instruction_seed stringlengths 18 5.08k | response_seed stringlengths 18 5.08k | reasoning stringlengths 0 99k | deepseek_solution stringlengths 0 4.03k | __original_row_idx int64 0 40k | source stringclasses 1
value | final_reasoning_trace stringlengths 19 102k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|
A snail is at the bottom of a 15-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well? | A snail is at the bottom of a 15-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well? | Okay, so there's this snail at the bottom of a 15-foot well. Every day, it climbs up 3 feet, but then at night, it slips back 2 feet. The question is, how many days will it take for the snail to reach the top of the well? Hmm, let me try to figure this out.
First, I need to visualize the situation. The well is 15 feet... | The snail is at the bottom of a 15-foot well. Each day, it climbs up 3 feet and slips back 2 feet at night. To determine how many days it will take for the snail to reach the top of the well, we need to consider the net progress each day and the final climb where the snail does not slip back.
1. **Net Progress Calcula... | 9,977 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so there's this snail at the bottom of a 15-foot well. Every day, it climbs up 3 feet, but then at night, it slips back 2 feet. The question is, how many days will it take for the snail to reach the top of the well? Hmm, let me try to figure this out.
First, I need to visualize the situation. The well is... | [
{
"from": "human",
"value": "A snail is at the bottom of a 15-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so there's this snail at the bottom of ... |
Compute the sum of the geometric series $-1 + 2 - 4 + 8 - \cdots + 512$. | Compute the sum of the geometric series $-1 + 2 - 4 + 8 - \cdots + 512$. | Okay, so I need to compute the sum of this geometric series: -1 + 2 - 4 + 8 - ... + 512. Let me think about how to approach this.
First, I remember that a geometric series is one where each term is multiplied by a constant ratio to get the next term. Let me verify if this series is geometric. Starting with the first ... | The given geometric series is \(-1 + 2 - 4 + 8 - \cdots + 512\).
First, we identify the parameters of the geometric series:
- The first term \(a = -1\)
- The common ratio \(r = -2\)
- The number of terms \(n\) needs to be determined.
The \(n\)-th term of a geometric series is given by \(a_n = a \cdot r^{n-1}\). We s... | 25,384 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to compute the sum of this geometric series: -1 + 2 - 4 + 8 - ... + 512. Let me think about how to approach this.
First, I remember that a geometric series is one where each term is multiplied by a constant ratio to get the next term. Let me verify if this series is geometric. Starting with th... | [
{
"from": "human",
"value": "Compute the sum of the geometric series $-1 + 2 - 4 + 8 - \\cdots + 512$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to compute the sum of this geometric series: -1 + 2 - 4 + 8 - ... + 512. Let me think about how to approach this. \n\nFirst, I remember t... |
In convex quadrilateral $ABCD$, $\angle A = \angle C$, $AB=CD=180$, and $AD \ne BC$. The perimeter of $ABCD$ is 640. Find $\cos A$.
A similar problem:
In convex quadrilateral $ABCD$, $\angle A = \angle C$, $AB=CD=180$, and $AD \ne BC$. The perimeter of $ABCD$ is 640. Find $\cos B$.
In this problem, we are asked to... | In convex quadrilateral $ABCD$, $\angle A = \angle C$, $AB=CD=180$, and $AD \ne BC$. The perimeter of $ABCD$ is 640. Find $\cos A$.
A similar problem:
In convex quadrilateral $ABCD$, $\angle A = \angle C$, $AB=CD=180$, and $AD \ne BC$. The perimeter of $ABCD$ is 640. Find $\cos B$.
In this problem, we are asked to... | Okay, so I have this problem about a convex quadrilateral ABCD where angle A equals angle C, sides AB and CD are both 180 units long, and the perimeter is 640. Also, it's given that AD is not equal to BC, and I need to find cos B. Hmm, interesting. Let me think about how to approach this.
First, let's note down the gi... | Given a convex quadrilateral \(ABCD\) with \(\angle A = \angle C\), \(AB = CD = 180\), and a perimeter of 640, we need to find \(\cos B\).
First, we note that the perimeter gives us \(AB + BC + CD + DA = 640\). Since \(AB = CD = 180\), we have:
\[
180 + BC + 180 + DA = 640 \implies BC + DA = 280
\]
Given \(AD \ne BC\... | 5,105 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I have this problem about a convex quadrilateral ABCD where angle A equals angle C, sides AB and CD are both 180 units long, and the perimeter is 640. Also, it's given that AD is not equal to BC, and I need to find cos B. Hmm, interesting. Let me think about how to approach this.
First, let's note dow... | [
{
"from": "human",
"value": "In convex quadrilateral $ABCD$, $\\angle A = \\angle C$, $AB=CD=180$, and $AD \\ne BC$. The perimeter of $ABCD$ is 640. Find $\\cos A$.\n\nA similar problem:\n\nIn convex quadrilateral $ABCD$, $\\angle A = \\angle C$, $AB=CD=180$, and $AD \\ne BC$. The perimeter of $ABCD$ is 6... |
Sides $\overline{AH}$ and $\overline{CD}$ of regular octagon $ABCDEFGH$ are extended to meet at point $P$. What is the degree measure of angle $P$? | Sides $\overline{AH}$ and $\overline{CD}$ of regular octagon $ABCDEFGH$ are extended to meet at point $P$. What is the degree measure of angle $P$? | Okay, so I need to figure out the degree measure of angle P in this regular octagon problem. Let me try to visualize the octagon first. A regular octagon has all sides equal and all internal angles equal. Each internal angle in a regular octagon is 135 degrees because the formula for internal angles is ((n-2)*180)/n, w... | To solve the problem of finding the degree measure of angle \( P \) formed by extending sides \(\overline{AH}\) and \(\overline{CD}\) of regular octagon \(ABCDEFGH\) to meet at point \(P\), we start by noting that a regular octagon has internal angles of \(135^\circ\) and each central angle is \(45^\circ\).
We place t... | 21,627 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to figure out the degree measure of angle P in this regular octagon problem. Let me try to visualize the octagon first. A regular octagon has all sides equal and all internal angles equal. Each internal angle in a regular octagon is 135 degrees because the formula for internal angles is ((n-2)*1... | [
{
"from": "human",
"value": "Sides $\\overline{AH}$ and $\\overline{CD}$ of regular octagon $ABCDEFGH$ are extended to meet at point $P$. What is the degree measure of angle $P$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the degree measure of angle P in this regular o... |
Let $z = e^{i\theta}$, where $\theta$ is a real number. Find the minimum value of $|z^{16} - z^{-16}|$. | Let $z = e^{i\theta}$, where $\theta$ is a real number. Find the minimum value of $|z^{16} - z^{-16}|$. | Okay, so I need to find the minimum value of |z¹⁶ - z⁻¹⁶| where z = e^(iθ) and θ is a real number. Hmm, let's start by understanding what this expression represents. Since z is on the unit circle in the complex plane, raising it to any power will just rotate it around the circle.
First, let me recall that for any com... | Given \( z = e^{i\theta} \) where \( \theta \) is a real number, we need to find the minimum value of \( |z^{16} - z^{-16}| \).
First, we express \( z^{16} \) and \( z^{-16} \) using Euler's formula:
\[ z^{16} = e^{i16\theta} \]
\[ z^{-16} = e^{-i16\theta} \]
The difference \( z^{16} - z^{-16} \) can be written as:
\... | 18,484 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to find the minimum value of |z¹⁶ - z⁻¹⁶| where z = e^(iθ) and θ is a real number. Hmm, let's start by understanding what this expression represents. Since z is on the unit circle in the complex plane, raising it to any power will just rotate it around the circle.
First, let me recall that for... | [
{
"from": "human",
"value": "Let $z = e^{i\\theta}$, where $\\theta$ is a real number. Find the minimum value of $|z^{16} - z^{-16}|$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the minimum value of |z¹⁶ - z⁻¹⁶| where z = e^(iθ) and θ is a real number. Hmm, let's start by un... |
"A cylindrical tank with a height of 12 meters and a radius of 4 meters is filled with water to a he(...TRUNCATED) | "A cylindrical tank with a height of 12 meters and a radius of 4 meters is filled with water to a he(...TRUNCATED) | "Okay, so there's this cylindrical tank, right? It has a height of 12 meters and a radius of 4 meter(...TRUNCATED) | "To determine the volume of water displaced by the sphere, we need to calculate the volume of the sp(...TRUNCATED) | 13,936 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so there's this cylindrical tank, right? It has a height of 12 meters and a radius o(...TRUNCATED) | [{"from":"human","value":"A cylindrical tank with a height of 12 meters and a radius of 4 meters is (...TRUNCATED) |
"There are four positive integers that are divisors of each number in the list $$36, 72, -12, 114, 9(...TRUNCATED) | "There are four positive integers that are divisors of each number in the list $$36, 72, -12, 114, 9(...TRUNCATED) | "Okay, so I need to find the four positive integers that are divisors of each number in the list: 36(...TRUNCATED) | "To find the four positive integers that are divisors of each number in the list \\(36, 72, -12, 114(...TRUNCATED) | 22,092 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the four positive integers that are divisors of each number in the(...TRUNCATED) | [{"from":"human","value":"There are four positive integers that are divisors of each number in the l(...TRUNCATED) |
"When an integer is divided by 21, the remainder is 10. Find the difference between the remainders w(...TRUNCATED) | "When an integer is divided by 21, the remainder is 10. Find the difference between the remainders w(...TRUNCATED) | "Okay, so I have this problem here: When an integer is divided by 21, the remainder is 10. I need to(...TRUNCATED) | "Given an integer \\( N \\) which, when divided by 21, leaves a remainder of 10, we can express \\( (...TRUNCATED) | 25,684 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I have this problem here: When an integer is divided by 21, the remainder is 10. (...TRUNCATED) | [{"from":"human","value":"When an integer is divided by 21, the remainder is 10. Find the difference(...TRUNCATED) |
"If $x$ is to $y$ as $13$ is to $28$, and $y$ is to $z$ as $5$ is to $7$, what is the ratio of $x$ t(...TRUNCATED) | "If $x$ is to $y$ as $13$ is to $28$, and $y$ is to $z$ as $5$ is to $7$, what is the ratio of $x$ t(...TRUNCATED) | "Okay, so I need to find the ratio of x to z, given that x is to y as 13 is to 28, and y is to z as (...TRUNCATED) | "Given that \\( x \\) is to \\( y \\) as \\( 13 \\) is to \\( 28 \\), we can write the ratio as:\n\\(...TRUNCATED) | 12,846 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the ratio of x to z, given that x is to y as 13 is to 28, and y is(...TRUNCATED) | [{"from":"human","value":"If $x$ is to $y$ as $13$ is to $28$, and $y$ is to $z$ as $5$ is to $7$, w(...TRUNCATED) |
"Find the smallest positive integer that can be expressed as the sum of three distinct powers of 3, (...TRUNCATED) | "Find the smallest positive integer that can be expressed as the sum of three distinct powers of 3, (...TRUNCATED) | "Okay, so I need to find the smallest positive integer that can be expressed as the sum of three dis(...TRUNCATED) | "To find the smallest positive integer that can be expressed as the sum of three distinct powers of (...TRUNCATED) | 5,851 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the smallest positive integer that can be expressed as the sum of (...TRUNCATED) | [{"from":"human","value":"Find the smallest positive integer that can be expressed as the sum of thr(...TRUNCATED) |
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