__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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2,937 | [{"role": "user", "content": "In the polar coordinate system, what is the polar coordinate of the center of the circle described by \\(\\rho = -2\\cos\\theta\\)?\n\nA: \\((1, \\frac{\\pi}{2})\\)\nB: \\((1, -\\frac{\\pi}{2})\\)\nC: \\((1, 0)\\)\nD: \\((1, \\pi)\\)"}, {"role": "assistant", "content": "<think>\n\nOkay, le... |
2,928 | [{"role": "user", "content": "\"The Nine Chapters on the Mathematical Art\" is one of the ancient Chinese mathematical works. In the book, there is a problem: Five sparrows and six swallows weigh one jin together. The sparrows are heavier than the swallows. If one of them is exchanged, they will weigh the same. The que... |
2,919 | [{"role": "user", "content": "What is the domain of the function \\( f(x) = \\log_5(\\log_7(\\log_4x - 1)) \\)?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out the domain of this function \\( f(x) = \\log_5(\\log_7(\\log_4x - 1)) \\). Hmm, domain means all the x-values that make the functi... |
2,887 | [{"role": "user", "content": "Suppose the function $f(x)=2\\sin (\\omega x+\\varphi)$, where $\\omega > 0$, $|\\varphi| < \\frac {\\pi}{2}$. The line $x= \\frac {5\\pi}{8}$ is an axis of symmetry for the graph of $y=f(x)$, and $x= \\frac {11\\pi}{8}$ is a zero of $f(x)$. Additionally, the smallest positive period of $f... |
2,912 | [{"role": "user", "content": "How many positive integers less than $201$ are multiples of either $4$ or $9$, but not both at once?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so th... |
2,958 | [{"role": "user", "content": "A number divided by 28 has a quotient of 7 and a remainder of 11. The dividend is ."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says a number divided by 28 has a quotient of 7 and a remainder of 11. We need to find the dividend. Hmm, I remember that whe... |
2,959 | [{"role": "user", "content": "Beryl has 88 radishes. She puts them into two baskets. If there are 37 radishes in the first basket, how many more radishes are there in the second basket than the first?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Beryl has 88 radishes total, and she puts them into tw... |
2,885 | [{"role": "user", "content": "Let $x^2 - mx + 36$ be a quadratic equation with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and cor... |
2,947 | [{"role": "user", "content": "For what value of \\(k\\) does the equation \\(x^2 + 14x + y^2 + 8y - k = 0\\) represent a circle of radius 10?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of \\( k \\) such that the equation \\( x^2 + 14x + y^2 + 8y - k = 0 \\) represents a ci... |
2,943 | [{"role": "user", "content": "Let $\\triangle ABC$ have sides $a$, $b$, and $c$ opposite to the internal angles $A$, $B$, and $C$, respectively. If $\\cos C=\\frac{2}{3}$ and $a=3b$, then $\\cos A=\\_\\_\\_\\_\\_\\_$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about triangle ABC, wh... |
2,951 | [{"role": "user", "content": "Given the set $A=\\{y|y=\\sqrt{x^2-2x+5}\\}$, and the set $B=\\{x|-1 < x \\leqslant 4\\}$, with the universal set $U=\\mathbb{R}$, then $(\\complement_U A) \\cap B=$\nA: $(2,+\\infty)$\nB: $(-1,4]$\nC: $[4,+\\infty)$\nD: $(-1,2)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's ... |
2,954 | [{"role": "user", "content": "A university's mathematics department has a total of $160$ students. After randomly assigning numbers to the students, a system sampling method is used to extract a sample with a capacity of $5$. It is known that students numbered $40$, $72$, and $136$ are in the sample. What should be the... |
2,967 | [{"role": "user", "content": "Find the simple interest on $10000 at 9% per annum for 12 months. How much interest is earned?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the simple interest on $10,000 at 9% per annum for 12 months. Hmm, first, I remember that simple interest is calcul... |
2,965 | [{"role": "user", "content": "The arithmetic mean (ordinary average) of the sixty successive positive integers beginning at 3 is:\nA) 31.5\nB) 32\nC) 32.5\nD) 33"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the arithmetic mean of sixty successive positive integers starting ... |
2,864 | [{"role": "user", "content": "Given a quadratic function $f(x)=ax^{2}+bx+c$ where $a,b \\in R, a\\neq 0$, it satisfies the following conditions:\n1. When $x \\in R$, the graph of $f(x)$ is symmetrical about the line $x=-1$.\n2. $f(1)=1$.\n3. The minimum value of $f(x)$ in $R$ is $0$.\n(1) Find the analytical expression... |
2,915 | [{"role": "user", "content": "Given the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1 (a > 0, b > 0)$ and four points $P_1(4, 2)$, $P_2(2, 0)$, $P_3(-4, 3)$, and $P_4(4, 3)$, only three of these points lie on the hyperbola. Determine the eccentricity of the hyperbola. The options are:\nA) $\\frac{\\sqrt{5}}{2}$\nB... |
2,908 | [{"role": "user", "content": "50 g of ice at a temperature of $t_{\\pi}=-10{ }^{\\circ} \\mathrm{C}$ is mixed with water at a temperature of $t_{B}=10{ }^{\\circ} \\mathrm{C}$. It is known that the final temperature in the vessel is $t=0{ }^{\\circ} \\mathrm{C}$. Determine the mass of the added water. The specific heat... |
2,916 | [{"role": "user", "content": "Solve for $x$ if $\\log_2(x^3 - 18x^2 + 81x) = 4$.\nA) $1, 2, 8$\nB) $2, 4, 8$\nC) $1, 3, 8$\nD) $1, 2, 4$\nE) None of these"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve the equation log base 2 of (x³ - 18x² + 81x) equals 4. Hmm, first, I remember that i... |
2,824 | [{"role": "user", "content": "Prove that there are infinitely many natural numbers $N$ such that the polynomial $x^{8} + N x^{4} + 1$ can be factored into a product of two fourth-degree polynomials with integer coefficients."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and ... |
2,821 | [{"role": "user", "content": "Using $m$ colors ($m \\geqslant 2$) to paint a $1 \\times n$ chessboard, where each cell is painted a different color. Let $h(m, n)$ represent the number of ways to paint the chessboard so that adjacent cells have different colors and each color is used at least once. Find the formula for ... |
2,971 | [{"role": "user", "content": "After a scaling transformation $\\begin{cases} x'=5x \\\\ y'=3y \\end{cases}$ in the same Cartesian coordinate system, the curve $C$ becomes the curve $2x'^2 + 8y'^2 = 1$. The equation of curve $C$ is ____.\nA: $25x^2 + 36y^2 = 1$\nB: $50x^2 + 72y^2 = 1$\nC: $10x^2 + 24y^2 = 1$\nD: $\\frac... |
2,962 | [{"role": "user", "content": "Eva, Frank, Gina, and Harry were discussing their possible grades in their physics class this semester. Eva said, \"If I get a B, then Frank will get a B.\" Frank said, \"If I get a B, then Gina will get a B.\" Gina said, \"If I get a B, then Harry will get a B.\" All of these statements w... |
2,907 | [{"role": "user", "content": "Which of the following conclusions are correct?\n\nA: If random variables $\\xi$ and $\\eta$ satisfy $\\eta = 2\\xi + 1$, then $D(\\eta) = 2D(\\xi) + 1$\n\nB: If the random variable $\\xi$ follows $N(3, \\sigma^2)$, and $P(\\xi < 6) = 0.84$, then $P(3 < \\xi < 6) = 0.34$\n\nC: The closer t... |
2,918 | [{"role": "user", "content": "The minimum distance from a point on an ellipse to a directrix is exactly equal to the semi-latus rectum of the ellipse. The eccentricity of this ellipse is ▲."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct... |
2,936 | [{"role": "user", "content": "Use a rectangular iron sheet measuring 90cm in length and 48cm in width to make an open-top rectangular container. First, cut out a small square at each of the four corners. Then, fold the four sides up at a 90-degree angle and weld them together. When the side length of the cut-out square... |
2,956 | [{"role": "user", "content": "Consider a regular decagon (10-sided polygon). How many triangles can be formed whose vertices are the vertices of the decagon?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to t... |
2,975 | [{"role": "user", "content": "Jonah decided to set up an aquarium. He started with 14 small fish. He added 2 more, but they ate a certain number of his original fish before he could remove them and take them back to the store. Let the number of fish eaten by each new fish be x. He exchanged them for 3 new fish. How man... |
2,944 | [{"role": "user", "content": "Given that the sum of the first $n$ terms of an increasing arithmetic sequence ${a_n}$ is $S_n$, $a_4a_6=117$, and $a_3+a_7=22$.\n\n1. Find $S_n$;\n2. Find the sum of the first $n$ terms of the sequence $\\{\\frac{1}{S_n+3n+6}\\}$, denoted as $T_n$."}, {"role": "assistant", "content": "<th... |
2,903 | [{"role": "user", "content": "In triangle \\(ABC\\), \\(AB = (b^2 - 1)\\) cm, \\(BC = a^2\\) cm, and \\(AC = 2a\\) cm, where \\(a\\) and \\(b\\) are positive integers greater than 1. Find the value of \\(a - b\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is diffi... |
2,953 | [{"role": "user", "content": "Given two points $O(0,0)$ and $Q(a,b)$, point $P_1$ is the midpoint of segment $OQ$, point $P_2$ is the midpoint of segment $QP_1$, $P_3$ is the midpoint of segment $P_1P_2$, ..., $P_{n+2}$ is the midpoint of segment $P_nP_{n+1}$, then the limit position of point $P_n$ should be $(\\quad)$... |
2,981 | [{"role": "user", "content": "If $f(x) = 3^x$, then $f(x+2) - f(x)$ equals?\n$\\text{(A)}\\ 4f(x)\\qquad\\text{(B)}\\ 6f(x)\\qquad\\text{(C)}\\ 8f(x)\\qquad\\text{(D)}\\ 9f(x)\\qquad\\text{(E)}\\ 11f(x)$"}, {"role": "assistant", "content": "<think>\n\nGot it, let's see. The problem says that f(x) = 3^x, and we need to ... |
2,979 | [{"role": "user", "content": "The average weight of a, b, and c is 45 kg. If the average weight of a and b is some kg and that of b and c is 43 kg, then the weight of b is 33 kg. What is the average weight of a and b?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by step. Fi... |
2,969 | [{"role": "user", "content": "Given the function $f(x)=mx^{2}+x-1$ is monotonically increasing on the interval $(-1,+\\infty)$, the range of values for $m$ is:\n\nA: $\\{m|m≤\\frac{1}{2}\\}$\n\nB: $\\{m|0＜m＜\\frac{1}{2}\\}$\n\nC: $\\{m|0＜m≤\\frac{1}{2}\\}$\n\nD: $\\{m|0≤m≤\\frac{1}{2}\\}$"}, {"role": "assistant", "cont... |
2,991 | [{"role": "user", "content": "If events E and F are independent, and $P(E) = P(F) = \\frac{1}{4}$, then the value of $P(E \\cap F)$ is equal to ( )\nA: 0\nB: $\\frac{1}{16}$\nC: $\\frac{1}{4}$\nD: $\\frac{1}{2}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that events E and F are i... |
2,935 | [{"role": "user", "content": "Determine the equation of the oblique asymptote of the graph of the function $\\frac{3x^2 + 10x + 5}{2x + 5}$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nW... |
2,927 | [{"role": "user", "content": "In Class 3 (1), consisting of 45 students, all students participate in the tug-of-war. For the other three events, each student participates in at least one event. It is known that 39 students participate in the shuttlecock kicking competition and 28 students participate in the basketball ... |
2,982 | [{"role": "user", "content": "George collects coins and divides them among boxes. He organizes them such that each box contains an equal number of coins. He has three different coin containers, with totals of 1050, 1260, and 210 coins. What is the greatest number of coins that George could be putting in each box?"}, {"... |
2,849 | [{"role": "user", "content": "Prove that if the orthocenter of a triangle divides the altitudes in the same ratio, then the triangle is equilateral."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think abou... |
2,900 | [{"role": "user", "content": "Given an arithmetic sequence $\\{a_n\\}$, where $a_1=3$, and the sum of its first $n$ terms is $S_n$. For a geometric sequence $\\{b_n\\}$ with positive terms, where $b_1=1$, the common ratio is $q$, and it's known that $b_2 + S_2 = 12$ and $q=\\frac{S_2}{b_2}$.\n(I) Find the formulas for ... |
2,939 | [{"role": "user", "content": "A football player scores 3 goals in his 15th match, thus increasing his average goals scored by 0.08. Calculate the total number of goals he scored in his first 15 matches using a weighted scoring system where a header goal = 1 point, a volley goal = 2 points, and a freekick goal = 3 point... |
2,989 | [{"role": "user", "content": "In triangle $\\triangle ABC$, given that $AB=4\\sqrt{3}$, $\\angle A=45^{\\circ}$, $\\angle C=60^{\\circ}$, find the length of side $BC$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the length of side BC in triangle ABC. They gave me AB = 4√3, angle A is... |
2,997 | [{"role": "user", "content": "The hypotenuse of a right triangle measures \\(8\\sqrt{2}\\) inches, and one angle is \\(45^{\\circ}\\). What is the number of square inches in the area of the triangle?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a right triangle with a hypotenuse... |
2,883 | [{"role": "user", "content": "Which positive integers can be written in the form \\[\\frac{\\operatorname{lcm}(x, y) + \\operatorname{lcm}(y, z)}{\\operatorname{lcm}(x, z)}\\] for positive integers $x$ , $y$ , $z$ ?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is ... |
2,964 | [{"role": "user", "content": "A fair 6-sided die is rolled once. If I roll $n$, then I win $(6-n)^2$ dollars. What is the expected value of my win, in dollars?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to... |
2,996 | [{"role": "user", "content": "If the line $y=2x+b$ is a tangent to the curve $y=e^{x}+x$, then the value of the real number $b$ is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the line y = 2x + b is tangent to the curve y = e^x + x, and we need to find the value of b. H... |
2,992 | [{"role": "user", "content": "Karl was attempting to calculate new economic indicators. He found the following equation to be true:\\[fp-w=15000\\] If $f=8$ and $w=10+200i$, what is $p$?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Karl has this equation: fp - w = 15000. He needs to find p, and they... |
2,978 | [{"role": "user", "content": "Let the function $f(x)= \\begin{cases} \\log_{0.2}x, & x\\in (1,+\\infty) \\\\ 2-2x, & x\\in (-\\infty,1] \\end{cases}$. If $a=f(2^{0.3})$, $b=f(\\log_{0.3}2)$, $c=f(\\log_{3}2)$, then the relationship among $a$, $b$, and $c$ is ( ).\n\nA: $b > c > a$\n\nB: $b > a > c$\n\nC: $a > c > b$\n\... |
2,934 | [{"role": "user", "content": "Let $a$, $b$, and $c$ be the roots of the cubic equation $$\n5x^3 - 2019x + 4029 = 0.\n$$ Compute $(a + b)^3 + (b + c)^3 + (c + a)^3.$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I ne... |
3,010 | [{"role": "user", "content": "The area of a rectangle is $12$. One side is of length $x$, and the other side is of length $y$. The function relationship between $y$ and $x$ is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says the area of a rectangle is 12. One side is length x, t... |
2,998 | [{"role": "user", "content": "Gauss is considered one of the most outstanding mathematicians in history, known as the \"Prince of Mathematics.\" There is a calculation formula defined by Gauss, where $\\left[x\\right]$ represents the largest integer not exceeding $x$. For example, $\\left[4.8\\right]=4$, $\\left[-0.8\\... |
2,875 | [{"role": "user", "content": "Let \\( z_{1}, z_{2}, z_{3}, z_{4} \\) be complex numbers. Prove:\n\\[ \\left|z_{1} - z_{3}\\right|^{2} + \\left|z_{2} - z_{4}\\right|^{2} \\leq \\left|z_{1} - z_{2}\\right|^{2} + \\left|z_{2} - z_{3}\\right|^{2} + \\left|z_{3} - z_{4}\\right|^{2} + \\left|z_{4} - z_{1}\\right|^{2} \\]\nwi... |
3,004 | [{"role": "user", "content": "Jonathan enjoys walking and running for exercise, and he has three different exercise routines. On Mondays, he walks at 2 miles per hour. On Wednesdays, he walks at a certain speed. And on Fridays, he runs at 6 miles per hour. On each exercise day, he travels 6 miles. The combined total ti... |
2,986 | [{"role": "user", "content": "Suppose that $4$ is a factor of $a$, $a$ is a divisor of $24$, and $a$ is positive. What is the number of possible values of $a$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to... |
2,921 | [{"role": "user", "content": "Given that $F\\_1$ and $F\\_2$ are the left and right foci of the ellipse $E$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ $(a > b > 0)$, and the line $l$ with a slope of $1$ passing through $F\\_1$ intersects $E$ at points $A$ and $B$. The distances $|AF\\_2|$, $|AB|$, and $|BF\\_2|$ form a... |
2,977 | [{"role": "user", "content": "Simplify the expression $\\sqrt{1-\\sin^2 \\frac{3\\pi}{5}}$.\n\nA: $\\cos \\frac{3\\pi}{5}$\n\nB: $-\\cos \\frac{3\\pi}{5}$\n\nC: $\\pm\\cos \\frac{3\\pi}{5}$\n\nD: $\\cos \\frac{2\\pi}{5}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify the expression ... |
3,006 | [{"role": "user", "content": "How many ways are there to place 7 balls into 3 boxes if the balls are distinguishable and the boxes are distinguishable?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking how many ways there are to place 7 distinguishable balls into 3 distinguishable b... |
2,952 | [{"role": "user", "content": "In the annual cultural programme of Indra Prastha, there was a math quiz going on. Yudhisthir faced the last question that would bring the champion's trophy. The function f is defined as f(2x + 3) = some expression, and f(29) = 170. What is the expression on the right side of the function ... |
3,005 | [{"role": "user", "content": "A train running at 1/2 of its own speed reached a place in a certain number of hours. If the train would have run at its own speed, it could have saved 4 hours. How many hours did it take for the train to reach the place at half speed?"}, {"role": "assistant", "content": "<think>\n\nOkay, ... |
3,011 | [{"role": "user", "content": "Compute $\\sin 720^\\circ$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to compute sin 720 degrees. Hmm, first, I remember that sine is a periodic function, right? So it repeats every 360 degrees. That means sin(θ + 360°n) = sinθ for any integer n. So maybe I ca... |
2,925 | [{"role": "user", "content": "If the function $f(x)=(x+1)^{2}-a\\ln x$ has two distinct real numbers $x_{1}$, $x_{2}$ in the interval $(0,+\\infty)$, and the inequality $\\dfrac {f(x_{1}+1)-f(x_{2}+1)}{x_{1}-x_{2}} > 1$ always holds, then the range of values for $a$ is $(\\quad)$ \nA: $(-\\infty,3)$ \nB: $(-\\infty,-... |
2,946 | [{"role": "user", "content": "Given a sequence $\\{a_n\\}$ with the sum of its first $n$ terms denoted as $S_n$, if $4S_n=(2n-1)a_{n+1}+1$ and $a_1=1$,\n\n$(1)$ Find the general formula for the sequence $\\{a_n\\}$;\n\n$(2)$ If the sequence $\\{b_n\\}$ satisfies $\\frac{b_n}{a_n}=(\\sqrt{2})^{1+a_n}$, find the sum of t... |
2,974 | [{"role": "user", "content": "How many four-digit numbers are divisible by 11?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find how many four-digit numbers are divisib... |
2,961 | [{"role": "user", "content": "For how many different digits $n$ is the three-digit number $15n$ divisible by $n$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so the problem is: for... |
3,007 | [{"role": "user", "content": "Find the base k of the number system, if ( 524 ) 8 = ( 664 ) k?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the base k such that the octal number (524)₈ is equal to the number (664)ₖ in base k. First, I should remember that when a number is written in a ... |
2,968 | [{"role": "user", "content": "Given the parabola $C$: $y^{2}=2px(p > 0)$ with focus $F$, and a point $M(x_{0},2 \\sqrt {2})$ on the parabola $C$, a circle $M$ is tangent to the $y$-axis and intersects the line segment $MF$ at point $A$. If $\\dfrac {|MA|}{|AF|}=2$, then $p=$ ______."}, {"role": "assistant", "content": ... |
3,017 | [{"role": "user", "content": "$\\cos ^{2}30^{\\circ}-\\left(2-\\pi \\right)^{0}=$____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve this problem: cos squared 30 degrees minus (2 minus pi) to the power of 0. Hmm, let's break it down step by step. First, I remember that cos squared 30 ... |
3,002 | [{"role": "user", "content": "Which of the following statements is incorrect? ( )\nA: The set of angles with terminal sides on the x-axis is $\\{α|α=kπ，k∈Z\\}$\nB: The set of angles with terminal sides on the y-axis is $\\{α|α= \\frac {π}{2}+kπ，k∈Z\\}$\nC: The set of angles with terminal sides on the coordinate axes i... |
3,003 | [{"role": "user", "content": "Find the distance between the center of the circle given by the equation $x^2 + y^2 = 8x - 2y + 23$ and the point $(-3, 4)$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the distance between the center of a circle and a given point. First, I remember that... |
2,899 | [{"role": "user", "content": "A quadrilateral $ABCD$ has a right angle at $\\angle ABC$ and satisfies $AB = 12$ , $BC = 9$ , $CD = 20$ , and $DA = 25$ . Determine $BD^2$ .\n.\n"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and... |
2,960 | [{"role": "user", "content": "Given the polynomial \\( P(x) = x^5 - x^2 + 1 \\) with roots \\( r_1, r_2, \\ldots, r_5 \\), and another polynomial \\( Q(x) = x^2 + 1 \\), find \\( Q(r_1) Q(r_2) Q(r_3) Q(r_4) Q(r_5) \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is ... |
2,902 | [{"role": "user", "content": "Given an arithmetic sequence $\\left\\{a_{n}\\right\\}$ with the sum of the first 12 terms being 60, find the minimum value of $\\left|a_{1}\\right| + \\left|a_{2}\\right| + \\cdots + \\left|a_{12}\\right|$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging q... |
3,021 | [{"role": "user", "content": "According to census statistics, the probability of a woman of childbearing age giving birth to a boy or a girl is equal. If a second child is allowed, the probability that a woman of childbearing age has two girls is ( ).\n\nA: $ \\dfrac {1}{2}$ \nB: $ \\dfrac {1}{3}$ \nC: $ \\dfrac {1}{... |
3,019 | [{"role": "user", "content": "Determine the measure of angle \\( Q \\) in a hexagon where the other angles measure \\( 134^\\circ, 108^\\circ, 122^\\circ, 99^\\circ, \\) and \\( 87^\\circ \\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the measure of angle Q in a hexagon, and they g... |
3,032 | [{"role": "user", "content": "Billy's age is three times Joe's age, and the sum of their ages is 64. How old is Billy?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Billy's age is three times Joe's age, and the sum of their ages is 64. I need to find Billy's age. Hmm, let's break thi... |
3,023 | [{"role": "user", "content": "Given a line $l$ with a direction vector $\\vec{m}=(2,m,1)$, and a plane $\\alpha$ with a normal vector $\\vec{n}=(1, \\frac{1}{2},2)$, and $l$ is parallel to $\\alpha$, find the value of $m$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that a line \\(... |
2,976 | [{"role": "user", "content": "A triangle is constructed with wooden sticks of lengths 7, 24, and 25 inches joined end-to-end. Determine the length of the smallest piece that can be cut from each of the three sticks so that the remaining pieces no longer form a triangle."}, {"role": "assistant", "content": "<think>\n\nT... |
2,914 | [{"role": "user", "content": "Let \\( K \\) be any arbitrary convex polygon with perimeter \\( L \\) and area \\( S \\); \\( O_r \\) be a circle of radius \\( r \\). Prove that the length of the curve \\( K + O_r \\) is \\( L + 2\\pi r \\), and the area of the convex figure bounded by this curve is \\( S + Lr + \\pi r^... |
3,014 | [{"role": "user", "content": "List D consists of 20 consecutive half-numbers (increments of 0.5). If -7.5 is the least number in list D, what is the range of positive numbers in list D?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. First, let's make sure I unde... |
3,012 | [{"role": "user", "content": "Convert $e^{13 \\pi i/2}$ to rectangular form."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to convert \\( e^{13 \\pi i / 2} \\) to rectangular form. Hmm, rectangular form is \\( a + bi \\), right? So I remember that Euler's formula relates complex exponentials t... |
2,963 | [{"role": "user", "content": "What is the $2023^\\text{rd}$ letter in the following modified sequence?\n\\[\\text{ABCDEDCBAABCEDCBAABCDEDCBAABCEDCBA}\\cdots\\]\n$\\text{(A)}\\ \\text{A} \\qquad \\text{(B)}\\ \\text{B} \\qquad \\text{(C)}\\ \\text{C} \\qquad \\text{(D)}\\ \\text{D} \\qquad \\text{(E)}\\ \\text{E}$"}, {"... |
3,013 | [{"role": "user", "content": "Find the maximum value of\n\\[f(x) = 3x - x^3\\]for $0 \\le x \\le \\sqrt{3}.$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find the maxim... |
2,988 | [{"role": "user", "content": "Given the equations $x^2+kx+10=0$ and $x^2-kx+10=0$. If, when the roots of the equations are suitably listed, each root of the second equation is $3$ more than the corresponding root of the first equation, then determine the value of $k$.\n$\\textbf{(A)}\\ 2 \\qquad \\textbf{(B)}\\ 3 \\qqu... |
2,901 | [{"role": "user", "content": "A torus (donut shape) has an inner radius of $3$ and an outer radius of $7$. It sits on a flat table. Determine the radius of the largest spherical ball that can be placed on top of the center of the torus such that the ball still touches the horizontal plane. (In this scenario, the torus ... |
3,045 | [{"role": "user", "content": "In the Cartesian coordinate system, the coordinates of point $A(-1,2)$ with respect to the $y$-axis are symmetrical to point $B$.\n\nA: $(-1,2)$\n\nB: $(1,2)$\n\nC: $(1,-2)$\n\nD: $(-1,-2)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that point A(-1, 2... |
3,027 | [{"role": "user", "content": "It is known that there are a total of 3000 students in the second year of high school in Qionghai City. In a certain educational quality assessment, the mathematics scores follow a normal distribution. The density function curve is shown in the figure. It is estimated that the number of st... |
2,949 | [{"role": "user", "content": "Given that the sum of the first $n$ terms of the sequence $\\{a\\_n\\}$ is $S\\_n$, and for any positive integer $n$, $2a\\_n - S\\_n = 4$.\n1. Find the general term formula for the sequence $\\{a\\_n\\}$.\n2. Let $b\\_n = (-1)^n \\cdot \\frac{2n+3}{\\log\\_2 a\\_n \\cdot \\log\\_2 a\\_{n+... |
3,047 | [{"role": "user", "content": "A university intends to understand the willingness of undergraduate students to participate in a certain social practice activity. It plans to use stratified sampling to draw a sample of 300 students from undergraduates across four grades. Given that the ratio of the number of undergraduat... |
3,022 | [{"role": "user", "content": "Given the functions $f(x)=x^{3}$ and $g(x)=2^{1-x}$, consider the propositions: $p$: $f(x)$ and $g(x)$ are increasing functions within their domain; $q$: The zero of the function $y=f(x)-g(x)$ lies within the interval $(0,2)$. Among the propositions: $p \\land q$, $p \\lor q$, $\\lnot p \\... |
3,033 | [{"role": "user", "content": "If the amount of DNA in a sperm is $a$, what are the amounts of DNA in a primary spermatocyte and a secondary spermatocyte, respectively?\n\nA: $2a$ and $a$\nB: $4a$ and $2a$\nC: $a$ and $2a$\nD: $2a$ and $4a$"}, {"role": "assistant", "content": "<think>\n\nOkay, so I need to figure out th... |
3,042 | [{"role": "user", "content": "Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 31 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach th... |
3,057 | [{"role": "user", "content": "The derivative of the function $y=\\cos \\frac{π}{3}$ is ( )\n\nA: $\\frac{\\sqrt{3}}{2}$\n\nB: $\\frac{1}{2}$\n\nC: $0$\n\nD: $-\\frac{\\sqrt{3}}{2}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the derivative of the function y = cos(π/3). Hmm... |
2,985 | [{"role": "user", "content": "Given the function $g(x)= \\frac {10^{x}-1}{10^{x}+1}$, where $x\\in\\mathbb{R}$, the function $y=f(x)$ is the inverse function of $y=g(x)$. \n(1) Find the expression for the function $y=f(x)$ and state its domain $D$; \n(2) Let $h(x)= \\frac {1}{x}-f(x)$, if the graph of the function $y... |
3,050 | [{"role": "user", "content": "Let $P = \\{x | x^2 - 9 < 0\\}$, and $Q = \\{x \\in \\mathbb{Z} | -1 \\leq x \\leq 3\\}$. What is $P \\cap Q$?\n\nA: $\\{x | -3 < x \\leq 3\\}$\n\nB: $\\{x | -1 \\leq x < 3\\}$\n\nC: $\\{-1, 0, 1, 2, 3\\}$\n\nD: $\\{-1, 0, 1, 2\\}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let'... |
3,055 | [{"role": "user", "content": "Determine the interval where the function $y = -x^2$ is monotonically increasing.\n\nA: $(0, -\\infty)$ \nB: $[0, +\\infty)$ \nC: $(-\\infty, 0]$ \nD: $(-\\infty, +\\infty)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking for the interval where... |
3,053 | [{"role": "user", "content": "Consider a geometric sequence {a_n} whose sum of the first n terms is S_n, and the common ratio is q. Given that a_n > 0, a_1 = 1, and S_3 = 7, find the value of q."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the common ratio q of a geometric sequence wh... |
3,034 | [{"role": "user", "content": "A seed mixture contains a certain percentage of ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. A mixture of X and Y contains 27 percent ryegrass. The weight of this mixture is 13.333333333333332 percent X. What percent of seed mixt... |
3,046 | [{"role": "user", "content": "A square has an area of $36.$ A rectangle has the same width as the square. The length of the rectangle is triple its width. What is the area of the rectangle?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct... |
3,030 | [{"role": "user", "content": "On square $ABCD$, point $G$ lies on side $AB$ and point $H$ lies on side $CD$, so that $AG=DH=10$ and $GB=HC=20$. Find the area of square $ABCD$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct a... |
2,973 | [{"role": "user", "content": "Compute\n\\[\n\\frac{3 + 4}{3^{100}} + \\frac{3 + 2 \\cdot 4}{3^{99}} + \\frac{3 + 3 \\cdot 4}{3^{98}} + \\dots + \\frac{3 + 98 \\cdot 4}{3^3} + \\frac{3 + 99 \\cdot 4}{3^2} + \\frac{3 + 100 \\cdot 4}{3}.\n\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging... |
3,000 | [{"role": "user", "content": "The bisector of a triangle divides one of its sides into two segments. Prove that the larger of the two segments is adjacent to the larger of the other two sides of the triangle."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult ... |
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