inclusionAI/Ring-lite-rl-data huggingface dataset:
In the Tenth Kingdom, there are 17 islands, each with 119 inhabitants. The inhabitants are divided into two castes: knights, who always tell the truth, and liars, who always lie. During a population census, each person was first asked, "Not including yourself, are there an equal number of knights and liars on your island?" It turned out that on 7 islands, everyone answered "Yes," while on the rest, everyone answered "No." Then, each person was asked, "Is it true that, including yourself, people of your caste are less than half of the inhabitants of the island?" This time, on some 7 islands, everyone answered "No," while on the others, everyone answered "Yes." How many liars are there in the kingdom?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1013}
Thirty girls - 13 in red dresses and 17 in blue dresses - were dancing around a Christmas tree. Afterwards, each was asked if the girl to her right was in a blue dress. It turned out that only those who stood between two girls in dresses of the same color answered correctly. How many girls could have answered affirmatively?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{17}
Determine the number of 19th power residues modulo 229.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
There is a moving point \( M \) on the base \( A_{1}B_{1}C_{1}D_{1} \) of the cube \( ABCD - A_{1}B_{1}C_{1}D_{1} \), and \( BM \parallel \) plane \( ADC \). Find the maximum value of \( \tan \angle D_{1}MD \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{2}}
Let \( r = \frac{1 + \sqrt{5}}{2} \). Calculate
\[ 
7 \arctan ^{2} r + 2 \arctan ^{2} r^{3} - \arctan ^{2} r^{5} =
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{7 \pi^{2}}{8}}
## Task B-3.7.

In a right-angled triangle, the sum of the lengths of the legs and three times the length of the height on the hypotenuse is 12. The triangle rotates around the line on which the hypotenuse lies, thus forming a rotational body of maximum surface area. What is the volume of the resulting body?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{8}{3}\pi(\sqrt{10}-1)}
Determine the smallest integer \( n \) such that \( |e^x - p_n(x)| < 10^{-15} \) for all \( x \) in the interval \([-1, 1]\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{17}
Given a square \(ABCD\) with point \(P\) inside such that \(PA = 1\), \(PB = 2\), and \(PC = 3\), calculate the angle \(\widehat{APB}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{135^\circ}
Let \( ABC \) be a triangle such that \(\angle CAB = 20^\circ\). Let \( D \) be the midpoint of segment \([AB]\). It is given that \(\angle CDB = 40^\circ\). What is the measure of \(\angle ABC\)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{70^\circ}
A point is randomly dropped onto the interval $[8, 13]$ and let $k$ be the resulting value. Find the probability that the roots of the equation $\left(k^{2}-2k-35\right)x^{2}+(3k-9)x+2=0$ satisfy the condition $x_{1} \leq 2x_{2}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.6}
已知函数$f\left( x \right)$，任取两个不相等的正数${{x}_{1}}$， ${{x2}}$，总有$\left[ f\left( {{x}_{1}} \right)-f\left( {{x2}} \right) \right]\left( {{x}_{1}}-{{x2}} \right)>0$，对于任意的$x>0$，总有$f\left[ f\left( x \right)-\text{ln}x \right]=1$，若$g\left( x \right)=f'\left( x \right)+f\left( x \right)-{{m}^{2}}+m$有两个不同的零点，则正实数$m$的取值范围为__________．
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$(2,+\infty )$}
Several sets of prime numbers, such as $\{7, 83, 421, 659\}$, use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{207}
During summer break, 644997 kids from Lawrence county stayed home and the other 893835 kids went to camp. An additional 78 kids from outside the county attended the camp. How many kids are in Lawrence county?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1,538,832}
How many positive integers $x$ less than $10000$ are there such that $2^x-x^2$ is divisible by $7$ ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2857}
A fair six-sided die is rolled repeatedly until an odd number appears. Calculate the probability that each even number (2, 4, 6) appears at least once before any odd number appears. Express your answer as a fraction.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{20}}
Compute the limit $$ \lim_{x\to 0}\frac{e^{f(x)}-e^x}{2x-\sin(f(2x))}, $$ where $f:\mathbb{R}\longrightarrow\mathbb{R}$ is a function defined as $f(x) = x - x^3 + o(x^3)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\frac{3}{28}}
Given that $m > 0$ and for any $x \in (1, +\infty)$, the inequality $2{e}^{2mx}-\frac{\ln x}{m} \geq 0$ always holds, find the minimum value of the real number $m$. Express your answer as a single real number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{2e}}
Jack Sparrow needed to distribute 150 piastres into 10 purses. After putting some amount of piastres in the first purse, he placed more in each subsequent purse than in the previous one. As a result, the number of piastres in the first purse was not less than half the number of piastres in the last purse. How many piastres are in the 6th purse?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{16}
Alice and Bob are playing a game with a string of 2015 beads. The player whose turn it is cuts the string between two beads. The other player decides which of the two pieces will be used for the rest of the game, and the other piece is discarded.

Alice starts, and they take turns cutting the string. The player who has to make a move when only one bead is left loses the game since no more cuts can be made.

Who has a winning strategy?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Bob}
Dad's birthday is May 1st, and Chunchun's birthday is July 1st. Starting from December 26, 2012 (Day 1), until the 2013th day, how many birthdays have Dad and Chunchun celebrated in total?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{ 11}
For positive numbers $a$ and $b$ such that $2a^2 + 7ab + 3b^2 = 7$, find the maximum value of $a + \sqrt{3ab} + 2b$. Provide your answer as a single number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{14}}
Given three composite numbers \( A, B, C \) that are pairwise coprime and \( A \times B \times C = 11011 \times 28 \). What is the maximum value of \( A + B + C \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1626}
已知椭圆 $\Gamma: \frac{x^{2}}{4}+\frac{y^{2}}{3}=1, F$ 为 $\Gamma$ 的右焦点。过 $F$ 作直线交 $\Gamma$ 于 $M 、 N$ 两点，直线 $l$ 过点 $F$ 且与直线 $M N$ 垂直, 并交直线 $x=4$ 于点 $P$, 直线 $O P$ 交 $\Gamma$ 于 $A 、 B$ 两点. 设直线 $M P 、 M N 、 M A 、 M B$ 的斜率依次为 $m 、 n 、 p$ 、 $q$ (四条直线的斜率均存在且均不为 0 ). 记 $m+n=s, p+q=t, m n=r, s t=f(r)$. 求 $f(\frac{3}{4})$。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Find the smallest positive integer $n$ for which the polynomial \[x^n-x^{n-1}-x^{n-2}-\cdots -x-1\] has a real root greater than $1.999$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
$\triangle ABC$ is a triangle and $D,E,F$ are points on $BC$, $CA$, $AB$ respectively. It is given that $BF=BD$, $CD=CE$ and $\angle BAC=48^{\circ}$. If the answer is $x^\circ$, find the value of $x$ for the angle $\angle EDF$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{66}
Let $P$ be the parabola in the plane determined by the equation $y = x^2$. Suppose a circle $C$ in the plane intersects $P$ at four distinct points. If three of these points are $(-28, 784)$, $(-2, 4)$, and $(13, 169)$, find the sum of the distances from the focus of $P$ to all four of the intersection points.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1247}
Example 6 Find the simplest fraction (with the smallest denominator) that approximates $\sqrt{8}$, with an error $\leqslant 10^{-6}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2786}{985}}
If the simplest quadratic radical $2\sqrt{4m-1}$ is of the same type as $\sqrt{2+3m}$, then $m=$____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
设四边形$ABCD$中$\overrightarrow{DC}=\frac{1}{2}\overrightarrow{AB}$且$|\overrightarrow{AD}|=|\overrightarrow{BC}|$，则这个四边形是_______．
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{等腰梯形}
Find the smallest $x \in \mathbb{N}$ for which $\frac{7x^{25}-10}{83}$ is an integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{69}
Given that p and q are natural numbers that do not end in zero and their product is always a power of 10, find the last digit that p - q cannot be when p > q. Express your answer as a single digit.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
At a math contest, $57$ students are wearing blue shirts, and another $75$ students are wearing yellow shirts. The $132$ students are assigned into $66$ pairs. In exactly $23$ of these pairs, both students are wearing blue shirts. How many pairs are there in which both students are wearing yellow shirts?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{32}
Determine the maximum distance between two points within the truncated cone defined by $2x^2 + 2y^2 \leq z^2$ for $z \in [1,2]$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{\frac{11}{2}}}
Given the real numbers \( x, y, \) and \( z \) that satisfy \( xy \neq 0 \) and \( x+y \neq 0 \), find the minimum value of the expression
$$
\left(\frac{y+z}{x}+2\right)^{2}+\left(\frac{z}{y}+2\right)^{2}+\left(\frac{z}{x+y}-1\right)^{2}.
$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
If 4 people stand in a row again, and exactly one person stands in their original position, calculate the total number of different ways to stand. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
The square-shaped cards are regularly arranged without gaps to form a large square. If the number of cards laid at the perimeter was 240, how many total cards in total were used?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3721}
Let $ABC$ be a triangle with $AB=5$, $BC=6$, and $AC=7$. Let its orthocenter be $H$ and the feet of the altitudes from $A, B, C$ to the opposite sides be $D, E, F$ respectively. Let the line $DF$ intersect the circumcircle of $AHF$ again at $X$. Find the length of $EX$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{190}{49}}
Mustafa bought a big rug. The seller measured the rug with a ruler that was supposed to measure one meter. As it turned out to be $30$ meters long by $20$ meters wide, he charged Rs $120,000$. When Mustafa arrived home, he measured the rug again and realized that the seller had overcharged him by $9,408$ Rs. How many centimeters long is the ruler used by the seller?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{96}
$n ^ { 2 } ( n \geq 4 )$个正数排列$n$行$n$列：

$a_{11}$ $a_{12}$ $a_{13}$ $a _ { 1 4 }$ $\cdots a _ { 1 n } ,$

$a _ { 2 1 }$ $a _ { 2 2 }$ $a _ { 2 3 }$ $a _ { 2 4 } \cdots a _ { 2 n } ,$

$a _ { 3 1 }$ $a _ { 3 2 }$ $a _ { 3 3 }$ $a _ { 3 4 } \cdots a _ { 3 n } ,$

$a _ { 4 1 }$ $a _ { 4 2 }$ $a _ { 4 3 }$ $a _ { 4 4 } \cdots a _ { 4 n } ,$

·.-

$a _ { n _ { 1 } } a _ { n _ { 2 } } a _ { n _ { 3 } } a _ { n _ { 4 } } \cdots a _ { n _ { n } }$

其中每一行的数成等差数列，每一列的数成等比数列，并且所有公比相等.已知

$a _ { 2 4 } = 1 , a _ { 4 2 } = \frac { 1 } { 8 }$ $, a _ { 4 3 } = \frac { 3 } { 1 6 } ,$

求 $a _ { 1 1 } + a _ { 2 2 } + \cdots + a _ { n n }$的值.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$2 - \frac { n + 2 } { 2 ^ { n } } $}
In a square, point \( M \) is located on side \( CD \) such that \( CM:MD = 1:3 \). Line \( AM \) intersects the circle circumscribed about the square at point \( E \). Given that the area of triangle \( ACE \) is 14, determine the side length of the square.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
A ship sails eastward at a speed of 15 km/h. At point A, the ship observes a lighthouse B at an angle of 60° northeast. After sailing for 4 hours, the ship reaches point C, where it observes the lighthouse at an angle of 30° northeast. At this time, the distance between the ship and the lighthouse is ______ km.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60}
Approximate the function $f(x) = e^x\cos x$ using a Taylor polynomial centered at $x_0 = 0$. Determine the degree of the polynomial such that the remainder in the interval $[-\frac{1}{100},\frac{1}{100}]$ is less than $10^{-8}$. 

Given the function's derivatives: 
- $f'(x) = e^x(\cos x - \sin x)$
- $f''(x) = -2e^x\sin x$
- $f'''(x) = -2e^x(\sin x + \cos x)$

How many terms of the Taylor series are needed to meet the error condition?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Let $S$ be a square of side length $1$. Two points are chosen independently at random on the sides of $S$. The probability that the straight-line distance between the points is at least $\frac{1}{2}$ is $\frac{a-b\pi}{c}$, where $a$, $b$, and $c$ are positive integers and $\gcd(a,b,c)=1$. Find the value of $a+b+c$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{59}
Boys and girls. Nine boys and three girls decided to share their pocket money equally. Each boy gave the same amount to each girl, and each girl gave the same amount (but a different one) to each boy. After this, all children ended up with an equal amount of money. What is the smallest amount that each of them could have had initially?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12 \text{ (cents)}}
Let $\varphi(n)$ denote the number of positive integers less than or equal to $n$ which are relatively prime to $n$. Let $S$ be the set of positive integers $n$ such that $\frac{2 n}{\varphi(n)}$ is an integer. Compute the sum $\sum_{n \in S} \frac{1}{n}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{10}{3}}
Find all positive integers $n \geq 1$ such that there exists a pair $(a, b)$ of positive integers, such that $a^2 + b + 3$ is not divisible by the cube of any prime, and 
$$ n = \frac{ab + 3b + 8}{a^2 + b + 3}. $$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Evaluate the double integral \( \int_0^2 \left( \int_{\frac{y}{2}}^1 e^{x^2} \, dx \right) dy. \)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{e - 1}
2015 people are sitting around a round table, each of whom is either a knight or a liar. Knights always tell the truth, liars always lie. They were each given a card, with a unique number written on it. After looking at the cards of their neighbors, each person at the table said: "My number is greater than that of each of my two neighbors." After this, $k$ of the people said: "My number is less than that of each of my two neighbors." What is the maximum possible value of $k?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2013}
Write the integers from 1 to 6 on the six faces of a cube so that any pair of consecutive numbers - including the pair 6 and 1 - are on adjacent faces. How many different arrangements are possible? (Two arrangements are not considered different if one can be transformed into the other by some symmetry of the cube - such as rotation or reflection on a plane through the center - or by replacing each number with the next one, with 6 replaced by 1.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Prince Zrychlený invited Princess Zpomalená to his castle. When she took too long, he set out to meet her. After two days of travel, he met her at one fifth of her journey. Together, they continued their journey twice as fast as when the princess was traveling alone. They arrived at Prince's castle the second Saturday after their meeting. Which day did they meet, if the princess set out from her castle on Friday?

(M. Dillingerová)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Wednesday}
Evaluate the integral \( \iint_{R} \lfloor x+y \rfloor \, \mathrm{d}x\, \mathrm{d}y \) where \( R= \{(x,y)| 1\leq x\leq 3, 2\leq y\leq 5\} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
若存在实数 $r$, 使得圆周 $x^{2}+y^{2}=r^{2}$ 上恰好有 $n$ 个整点, 则 $n$ 可以等于多少？请给出所有可能的n值之和。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
Two equilateral triangles with perimeters of 12 and 15 are positioned such that their sides are respectively parallel. Find the perimeter of the resulting hexagon.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{27}
In a plane, a set of points is given such that no three points are collinear. Each point is colored either red, white, or green. There are 213 lines connecting points of different colors and 112 lines connecting points of the same color. Among the triangles formed by these points, 540 triangles have vertices of all different colors, and 612 triangles have exactly two red vertices. Determine the number of triangles with exactly two white vertices.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{210}
William is biking from his home to his school and back, using the same route. When he travels to school, there is an initial $20^\circ$ incline for $0.5$ kilometers, a flat area for $2$ kilometers, and a $20^\circ$ decline for $1$ kilometer. If William travels at $8$ kilometers per hour during uphill $20^\circ$ sections, $16$ kilometers per hour during flat sections, and $20$ kilometers per hour during downhill $20^\circ$ sections, find the closest integer to the number of minutes it takes William to get to school and back.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{31}
Find an element in $\mathbb{Z}[\sqrt{-17}]$ that can be expressed both as a product of two irreducible elements and as a product of three irreducible elements.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
If the mutually prime integers \(A\), \(B\), and \(C\) satisfy \( A \log_{200} 5 + B \log_{200} 2 = C \), then calculate \( A + B + C \). Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
$\bigcirc \bigcirc \div \square=14 \cdots 2$, how many ways are there to fill the square?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Evaluate the limit: $$\lim_{x\to0}\frac{x\sin(\sin x) - \sin^2x}{x^6}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{1}{18}}
Given the function $f(x) = \cos(a\sin x) - \sin(b\cos x)$, derive the range of $a^2+b^2$ such that $f(x)$ has no zeros. Express your answer as an interval.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[0, \frac{\pi^2}{4})}
Twenty pairs of integers are formed using each of the integers \( 1, 2, 3, \ldots, 40 \) once. The positive difference between the integers in each pair is 1 or 3. If the resulting differences are added together, what is the greatest possible sum?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{58}
Analyze the following relationships to determine the number of distinct, unambiguous functions of y with respect to x:

1. x - y = 0
2. y^2 = x
3. |y| = 2x
4. y^2 = x^2
5. y = 3 - x
6. y = 2x^2 - 1
7. y = 3/x

Express your answer as a whole number representing the count of such functions.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
If $(1-2)^{9}=a_{9}x^{9}+a_{8}x^{8}+\ldots+a_{1}x+a_{0}$, then the sum of $a_1+a_2+\ldots+a$ is \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2}
A structure with a design life of 50 years is planned for a site where high intensity earthquakes may occur with a return period of 100 years. The structure is designed to have a 0.98 probability of not suffering damage within its design life. Assuming that the occurrence of high intensity earthquakes at the site follows a Bernoulli sequence and that damage effects between earthquakes are statistically independent, what is the probability of damage to the structure under a single earthquake?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.0404}
Find the smallest two-digit number \( N \) such that the sum of digits of \( 10^N - N \) is divisible by 170.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
Given a quadratic equation $ax^2+bx+c=0$ (where $a>0$) has no real roots, find the solution set for $ax^2+bx+c<0$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\emptyset}
Suppose $x, y \in \mathbb{Z}$ satisfy the equation:
\[
y^4 + 4y^3 + 28y + 8x^3 + 6y^2 + 32x + 1 = (x^2 - y^2)(x^2 + y^2 + 24).
\]
Find the sum of all possible values of $|xy|$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
For positive integers \( a \) and \( N \) ,let
 \( r\left( {a,N}\right)  \in  \{ 0,1,\ldots ,N - 1\} \) denote the remainder of \( a \)
 when divided by \( N \) . Determine the number of positive
 integers \( n \leq  {1000000} \) for which
 \( r\left( {n,{1000}}\right)  > r\left( {n,{1001}}\right) \) .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{499500}
Determine the number of distinct ways to completely cover a $10 \times 10$ checkerboard using exactly 25 T-shaped tetrominoes.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
1 kilogram of soybeans can be made into 3 kilograms of tofu. To produce 1 kilogram of soybean oil, 6 kilograms of soybeans are required. Tofu costs 3 yuan per kilogram, and soybean oil costs 15 yuan per kilogram. A batch of soybeans weighs 460 kilograms, and the total sales revenue from the tofu and soybean oil produced from this batch is 1800 yuan. How many kilograms of this batch of soybeans were made into soybean oil?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{360}
Given the initial position of a submarine at \((-230, 75)\) and a convoy at \((0, 0)\), with the submarine having a maximum speed of 30 km/h and the convoy traveling southwest at 18.5 km/h, determine the direction the submarine should travel to intercept the convoy most quickly. Assume the units are in kilometers for distance and kilometers per hour for speed.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{308.6^\circ}
求$1 1 ^ { 1 2 ^ { 1 3 } }$的十位数字（其中，$1 1 ^ { 1 2 ^ { 1 3 } }$表示11的1213次幂）.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}