messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Find the solution to this equation and report it. -934x + 262 = -102"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -934x + 262 = -102 $\n\nMove all terms to the left (standard form):\n$ -934x + 364 = 0 $\n\nIsolate the $x$ term:\n$ -934x = -364 $\n\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 7100
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 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 = \... | {
"type": "trigonometry",
"seed": 1337,
"index": 7101
} |
[
{
"role": "user",
"content": "solve -10x^2 + 188x + 40 = -191"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -10x^2 + 188x + 40 = -191 $\n\nMove all terms to the left (standard form):\n$ -10x^2 + 188x + 231 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7102
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. -20 + 64x^2 + 11x = -152"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20 + 64x^2 + 11x = -152 $\n\nMove all terms to the left (standard form):\n$ 64x^2 + 11x + 132 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7103
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Find the modular inverse of 7 modulo 13, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{13}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7104
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-164 + -266/14) * 5) + 7^2 - log_8(512) + (374 mod 13) + floor(170/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-164 + -266/14) * 5) + 7^2 - log_8(512) + (374 mod 13) + floor(170/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 7105
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Evaluate: ((120 + 320/8) * 17) + 8^4 - log_3(3) + (310 mod 30) + round(-45/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((120 + 320/8) * 17) + 8^4 - log_3(3) + (310 mod 30) + round(-45/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 7106
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Evaluate: ((-122 + -161/23) * 17) + 3^3 - log_10(1000) + (-144 mod 17) + ceil(-62/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-122 + -161/23) * 17) + 3^3 - log_10(1000) + (-144 mod 17) + ceil(-62... | {
"type": "arithmetic",
"seed": 1337,
"index": 7107
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((-71 + -390/10) * 18) + 2^4 - log_4(4096) + (-48 mod 22) + round(-182/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-71 + -390/10) * 18) + 2^4 - log_4(4096) + (-48 mod 22) + round(-18... | {
"type": "arithmetic",
"seed": 1337,
"index": 7108
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((-6 + 494/13) * 2) + 5^4 - log_2(2) + (-82 mod 9) + floor(-17/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-6 + 494/13) * 2) + 5^4 - log_2(2) + (-82 mod 9) + floor(-17/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 7109
} |
[
{
"role": "user",
"content": "solve: 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}{\\partial x\\partial y} ... | {
"type": "optimization",
"seed": 1337,
"index": 7110
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Prove that $f(x,y)=\\frac12(4x^2+10y^2)+1x+-5y+6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+10y^2)+1x+-5y+6 $\n\n$ \\frac{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 7111
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Prove that $f(x,y)=\\frac12(1x^2+5y^2)+5x+1y+-10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+5y^2)+5x+1y+-10 $\n\n$ \\frac{\\partial^2 f}{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 7112
} |
[
{
"role": "user",
"content": "Compute the outcome of 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$ 4... | {
"type": "optimization",
"seed": 1337,
"index": 7113
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Differentiate with respect to $x$: $f(x) = (-2x + -1)\\sin(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-2x + -1)\\sin(6x) $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 7114
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Prove that $(\\mathbb{Z}_17, +)$ is a group under addition modulo 17."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_17=\\{0,1,\\dots,16\\}$ with operation $+$ modulo $17$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7115
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((122 + -432/24) * 20) + 12^5 - log_3(27) + (-475 mod 6) + ceil(194/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((122 + -432/24) * 20) + 12^5 - log_3(27) + (-475 mod 6) + ceil(194/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 7116
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 8 + 75x^2 + 160x = 94"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 8 + 75x^2 + 160x = 94 $\n\nMove all terms to the left (standard form):\n$ 75x^2 + 160x + -86 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7117
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the indefinite integral: $\\int 8\\sin(6x) + -2\\cos(4x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 8\\sin(6x) + -2\\cos(4x)\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 7118
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Differentiate with respect to $x$: $f(x) = -3\\sin(3x) + -1\\cos(2x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3\\sin(3x) + -1\\cos(2x) $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 7119
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-1&-8\\\\9&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -1 & -8 \\\\ 9 & 8 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7120
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Differentiate with respect to $x$: $f(x) = (6x + 0)e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (6x + 0)e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{6e... | {
"type": "calculus",
"seed": 1337,
"index": 7121
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Differentiate with respect to $x$: $f(x) = 3\\sin(5x) + 7\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3\\sin(5x) + 7\\cos(7x) $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 7122
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 18 - 193x + 99x^2 = 38"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 18 - 193x + 99x^2 = 38 $\n\nMove all terms to the left (standard form):\n$ 99x^2 + -193x + -20 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7123
} |
[
{
"role": "user",
"content": "Work out the result of 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{\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 7124
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -4 + 157 - 98x = 139x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4 + 157 - 98x = 139x^2 $\n\nMove all terms to the left (standard form):\n$ -139x^2 + -98x + 153 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7125
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -18 + 134x^2 - 46x = -177"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -18 + 134x^2 - 46x = -177 $\n\nMove all terms to the left (standard form):\n$ 134x^2 + -46x + 159 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7126
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 26x - 179 + 142 = -150x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 26x - 179 + 142 = -150x^2 $\n\nMove all terms to the left (standard form):\n$ 150x^2 + 26x + -37 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7127
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -777x + 559 = -555"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -777x + 559 = -555 $\n\nMove all terms to the left (standard form):\n$ -777x + 1114 = 0 $\n\nIsolate the $x$ term:\n$ -777x = -1114 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 7128
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Differentiate with respect to $x$: $f(x) = 1\\sin(8x) + 8\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1\\sin(8x) + 8\\cos(1x) $\n\nApply the standard differentiation rules:\n$ f'... | {
"type": "calculus",
"seed": 1337,
"index": 7129
} |
[
{
"role": "user",
"content": "Can you compute this equation? -88 + 80 = 668x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -88 + 80 = 668x $\n\nMove all terms to the left (standard form):\n$ -668x + -8 = 0 $\n\nIsolate the $x$ term:\n$ -668x = 8 $\n\nDivide both sides by the coef... | {
"type": "linear_equation",
"seed": 1337,
"index": 7130
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Find the modular inverse of 23 modulo 31, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $23\\cdot a^{-1} \\equiv 1 \\pmod{31}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7131
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 9 + 86x - 63x^2 = 98"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 9 + 86x - 63x^2 = 98 $\n\nMove all terms to the left (standard form):\n$ -63x^2 + 86x + -89 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7132
} |
[
{
"role": "user",
"content": "Please find and report the solution to 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 v... | {
"type": "trigonometry",
"seed": 1337,
"index": 7133
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 2x - 78 - 132 = -25x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 2x - 78 - 132 = -25x^2 $\n\nMove all terms to the left (standard form):\n$ 25x^2 + 2x + -210 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7134
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. -58x + 632 = 203"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -58x + 632 = 203 $\n\nMove all terms to the left (standard form):\n$ -58x + 429 = 0 $\n\nIsolate the $x$ term:\n$ -58x = -429 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 7135
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 30x - 167x^2 - 25 = 181"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 30x - 167x^2 - 25 = 181 $\n\nMove all terms to the left (standard form):\n$ -167x^2 + 30x + -206 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7136
} |
[
{
"role": "user",
"content": "Solve the following math equation. 10 - 157 - 8x^2 = -111x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 - 157 - 8x^2 = -111x $\n\nMove all terms to the left (standard form):\n$ -8x^2 + 111x + -147 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7137
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Prove that $(\\mathbb{Z}_7, +)$ is a group under addition modulo 7."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_7=\\{0,1,\\dots,6\\}$ with operation $+$ modulo $7$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, th... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7138
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Compute the indefinite integral: $\\int 1x^3 + 8x^2 + -5x + -4\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1x^3 + 8x^2 + -5x + -4\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 7139
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Compute the determinant: $A=\\begin{pmatrix}-6&-7\\\\-4&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-6&-7\\\\\\-4&9\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7140
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 7141
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((-193 + 138/23) * 12) + 7^2 - log_4(64) + (86 mod 21) + floor(-136/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-193 + 138/23) * 12) + 7^2 - log_4(64) + (86 mod 21) + floor(-136/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 7142
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 7143
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. -381 - 19 = 781x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -381 - 19 = 781x $\n\nMove all terms to the left (standard form):\n$ -781x + -400 = 0 $\n\nIsolate the $x$ term:\n$ -781x = 400 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 7144
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}0&7\\\\\\6&3\\end{pmatrix},\\quad b=\\begin{pmatrix}63\\\\\\9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}0&7\\\\\\6&3\\end{pmat... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7145
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 248 + 314 = 382x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 248 + 314 = 382x $\n\nMove all terms to the left (standard form):\n$ -382x + 562 = 0 $\n\nIsolate the $x$ term:\n$ -382x = -562 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 7146
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Compute $(87+-123) \\bmod 9$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (87+-123) \\bmod 9 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7147
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 37 + 29 + 174x = 3x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 + 29 + 174x = 3x^2 $\n\nMove all terms to the left (standard form):\n$ -3x^2 + 174x + 66 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7148
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-3&-5\\\\\\4&-1&2\\\\\\-3&-4&5\\end{pmatrix},\\quad b=\\begin{pmatrix}37\\\\\\12\\\\\\-3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7149
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. -303x - 727 = 938"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -303x - 727 = 938 $\n\nMove all terms to the left (standard form):\n$ -303x + -1665 = 0 $\n\nIsolate the $x$ term:\n$ -303x = 1665 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 7150
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-2&-4\\\\\\7&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-30\\\\\\3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-2&-4\\\\\\7&-3\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7151
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -113 - 682x = 269"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -113 - 682x = 269 $\n\nMove all terms to the left (standard form):\n$ -682x + -382 = 0 $\n\nIsolate the $x$ term:\n$ -682x = 382 $\n\nDivide both sides by the coefficient... | {
"type": "linear_equation",
"seed": 1337,
"index": 7152
} |
[
{
"role": "user",
"content": "Please calculate 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{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 7153
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute the determinant: $A=\\begin{pmatrix}3&4\\\\6&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&4\\\\\\6&-7\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7154
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((188 + -104/4) * 15) + 6^3 - log_5(3125) + (-271 mod 4) + round(-77/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((188 + -104/4) * 15) + 6^3 - log_5(3125) + (-271 mod 4) + round(-77/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 7155
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((-167 + -84/4) * 3) + 5^3 - log_8(64) + (-149 mod 4) + ceil(-65/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-167 + -84/4) * 3) + 5^3 - log_8(64) + (-149 mod 4) + ceil(-65/2) $\n\nCompute each com... | {
"type": "arithmetic",
"seed": 1337,
"index": 7156
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 7157
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 106 + 993x = -374"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 106 + 993x = -374 $\n\nMove all terms to the left (standard form):\n$ 993x + 480 = 0 $\n\nIsolate the $x$ term:\n$ 993x = -480 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 7158
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Compute the indefinite integral: $\\int 2x^3 + 2x^2 + -17x + 20\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2x^3 + 2x^2 + -17x + 20\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 7159
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. -144 - 526x = -761"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -144 - 526x = -761 $\n\nMove all terms to the left (standard form):\n$ -526x + 617 = 0 $\n\nIsolate the $x$ term:\n$ -526x = -617 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 7160
} |
[
{
"role": "user",
"content": "Compute the result for the following 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": 7161
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find the modular inverse of 3 modulo 19, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{19}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees intege... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7162
} |
[
{
"role": "user",
"content": "Determine the solution of the given 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 $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 7163
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 37x^2 + 197x - 102 = -135"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37x^2 + 197x - 102 = -135 $\n\nMove all terms to the left (standard form):\n$ 37x^2 + 197x + 33 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7164
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Compute the determinant: $A=\\begin{pmatrix}-5&1\\\\-9&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&1\\\\\\-9&9\\end{pmatrix} $\n\nUse $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7165
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -29 + 153 + 192x^2 = -121x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29 + 153 + 192x^2 = -121x $\n\nMove all terms to the left (standard form):\n$ 192x^2 + 121x + 124 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7166
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Find the modular inverse of 6 modulo 7, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $6\\cdot a^{-1} \\equiv 1 \\pmod{7}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7167
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 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 $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 7168
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. -5x^2 + 122 - 11x = 71"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -5x^2 + 122 - 11x = 71 $\n\nMove all terms to the left (standard form):\n$ -5x^2 + -11x + 51 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7169
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -136x + 168 = -934"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -136x + 168 = -934 $\n\nMove all terms to the left (standard form):\n$ -136x + 1102 = 0 $\n\nIsolate the $x$ term:\n$ -136x = -1102 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 7170
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Prove that $f(x,y)=\\frac12(6x^2+4y^2)+-4x+1y+-6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+4y^2)+-4x+1y+-6 $\n\n$ \\frac{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 7171
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Prove that $f(x)=2x^2+2x+10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+2x+10$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'... | {
"type": "optimization",
"seed": 1337,
"index": 7172
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 7173
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((-152 + -126/7) * 18) + 5^2 - log_5(625) + (-73 mod 2) + floor(-57/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-152 + -126/7) * 18) + 5^2 - log_5(625) + (-73 mod 2) + floor(-57/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 7174
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. -149 + 147 = -178x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -149 + 147 = -178x $\n\nMove all terms to the left (standard form):\n$ 178x + -2 = 0 $\n\nIsolate the $x$ term:\n$ 178x = 2 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 7175
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((195 + 390/15) * 20) + 3^4 - log_9(81) + (213 mod 22) + ceil(91/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((195 + 390/15) * 20) + 3^4 - log_9(81) + (213 mod 22) + ceil(91/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 7176
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((-46 + -645/15) * 6) + 8^4 - log_9(81) + (176 mod 13) + round(-99/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-46 + -645/15) * 6) + 8^4 - log_9(81) + (176 mod 13) + round(-99/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 7177
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&1&1\\\\\\-4&-1&0\\\\\\4&-2&1\\end{pmatrix},\\quad b=\\begin{pmatrix}1\\\\\\-2\\\\\\-5\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7178
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((-41 + -32/4) * 16) + 9^5 - log_8(512) + (94 mod 16) + floor(67/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-41 + -32/4) * 16) + 9^5 - log_8(512) + (94 mod 16) + floor(67/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 7179
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 4x - 31 + 152x^2 = -176"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 4x - 31 + 152x^2 = -176 $\n\nMove all terms to the left (standard form):\n$ 152x^2 + 4x + 145 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7180
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 85 - 432x = 451"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 85 - 432x = 451 $\n\nMove all terms to the left (standard form):\n$ -432x + -366 = 0 $\n\nIsolate the $x$ term:\n$ -432x = 366 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7181
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Prove that $(\\mathbb{Z}_30, +)$ is a group under addition modulo 30."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_30=\\{0,1,\\dots,29\\}$ with operation $+$ modulo $30$.\n\n**Closure:** If $a,b\\in... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7182
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Prove that $f(x)=1x^2+-2x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+-2x+-1$.\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": 7183
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 5 + 100x^2 + 69 = -184x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 5 + 100x^2 + 69 = -184x $\n\nMove all terms to the left (standard form):\n$ 100x^2 + 184x + 74 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7184
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. 15 - 20x^2 + 194 = -14x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15 - 20x^2 + 194 = -14x $\n\nMove all terms to the left (standard form):\n$ -20x^2 + 14x + 209 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7185
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Differentiate with respect to $x$: $f(x) = (-4x + -9)\\sin(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-4x + -9)\\sin(1x) $\n\nApply the standard differentiation rules:\n$ f'... | {
"type": "calculus",
"seed": 1337,
"index": 7186
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Differentiate with respect to $x$: $f(x) = \\ln(2x + -2)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(2x + -2) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\... | {
"type": "calculus",
"seed": 1337,
"index": 7187
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Find the modular inverse of 19 modulo 26, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{26}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees i... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7188
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -423x + 264 = -734"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -423x + 264 = -734 $\n\nMove all terms to the left (standard form):\n$ -423x + 998 = 0 $\n\nIsolate the $x$ term:\n$ -423x = -998 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 7189
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. 20x^2 - 54x + 19 = 188"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20x^2 - 54x + 19 = 188 $\n\nMove all terms to the left (standard form):\n$ 20x^2 + -54x + -169 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7190
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 616x + 694 = 771"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 616x + 694 = 771 $\n\nMove all terms to the left (standard form):\n$ 616x + -77 = 0 $\n\nIsolate the $x$ term:\n$ 616x = 77 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7191
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Evaluate: ((91 + 432/9) * 15) + 9^3 - log_8(512) + (128 mod 14) + round(-101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((91 + 432/9) * 15) + 9^3 - log_8(512) + (128 mod 14) + round(-101/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 7192
} |
[
{
"role": "user",
"content": "solve: Compute the indefinite integral: $\\int \\ln(5x + 2)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + 2)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int \\ln(5x + 2)\\,dx ... | {
"type": "calculus",
"seed": 1337,
"index": 7193
} |
[
{
"role": "user",
"content": "Evaluate and solve the given 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": 7194
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Evaluate: ((-134 + -765/17) * 16) + 10^2 - log_8(4096) + (340 mod 4) + floor(116/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-134 + -765/17) * 16) + 10^2 - log_8(4096) + (340 mod 4) + f... | {
"type": "arithmetic",
"seed": 1337,
"index": 7195
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Find the modular inverse of 2 modulo 21, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $2\\cdot a^{-1} \\equiv 1 \\pmod{21}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees i... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7196
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((-161 + 128/16) * 19) + 6^2 - log_6(1296) + (-340 mod 23) + floor(-144/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-161 + 128/16) * 19) + 6^2 - log_6(1296) + (-340 mod 23) + floor(-144/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 7197
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute the indefinite integral: $\\int (1x + 0)\\sin(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + 0)\\sin(6x)\\,dx $\n\nUse standard antiderivatives (and integration b... | {
"type": "calculus",
"seed": 1337,
"index": 7198
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-1&-4\\\\\\8&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}25\\\\\\5\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-1&-4\\\\\\8&-9\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7199
} |
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