conversations listlengths 2 2 | token_length int64 298 93.4k |
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"value": "1. On the table lie 54 piles of stones with $1,2,3, \\ldots, 54$ stones. In each step, we select any pile, say with $k$ stones, and remove it from the table along with $k$ stones from each pile that has at least $k$ stones. For example, after the first step, if we select the pile... | 11,051 |
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"value": "Return your final response within \\boxed{}. An acute angle at the base of a trapezoid inscribed in a circle with a radius of 13 is $30^{\\circ}$. The leg (non-parallel side) of the trapezoid is 10. Find the median (the midsegment) of the trapezoid."
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"value": "Given the function $f(x) = \\log_2 (2^{x}-b)$ where $b$ is a constant, if $x \\geqslant 1$, then $f(x) \\geqslant 0$ always holds true. Determine the range of values for $b$."
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"value": "<think>\nOkay, so I need to figure out the range of valu... | 2,733 |
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"value": "Given the polar equation of curve $C_1$ is $\\rho^2=\\frac {2}{3+\\cos2\\theta}$, establish a rectangular coordinate system with the pole O as the origin and the polar axis as the positive direction of the x-axis. After stretching all the x-coordinates of points on curve $C_1$ to... | 5,781 |
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"value": "Return your final response within \\boxed{}. \nGiven a circle \\( K \\) and a line \\( e \\), which intersects \\( K \\) at two distinct points \\( P \\) and \\( Q \\). Let \\( F \\) be the midpoint of one of the arcs \\( PQ \\). Consider the circles \\( k \\) that are tangent to... | 5,674 |
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"value": "Five times $A$'s money added to $B$'s money is more than $$51.00$. Three times $A$'s money minus $B$'s money is $$21.00$.\nIf $a$ represents $A$'s money in dollars and $b$ represents $B$'s money in dollars, then:\n$\\textbf{(A)}\\ a>9, b>6 \\qquad \\textbf{(B)}\\ a>9, b9, b=6\\qq... | 3,446 |
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"value": "Given the inequality $ax^{2}-bx-1\\geqslant 0$ has solutions $[-\\frac{1}{2},-\\frac{1}{3}]$ \n$(1)$ Find the values of $a$ and $b$; \n$(2)$ Find the solution set of the inequality $x^{2}-bx-a < 0$."
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"value": "<think>\nAlright, let's tackle... | 3,398 |
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"value": "Return your final response within \\boxed{}. The students take a bus to the Martyrs' Cemetery for the Qingming Festival. If the bus increases its speed by one-fifth after driving for 1 hour, they can arrive 20 minutes earlier than the scheduled time; if the bus first travels 72 k... | 2,725 |
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"value": "Given that $a$ and $b$ are the roots of the equation $x^{2}-3x-5=0$, then the value of the expression $\\frac{1}{a}+\\frac{1}{b}$ is ____."
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"value": "<think>\nOkay, so I have this problem here where I need to find the value of the expression ... | 2,275 |
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"value": "Let the complex number $z$ satisfy $\\frac{i}{1+i}z=1$, then $|z|=\\left(\\ \\ \\right)$\n\nA: $1$\n\nB: $5$\n\nC: $\\sqrt{2}$\n\nD: $2$"
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"value": "<think>\nOkay, so I need to solve this complex number problem. Let me read it again. It says, ... | 2,629 |
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"value": "The solution to the system of equations $\\left\\{\\begin{array}{l}{x=4y}\\\\{x+2y=-12}\\end{array}\\right.$ is ()\n\nA: $\\left\\{\\begin{array}{l}{x=-4,}\\\\{y=-1}\\end{array}\\right.$\n\nB: $\\left\\{\\begin{array}{l}{x=-8,}\\\\{y=-2}\\end{array}\\right.$\n\nC: $\\left\\{\\beg... | 1,262 |
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"value": "[u]Round 1[/u]\n\n\n[b]p1.[/b] How many powers of $2$ are greater than $3$ but less than $2013$?\n\n\n[b]p2.[/b] What number is equal to six greater than three times the answer to this question? \n\n\n[b]p3.[/b] Surya Cup-a-tea-raju goes to Starbucks Coffee to sip coffee out of a... | 10,683 |
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