side by 4 to get y on its own: 4y/4 = 12x/4 +20/4 Slope-intercept form: y = 3x + 5. Remember, when two lines are parallel to each other, they will have the exact same slope. Using the equation y = mx + b where m is the slope of the line, you can identify and compare the slopes of two lines.  In our example, the first line has an equation of y = 3x + 5, therefore it’s slope is 3. The other line has an equation of y = 3x – 1 which also has a slope of 3. Since the slopes are identical, these two lines are parallel. Note that if these equations had the same y-intercept, they would be the same line instead of parallel.

TL;DR in Russian:

Запишите линейное уравнение. Перепишите уравнение в виде линейного уравнения. Сравните угловые коэффициенты.


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}}}}

TL;DR in Russian:

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