source_hf stringclasses 2 values | in_source_id stringlengths 5 38 | fine_source stringclasses 19 values | messages listlengths 2 2 |
|---|---|---|---|
openr1_math | 1d57f4b3-c516-5522-91cc-a60dd91f6f66_0 | olympiads | [
{
"content": "3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was completed at the original speed, they started using new equipment, which increased the construction speed by $20 \\%$ and reduced the working hours to $80 \\%$ of the original. As a result, it took a ... |
openr1_math | 1d57f4b3-c516-5522-91cc-a60dd91f6f66_1 | olympiads | [
{
"content": "3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was completed at the original speed, they started using new equipment, which increased the construction speed by $20 \\%$ and reduced the working hours to $80 \\%$ of the original. As a result, it took a ... |
openr1_math | ea24dff6-9e4d-5c55-9ec0-c4d55424997a_0 | cn_contest | [
{
"content": "4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ( ).\n(A) $1<x<7$.\n(B) $5 \\ll x<7$.\n(C) $1<x<\\sqrt{7}$.\n(D) $5<x<7$ or $1<x<\\sqrt{7}$.",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, so I have... |
openr1_math | ea24dff6-9e4d-5c55-9ec0-c4d55424997a_1 | cn_contest | [
{
"content": "4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ( ).\n(A) $1<x<7$.\n(B) $5 \\ll x<7$.\n(C) $1<x<\\sqrt{7}$.\n(D) $5<x<7$ or $1<x<\\sqrt{7}$.",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, so I need... |
openr1_math | a583d65c-9b4c-56ce-8263-47edbc22baa3_0 | olympiads | [
{
"content": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$.",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, so I need to solve this equation: (8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6). Hmm, that looks a... |
openr1_math | a583d65c-9b4c-56ce-8263-47edbc22baa3_1 | olympiads | [
{
"content": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$.",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, so I need to solve this equation: (8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6). Hmm, that looks a... |
openr1_math | 79e837be-2801-5a6a-bc7a-0acee3cdd5fd_0 | olympiads | [
{
"content": "A right-angled triangle has side lengths that are integers. What could be the last digit of the area's measure, if the length of the hypotenuse is not divisible by 5?",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, so I need to figure out the possi... |
openr1_math | 79e837be-2801-5a6a-bc7a-0acee3cdd5fd_1 | olympiads | [
{
"content": "A right-angled triangle has side lengths that are integers. What could be the last digit of the area's measure, if the length of the hypotenuse is not divisible by 5?",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, so I need to figure out the possi... |
openr1_math | 167ecbbb-4270-534f-afa5-75d01d968ab5_0 | aops_forum | [
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, so I need to find the limit as n approaches infinity of the natur... |
openr1_math | 167ecbbb-4270-534f-afa5-75d01d968ab5_1 | aops_forum | [
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, so I have this problem here where I need to find the limit as n a... |
openr1_math | 167ecbbb-4270-534f-afa5-75d01d968ab5_2 | aops_forum | [
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, let's try to tackle this problem step by step. So, we have this i... |
openr1_math | 167ecbbb-4270-534f-afa5-75d01d968ab5_3 | aops_forum | [
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$",
"from": null,
"role": "user",
"value": null
},
{
"content": "<think>\nOkay, let me try to work through this problem step by step. The problem... |
openr1_math | 84f224e8-719b-5b42-a410-27816014bdd3_0 | olympiads | [
{
"content": "11. Given that the internal angles $A, B, C$ of $\\triangle ABC$ have opposite sides $a, b, c$ respectively, and $\\sqrt{3} b \\cos \\frac{A+B}{2}=c \\sin B$.\n(1) Find the size of $\\angle C$;\n(2) If $a+b=\\sqrt{3} c$, find $\\sin A$.",
"from": null,
"role": "user",
"value": null
}... |
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 5