messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((164 + -188/4) * 2) + 4^5 - log_2(64) + (-452 mod 7) + floor(167/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((164 + -188/4) * 2) + 4^5 - log_2(64) + (-452 mod 7) + floor(167/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 2000
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Evaluate: ((19 + 483/21) * 19) + 2^5 - log_10(100) + (-44 mod 17) + ceil(31/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((19 + 483/21) * 19) + 2^5 - log_10(100) + (-44 mod 17) + ceil(31/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 2001
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 34 - 56x^2 - 18 = 62x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 34 - 56x^2 - 18 = 62x $\n\nMove all terms to the left (standard form):\n$ -56x^2 + -62x + 16 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2002
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n... | {
"type": "optimization",
"seed": 1337,
"index": 2003
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((-4 + 288/9) * 11) + 3^4 - log_5(5) + (461 mod 7) + ceil(-185/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-4 + 288/9) * 11) + 3^4 - log_5(5) + (461 mod 7) + ceil(-185/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 2004
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&-3\\\\7&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & -3 \\\\ 7 & -2 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2005
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $\n\nThe gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 2006
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. -42x + 123 + 76x^2 = 169"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -42x + 123 + 76x^2 = 169 $\n\nMove all terms to the left (standard form):\n$ 76x^2 + -42x + -46 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2007
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((165 + 117/3) * 19) + 5^5 - log_5(125) + (207 mod 8) + ceil(-152/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((165 + 117/3) * 19) + 5^5 - log_5(125) + (207 mod 8) + ceil(-152/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 2008
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\nThe general... | {
"type": "trigonometry",
"seed": 1337,
"index": 2009
} |
[
{
"role": "user",
"content": "Please solve this math problem. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-... | {
"type": "optimization",
"seed": 1337,
"index": 2010
} |
[
{
"role": "user",
"content": "Solve the following math equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-1&-2\\\\-5&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -1 & -2 \\\\ -5 & 5 \\end{pmatrix} $\n\nCompute the determ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2011
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 38 - 108x - 139 = 24x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38 - 108x - 139 = 24x^2 $\n\nMove all terms to the left (standard form):\n$ -24x^2 + -108x + -101 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2012
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Evaluate: ((-129 + -27/3) * 15) + 3^4 - log_7(117649) + (-16 mod 14) + ceil(-58/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-129 + -27/3) * 15) + 3^4 - log_7(117649) + (-16 mod 14) + ceil(-58/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2013
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 873 - 565x = -176"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 873 - 565x = -176 $\n\nMove all terms to the left (standard form):\n$ -565x + 1049 = 0 $\n\nIsolate the $x$ term:\n$ -565x = -1049 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 2014
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Prove that $f(x)=7x^2+-7x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+-7x+4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x... | {
"type": "optimization",
"seed": 1337,
"index": 2015
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Find $A^{-1}$ for $A=\\begin{pmatrix}7&-9\\\\-8&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 7 & -9 \\\\ -8 & -3 \\end{pmatrix} $\n\nC... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2016
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -20x - 120x^2 + 174 = 147"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20x - 120x^2 + 174 = 147 $\n\nMove all terms to the left (standard form):\n$ -120x^2 + -20x + 27 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2017
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 176x + 97 = -919"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 176x + 97 = -919 $\n\nMove all terms to the left (standard form):\n$ 176x + 1016 = 0 $\n\nIsolate the $x$ term:\n$ 176x = -1016 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2018
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. 16x^2 - 12 + 9x = 153"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 16x^2 - 12 + 9x = 153 $\n\nMove all terms to the left (standard form):\n$ 16x^2 + 9x + -165 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2019
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&2\\\\\\-4&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-56\\\\\\28\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&2\\\\\\-4&6\\end{... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2020
} |
[
{
"role": "user",
"content": "Please solve this math problem. Compute the determinant: $A=\\begin{pmatrix}5&0\\\\-9&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}5&0\\\\\\-9&-6\\end{pmatrix} $\n\nUse $\\det(A)=a... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2021
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&-2&4\\\\\\5&-3&-4\\\\\\-4&2&0\\end{pmatrix},\\quad b=\\begin{pmatrix}-16\\\\\\-1\\\\\\8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2022
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Compute the indefinite integral: $\\int \\ln(5x + 6)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + 6)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 2023
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Evaluate: ((129 + -357/21) * 18) + 4^4 - log_6(7776) + (-354 mod 12) + ceil(-149/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((129 + -357/21) * 18) + 4^4 - log_6(7776) + (-354 mod 12) + ceil(-149/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 2024
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -804 + 11 = -593x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -804 + 11 = -593x $\n\nMove all terms to the left (standard form):\n$ 593x + -793 = 0 $\n\nIsolate the $x$ term:\n$ 593x = 793 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2025
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((-34 + 336/8) * 1) + 10^3 - log_4(64) + (472 mod 16) + round(77/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-34 + 336/8) * 1) + 10^3 - log_4(64) + (472 mod 16) + round(77/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2026
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((15 + 270/18) * 16) + 6^5 - log_7(7) + (439 mod 27) + floor(17/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((15 + 270/18) * 16) + 6^5 - log_7(7) + (439 mod 27) + floor(17/2) $\n\nCompute each component:\n$ 270/18 ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2027
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 48 - 1 + 111x = -94x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 48 - 1 + 111x = -94x^2 $\n\nMove all terms to the left (standard form):\n$ 94x^2 + 111x + 47 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2028
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute $(-59+-5) \\bmod 7$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-59+-5) \\bmod 7 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2029
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. 46 - 175x - 158 = -174x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 46 - 175x - 158 = -174x^2 $\n\nMove all terms to the left (standard form):\n$ 174x^2 + -175x + -112 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2030
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Prove that $(\\mathbb{Z}_14, +)$ is a group under addition modulo 14."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_14=\\{0,1,\\dots,13\\}$ with operation $+$ modulo $14$.\n\n**Closure:** If $a,b\\in\\math... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2031
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 2032
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Prove that $f(x,y)=\\frac12(7x^2+8y^2)+-5x+5y+3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+8y^2)+-5x+5y+3 $\n\n$ \\frac{\\partial^2 f}{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 2033
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 11x^2 + 1x - 103 = -176"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11x^2 + 1x - 103 = -176 $\n\nMove all terms to the left (standard form):\n$ 11x^2 + 1x + 73 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2034
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -404 + 148 = -811x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -404 + 148 = -811x $\n\nMove all terms to the left (standard form):\n$ 811x + -256 = 0 $\n\nIsolate the $x$ term:\n$ 811x = 256 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2035
} |
[
{
"role": "user",
"content": "Solve the following math equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x... | {
"type": "optimization",
"seed": 1337,
"index": 2036
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Prove that $f(x,y)=\\frac12(9x^2+3y^2)+-6x+-2y+-4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+3y^2)+-6x+-2y+-4 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 2037
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the determinant: $A=\\begin{pmatrix}-4&1\\\\-7&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&1\\\\\\-7&2\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2038
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Find the modular inverse of 15 modulo 16, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $15\\cdot a^{-1} \\equiv 1 \\pmod{16}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integer... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2039
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Find the modular inverse of 19 modulo 25, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{25}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2040
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Prove that $f(x,y)=\\frac12(6x^2+2y^2)+-3x+-4y+-8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+2y^2)+-3x+-4y+-8 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 2041
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Find the modular inverse of 17 modulo 26, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{26}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2042
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=... | {
"type": "optimization",
"seed": 1337,
"index": 2043
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&-3\\\\\\4&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}57\\\\\\-76\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&-3\\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2044
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Evaluate: ((197 + 1104/23) * 9) + 3^3 - log_3(27) + (-455 mod 18) + floor(159/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((197 + 1104/23) * 9) + 3^3 - log_3(27) + (-455 mod 18) + floor(159/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 2045
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 2046
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((-143 + -110/22) * 2) + 6^2 - log_10(100) + (64 mod 26) + floor(109/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-143 + -110/22) * 2) + 6^2 - log_10(100) + (64 mod 26) + floor(109/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2047
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Solve for $x$ (in radians): sin(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-\\frac{1}... | {
"type": "trigonometry",
"seed": 1337,
"index": 2048
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -39x^2 + 61x - 166 = -29"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -39x^2 + 61x - 166 = -29 $\n\nMove all terms to the left (standard form):\n$ -39x^2 + 61x + -137 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2049
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 27 + 131x + 161 = 48x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27 + 131x + 161 = 48x^2 $\n\nMove all terms to the left (standard form):\n$ -48x^2 + 131x + 188 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2050
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Prove that $(\\mathbb{Z}_23, +)$ is a group under addition modulo 23."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_23=\\{0,1,\\dots,22\\}$ with operation $+$ modulo $23$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2051
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. -212 + 442x = -964"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -212 + 442x = -964 $\n\nMove all terms to the left (standard form):\n$ 442x + 752 = 0 $\n\nIsolate the $x$ term:\n$ 442x = -752 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2052
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. -29x - 150 + 86x^2 = -87"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29x - 150 + 86x^2 = -87 $\n\nMove all terms to the left (standard form):\n$ 86x^2 + -29x + -63 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2053
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Prove that $f(x,y)=\\frac12(3x^2+9y^2)+2x+5y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+9y^2)+2x+5y+4 $\n\n$ \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 2054
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -496 + 566 = -597x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -496 + 566 = -597x $\n\nMove all terms to the left (standard form):\n$ 597x + 70 = 0 $\n\nIsolate the $x$ term:\n$ 597x = -70 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 2055
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$... | {
"type": "optimization",
"seed": 1337,
"index": 2056
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&-5&-1\\\\\\0&4&5\\\\\\-5&4&0\\end{pmatrix},\\quad b=\\begin{pmatrix}11\\\\\\-24\\\\\\1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2057
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&-1&-2\\\\\\0&-3&-1\\\\\\-1&3&1\\end{pmatrix},\\quad b=\\begin{pmatrix}12\\\\\\9\\\\\\-11\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2058
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((48 + -252/6) * 4) + 10^4 - log_6(216) + (-473 mod 22) + floor(-72/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((48 + -252/6) * 4) + 10^4 - log_6(216) + (-473 mod 22) + floor(-72/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 2059
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Evaluate: ((189 + -80/8) * 20) + 5^2 - log_4(1024) + (159 mod 8) + round(-26/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((189 + -80/8) * 20) + 5^2 - log_4(1024) + (159 mod 8) + round(-26/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 2060
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. 21 + 7 - 112x = -176x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 21 + 7 - 112x = -176x^2 $\n\nMove all terms to the left (standard form):\n$ 176x^2 + -112x + 28 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2061
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Compute the indefinite integral: $\\int \\ln(4x + 9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(4x + 9)\\,dx $\n\nUse standard antiderivatives (and integration by parts if ... | {
"type": "calculus",
"seed": 1337,
"index": 2062
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}-1&8\\\\-5&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -1 & 8 \\\\ -5 & -3 \\end{pmatrix} $\n\nCompute the... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2063
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the indefinite integral: $\\int \\ln(2x + -4)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + -4)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 2064
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Find the modular inverse of 5 modulo 18, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{18}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2065
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 449 - 790 = -932x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 449 - 790 = -932x $\n\nMove all terms to the left (standard form):\n$ 932x + -341 = 0 $\n\nIsolate the $x$ term:\n$ 932x = 341 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 2066
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\... | {
"type": "optimization",
"seed": 1337,
"index": 2067
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -27x + 16 - 99x^2 = 59"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -27x + 16 - 99x^2 = 59 $\n\nMove all terms to the left (standard form):\n$ -99x^2 + -27x + -43 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2068
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the indefinite integral: $\\int -3x^3 + -2x^2 + -2x + -13\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3x^3 + -2x^2 + -2x + -13\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 2069
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Find $A^{-1}$ for $A=\\begin{pmatrix}4&-7\\\\2&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 4 & -7 \\\\ 2 & 6 \\end{pmatrix} $\n\nCompute the det... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2070
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the indefinite integral: $\\int 5x^3 + -2x^2 + -17x + 8\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5x^3 + -2x^2 + -17x + 8\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 2071
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Solve for $x$ (in radians): sin(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(1) = 1.5708 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 2072
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. 255 + 631 = -953x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 255 + 631 = -953x $\n\nMove all terms to the left (standard form):\n$ 953x + 886 = 0 $\n\nIsolate the $x$ term:\n$ 953x = -886 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2073
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Compute $(123+191) \\bmod 16$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (123+191) \\bmod 16 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2074
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. -943 - 824 = -113x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -943 - 824 = -113x $\n\nMove all terms to the left (standard form):\n$ 113x + -1767 = 0 $\n\nIsolate the $x$ term:\n$ 113x = 1767 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 2075
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Evaluate: ((3 + 576/18) * 3) + 8^4 - log_7(7) + (14 mod 30) + round(-67/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((3 + 576/18) * 3) + 8^4 - log_7(7) + (14 mod 30) + round(-67/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 2076
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 2077
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Compute the indefinite integral: $\\int 6x^3 + 9x^2 + -19x + 18\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6x^3 + 9x^2 + -19x + 18\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 2078
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Prove that $f(x,y)=\\frac12(7x^2+3y^2)+3x+5y+8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+3y^2)+3x+5y+8 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 2079
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((8 + 532/14) * 18) + 6^5 - log_6(36) + (-424 mod 5) + round(-51/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((8 + 532/14) * 18) + 6^5 - log_6(36) + (-424 mod 5) + round(-51/2) $\n\nCompute each com... | {
"type": "arithmetic",
"seed": 1337,
"index": 2080
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&-2&3\\\\\\2&-3&0\\\\\\5&5&2\\end{pmatrix},\\quad b=\\begin{pmatrix}-2\\\\\\-5\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.,... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2081
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal ... | {
"type": "trigonometry",
"seed": 1337,
"index": 2082
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((-99 + 30/5) * 7) + 2^4 - log_2(2) + (-438 mod 6) + ceil(160/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-99 + 30/5) * 7) + 2^4 - log_2(2) + (-438 mod 6) + ceil(160/2) $\n\nCompute each c... | {
"type": "arithmetic",
"seed": 1337,
"index": 2083
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Find the modular inverse of 9 modulo 11, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{11}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2084
} |
[
{
"role": "user",
"content": "Work out the result of this equation. 385 + 967 = -26x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 385 + 967 = -26x $\n\nMove all terms to the left (standard form):\n$ 26x + 1352 = 0 $\n\nIsolate the $x$ term:\n$ 26x = -1352 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2085
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. -416 - 430 = 186x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -416 - 430 = 186x $\n\nMove all terms to the left (standard form):\n$ -186x + -846 = 0 $\n\nIsolate the $x$ term:\n$ -186x = 846 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 2086
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute the indefinite integral: $\\int -5\\sin(8x) + 1\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5\\sin(8x) + 1\\cos(5x)\\,dx $\n\nUse standard antiderivatives (and int... | {
"type": "calculus",
"seed": 1337,
"index": 2087
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((166 + 6/3) * 14) + 2^4 - log_6(46656) + (-258 mod 19) + round(-142/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((166 + 6/3) * 14) + 2^4 - log_6(46656) + (-258 mod 19) + round(-142/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 2088
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -733x + 954 = -878"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -733x + 954 = -878 $\n\nMove all terms to the left (standard form):\n$ -733x + 1832 = 0 $\n\nIsolate the $x$ term:\n$ -733x = -1832 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 2089
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve for $x$ (in radians): cos(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(\\fr... | {
"type": "trigonometry",
"seed": 1337,
"index": 2090
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Compute the indefinite integral: $\\int (-6x + 3)\\sin(4x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-6x + 3)\\sin(4x)\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 2091
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Differentiate with respect to $x$: $f(x) = -9\\sin(2x) + -6\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9\\sin(2x) + -6\\cos(4x) $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 2092
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. 605x + 840 = -145"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 605x + 840 = -145 $\n\nMove all terms to the left (standard form):\n$ 605x + 985 = 0 $\n\nIsolate the $x$ term:\n$ 605x = -985 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2093
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Compute the indefinite integral: $\\int 1\\sin(9x) + 1\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1\\sin(9x) + 1\\cos(5x)\\,dx $\n\nUse standard antiderivatives (and integ... | {
"type": "calculus",
"seed": 1337,
"index": 2094
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. -48x^2 - 13x - 43 = 151"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48x^2 - 13x - 43 = 151 $\n\nMove all terms to the left (standard form):\n$ -48x^2 + -13x + -194 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2095
} |
[
{
"role": "user",
"content": "Please solve this math problem. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 2096
} |
[
{
"role": "user",
"content": "Please calculate this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&4\\\\\\0&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-39\\\\\\4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&4\\\\\\0&-4\\end{pmatrix} ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2097
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Evaluate: ((-194 + -703/19) * 2) + 11^5 - log_2(4) + (408 mod 9) + ceil(131/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-194 + -703/19) * 2) + 11^5 - log_2(4) + (408 mod 9) + ceil(131/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2098
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac... | {
"type": "optimization",
"seed": 1337,
"index": 2099
} |
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