id stringlengths 32 32 | conversations listlengths 2 2 | status stringclasses 3
values |
|---|---|---|
caada08c3f565a658d6d5122067aea3f | [
{
"role": "user",
"content": "Calculate $(5-5i) + (-2-i) - (3+4i) = $\n\nA: $-2i$\n\nB: $-10i$\n\nC: $10$\n\nD: $-2$"
},
{
"role": "assistant",
"content": "\n\n\\boxed{B}",
"reasoning_content": "Okay, let's see. I need to calculate (5 - 5i) + (-2 - i) - (3 + 4i). Hmm, complex numbers. Alrigh... | success |
0bab8e96153a5bc591b0914b636fe79b | [
{
"role": "user",
"content": "Given proposition \\\\(p\\\\): For all \\\\(x \\in \\mathbb{R}\\\\), \\\\(3^{x} > 0\\\\), then\n\nA: \\\\(\\neg p\\\\): There exists an \\\\(x \\in \\mathbb{R}\\\\) such that \\\\(3^{x} \\leqslant 0\\\\)\n\nB: \\\\(\\neg p\\\\): For all \\\\(x \\in \\mathbb{R}\\\\), \\\\(3^{x} ... | success |
1f1598d874235cbfbcfbde71ed6cde99 | [
{
"role": "user",
"content": "(2006•Bazhong) If the radii of two circles are 3cm and 5cm respectively, and the distance between their centers is 10cm, then the number of common tangents these two circles have is ( )\nA: 1\nB: 2\nC: 3\nD: 4"
},
{
"role": "assistant",
"content": "\n\nThe two circl... | success |
3a555277ee095a71b9ae01331ec762d7 | [
{
"role": "user",
"content": "In one American company, every employee is either a Democrat or a Republican. After one Republican decided to become a Democrat, the number of each became equal. Then, three more Republicans decided to become Democrats, and the number of Democrats became twice the number of Rep... | success |
757bc5a7a6bb5f5bad165ecad4a92b79 | [
{
"role": "user",
"content": "G3.3 If $c$ is the maximum value of $\\log (\\sin x)$, where $0<x<\\pi$, find the value of $c$."
},
{
"role": "assistant",
"content": "\n\nThe maximum value of \\(\\log(\\sin x)\\) occurs where \\(\\sin x\\) is maximized. The function \\(\\sin x\\) reaches its maxim... | success |
025e888681f554bbb54ce494c370dd25 | [
{
"role": "user",
"content": "Given the universal set $U = \\{1,2,3\\}$, set $B = \\{1,2\\}$, and $A \\cap B = \\{1\\}$, the number of sets $A$ that satisfy the condition is $(\\ \\ \\ \\ )$\n\nA: $0$\nB: $1$\nC: $2$\nD: $3$"
},
{
"role": "assistant",
"content": "\n\nThe universal set \\( U = \\... | success |
4b2564b2e336597a901b924bf44c3608 | [
{
"role": "user",
"content": "29. Jigsaw Puzzle. Everyone is familiar with the puzzle that involves cutting a piece of plywood with a picture drawn on it into small pieces, and then proposing to reassemble the original picture from these mixed pieces. Let the picture be cut into $n$ small pieces. We will ca... | success |
e24838a8aaf65a62bc39572f4cddfe6b | [
{
"role": "user",
"content": "Determine the largest number among the following three: $\\log_{\\frac{1}{2}}3$, $(\\frac{1}{3})^{0.2}$, and $2^{\\frac{1}{3}}$."
},
{
"role": "assistant",
"content": "\n\nTo determine the largest number among \\(\\log_{\\frac{1}{2}}3\\), \\((\\frac{1}{3})^{0.2}\\),... | success |
55bdbef7a330564da747cb6b42b95d6f | [
{
"role": "user",
"content": "9.043. $\\sqrt{x^{2}-x-12}<x$."
},
{
"role": "assistant",
"content": "\n\nTo solve the inequality \\(\\sqrt{x^2 - x - 12} < x\\), we first determine the domain where the expression under the square root is non-negative and \\(x\\) is positive.\n\n1. **Domain Conditi... | success |
c726d45d3ba25eb4901e0025d0469f1a | [
{
"role": "user",
"content": "Given the sequence {an}, the sum of its first n terms is Sn, and an + an+2 = 2an+1. Also, a1 = 13 and a2 = 11. When Sn reaches its maximum value, n equals ( ).\nA: 5\nB: 6\nC: 7\nD: 8"
},
{
"role": "assistant",
"content": "\n\nGiven the sequence \\(\\{a_n\\}\\) wi... | success |
bb867f4053b5525b8966b746b282d3d3 | [
{
"role": "user",
"content": "Determine the distance from the point $(2,4,1)$ to the plane $x+2y+3z+3=0$."
},
{
"role": "assistant",
"content": "\n\nThe distance from the point \\((2, 4, 1)\\) to the plane \\(x + 2y + 3z + 3 = 0\\) is calculated using the formula for the distance from a point to... | success |
92f66013b6365e77b066e6e1196faac3 | [
{
"role": "user",
"content": "7. Highway (from 7th grade, 3 points). A highway running from west to east intersects with $n$ equal roads, numbered from 1 to $n$ in order. Cars travel on these roads from south to north and from north to south. The probability that a car will approach the highway from each of... | success |
2947537346785d34bb7ad1b709972e03 | [
{
"role": "user",
"content": "Given that \\\\(\\alpha\\\\) is an obtuse angle, and \\\\(\\sin \\left(\\frac{\\pi }{4}+\\alpha \\right)=\\frac{3}{4}\\\\), then \\\\(\\sin \\left(\\frac{\\pi }{4}-\\alpha \\right)=\\\\)\\_\\_\\_\\_\\_\\_\\_\\_．"
},
{
"role": "assistant",
"content": "\n\nGiven that ... | success |
192c391fdeba5ede8b23f35f2a8391c4 | [
{
"role": "user",
"content": "Convert the parametric equation $\\begin{cases} x= \\frac{a}{2}\\left( t+ \\frac{1}{t} \\right), \\\\ y= \\frac{b}{2}\\left( t- \\frac{1}{t} \\right) \\end{cases}$ (where $t$ is the parameter) into a standard equation."
},
{
"role": "assistant",
"content": "\n\nTo c... | success |
13ccca099c0b525296e91bd6349c8ace | [
{
"role": "user",
"content": "39. As shown in the figure, $P A=P B, \\angle A P B=2 \\angle A C B, A C$ intersects $P B$ at point $D$, and $P B=4, P D=3$, then $A D \\cdot D C=$ . $\\qquad$"
},
{
"role": "assistant",
"content": "\n\nGiven that \\( PA = PB \\), \\( \\angle APB = 2 \\angle ACB \\)... | success |
c94908f10518587584db8ae58877ed5a | [
{
"role": "user",
"content": "3. There is a sequence $a_{1}, a_{2}, \\cdots, a_{2010}$. For $1 \\leqslant n$ $\\leqslant 2010$ ( $n$ being a positive integer), let\n$$\nS_{n}=a_{1}+a_{2}+\\cdots+a_{n} \\text {. }\n$$\n\nIf $a_{1}=2010$ and for all $n$, $S_{n}=$ $n^{2} a_{n}$, then what is $a_{2010}$?"
},
... | truncated |
e4d885b2bf845f50b54755eefbb7e4ea | [
{
"role": "user",
"content": "Given rational numbers $a$ and $b$ that satisfy $(a-b)^2 + (b-a)|a-b| = ab$, with $ab \\neq 0$, the relationship that definitely does not hold is ( )\nA: $ab 0$\nC: $a + b > 0$\nD: $a + b < 0$"
},
{
"role": "assistant",
"content": "",
"reasoning_content": "Oka... | truncated |
2014ffacc1c05e34ab01d6f75c1a3094 | [
{
"role": "user",
"content": "How many solutions does the equation\n\n$$\n\\{x\\}^{2}=\\left\\{x^{2}\\right\\}\n$$\n\nhave in the interval $[1 ; 100]$? $(\\{u\\}-a$ is the fractional part of $u$ - the difference between $u$ and the greatest integer not greater than $u$.)"
},
{
"role": "assistant",
... | truncated |
842165393ec15e8c95bb53d01efb3e09 | [
{
"role": "user",
"content": "Find all integers $n\\ge1$ such that $2^n-1$ has exactly $n$ positive integer divisors. \n\n[i]Proposed by Ankan Bhattacharya [/i]"
},
{
"role": "assistant",
"content": "",
"reasoning_content": "Okay, so I need to find all integers n ≥ 1 such that 2^n - 1 has ex... | truncated |
3e428f5b06e6505bb2a4e43e06a9b53f | [
{
"role": "user",
"content": "If $a > b$, then which of the following equations is correct? ( )\nA: $a \\cdot \\lg x > b \\cdot \\lg x$ ($x > 0$)\nB: $a x^2 > b x^2$\nC: $a^2 > b^2$\nD: $a \\cdot 2^x > b \\cdot 2^x$"
},
{
"role": "assistant",
"content": "",
"reasoning_content": "Okay, let's ... | truncated |
913f2922cad7593bb29a5b5330d61c64 | [
{
"role": "user",
"content": "4. In the triangular prism $A B C-A_{1} B_{1} C_{1}$, the side length of the square $A A_{1} C_{1} C$ is 4, the plane $A B C \\perp$ plane $A A_{1} C_{1} C, A B=$ $3, B C=5$. If there is a point $D$ on the line segment $B C_{1}$ such that $A D \\perp A_{1} B$, then the value of... | truncated |
c84cbc3cd20f519a81c03bded34a481f | [
{
"role": "user",
"content": "8. A light ray $l$ emitted from point $A(-3,3)$ is reflected by the $x$-axis. The straight line of the reflected ray is tangent to the circle $x^{2}+y^{2}-4 x-4 y+7=0$. Then the equation of the straight line $l$ is $\\qquad$ ."
},
{
"role": "assistant",
"content": "... | truncated |
9dec0c1836ac5494aceb15f8ad199df6 | [
{
"role": "user",
"content": "Let's find all integer roots of the following equation: $x+y+z=x y z$."
},
{
"role": "assistant",
"content": "",
"reasoning_content": "Okay, so I need to find all integer roots for the equation x + y + z = xyz. Hmm, let's see. Since we're dealing with integers, ... | truncated |
a7d8e2e98ff556a498232690547f2c0f | [
{
"role": "user",
"content": "4. Determine the real values of $x, y, z$, for which\n\n$$\n\\left\\{\\begin{array}{l}\n\\frac{2 x^{2}}{x^{2}+1}=y \\\\\n\\frac{3 y^{3}}{y^{4}+y^{2}+1}=z \\\\\n\\frac{4 z^{4}}{z^{6}+z^{4}+z^{2}+1}=x\n\\end{array}\\right.\n$$"
},
{
"role": "assistant",
"content": "",... | truncated |
123a0a7cf7f0507cb84b37252906fe79 | [
{
"role": "user",
"content": "5. (ROM) Five points are given in the plane. Among the lines that connect these five points, no two coincide and no two are parallel or perpendicular. Through each point we construct an altitude to each of the other lines. What is the maximal number of intersection points of th... | truncated |
e2389bb9a69357199e1390f5d8bb439d | [
{
"role": "user",
"content": "$2 \\cdot 111$ two-digit number set $\\{00,01, \\cdots, 98,99\\}$ has a subset $X$ with the following property: in any infinite sequence of digits, there are two adjacent digits that form an element of $X$. How many elements does $X$ have at minimum?"
},
{
"role": "assi... | truncated |
365467410da05638b5b5b5db0bea8e72 | [
{
"role": "user",
"content": "In triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $B = \\frac{\\pi}{3}$, $\\cos A = \\frac{4}{5}$, and $b = \\sqrt{3}$.\n\n(1) Find the value of $\\sin C$.\n\n(2) Find the area of $\\triangle ABC$."
},
... | truncated |
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