messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please find the solution of this equation. 896 + 312 = 41x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 896 + 312 = 41x $\n\nMove all terms to the left (standard form):\n$ -41x + 1208 = 0 $\n\nIsolate the $x$ term:\n$ -41x = -1208 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 100
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&-4\\\\\\-2&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}28\\\\\\31\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&-4\\\\\\-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 101
} |
[
{
"role": "user",
"content": "Compute the outcome of this 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\nThe genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 102
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Find the modular inverse of 5 modulo 24, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{24}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 103
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Evaluate: ((-182 + -850/25) * 9) + 9^5 - log_7(343) + (-274 mod 23) + floor(42/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-182 + -850/25) * 9) + 9^5 - log_7(343) + (-274 mod 23) + floor(42/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 104
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((-189 + 714/17) * 11) + 8^5 - log_7(2401) + (-430 mod 22) + round(-65/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-189 + 714/17) * 11) + 8^5 - log_7(2401) + (-430 mod 22) + rou... | {
"type": "arithmetic",
"seed": 1337,
"index": 105
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((-24 + -140/4) * 8) + 9^5 - log_3(243) + (-403 mod 22) + round(119/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-24 + -140/4) * 8) + 9^5 - log_3(243) + (-403 mod 22) + round(119... | {
"type": "arithmetic",
"seed": 1337,
"index": 106
} |
[
{
"role": "user",
"content": "Please evaluate and compute this 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\\mathbb{... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 107
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 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{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 108
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((-54 + -100/2) * 3) + 7^5 - log_5(3125) + (358 mod 27) + round(-134/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-54 + -100/2) * 3) + 7^5 - log_5(3125) + (358 mod 27) + round(-134/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 109
} |
[
{
"role": "user",
"content": "Please solve this math problem. 31x^2 - 62x + 64 = -20"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31x^2 - 62x + 64 = -20 $\n\nMove all terms to the left (standard form):\n$ 31x^2 + -62x + 84 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 110
} |
[
{
"role": "user",
"content": "Can you solve the equation below? -28x^2 - 67x - 194 = -81"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -28x^2 - 67x - 194 = -81 $\n\nMove all terms to the left (standard form):\n$ -28x^2 + -67x + -113 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 111
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the determinant: $A=\\begin{pmatrix}6&4\\\\-2&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&4\\\\\\-2&2\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 112
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute the indefinite integral: $\\int -2e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 113
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 42x - 107 - 81 = -35x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 42x - 107 - 81 = -35x^2 $\n\nMove all terms to the left (standard form):\n$ 35x^2 + 42x + -188 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 114
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Prove that $f(x)=3x^2+-5x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+-5x+0$.\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": 115
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 2x + 178 - 91x^2 = 186"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 2x + 178 - 91x^2 = 186 $\n\nMove all terms to the left (standard form):\n$ -91x^2 + 2x + -8 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 116
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. -22 + 117x^2 - 39x = 180"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -22 + 117x^2 - 39x = 180 $\n\nMove all terms to the left (standard form):\n$ 117x^2 + -39x + -202 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 117
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Prove that $(\\mathbb{Z}_27, +)$ is a group under addition modulo 27."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_27=\\{0,1,\\dots,26\\}$ with operation $+$ modulo $27$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 118
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Compute $(165+27) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (165+27) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction mo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 119
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Differentiate with respect to $x$: $f(x) = (6x + -7)e^{6x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (6x + -7)e^{6x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{6e^{6x} + (6x + -7)\\cdot 6e^{... | {
"type": "calculus",
"seed": 1337,
"index": 120
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 7x + 85 + 33x^2 = 9"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 7x + 85 + 33x^2 = 9 $\n\nMove all terms to the left (standard form):\n$ 33x^2 + 7x + 76 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 121
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Compute $(161+110) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (161+110) \\bmod 12 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 122
} |
[
{
"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": 123
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Prove that $(\\mathbb{Z}_29, +)$ is a group under addition modulo 29."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_29=\\{0,1,\\dots,28\\}$ with operation $+$ modulo $29$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 124
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((9 + -644/14) * 12) + 2^2 - log_4(16) + (-246 mod 2) + ceil(-83/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((9 + -644/14) * 12) + 2^2 - log_4(16) + (-246 mod 2) + ceil(-83/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 125
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-2&-1\\\\6&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -2 & -1 \\\\ 6 & -3 \\end{pmatrix} $\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 126
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 590x - 447 = -359"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 590x - 447 = -359 $\n\nMove all terms to the left (standard form):\n$ 590x + -88 = 0 $\n\nIsolate the $x$ term:\n$ 590x = 88 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 127
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Compute the indefinite integral: $\\int \\ln(6x + -6)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(6x + -6)\\,dx $\n\nUse standard antiderivatives (and integration by parts if nee... | {
"type": "calculus",
"seed": 1337,
"index": 128
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Prove that $(\\mathbb{Z}_22, +)$ is a group under addition modulo 22."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_22=\\{0,1,\\dots,21\\}$ with operation $+$ modulo $22$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, the... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 129
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 487x + 697 = -75"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 487x + 697 = -75 $\n\nMove all terms to the left (standard form):\n$ 487x + 772 = 0 $\n\nIsolate the $x$ term:\n$ 487x = -772 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 130
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 809 - 582x = 764"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 809 - 582x = 764 $\n\nMove all terms to the left (standard form):\n$ -582x + 45 = 0 $\n\nIsolate the $x$ term:\n$ -582x = -45 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 131
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Differentiate with respect to $x$: $f(x) = -3x^3 + 8x^2 + -4x + -4$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + 8x^2 + -4x + -4 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 132
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((154 + 25/5) * 7) + 9^5 - log_4(4) + (-395 mod 6) + round(38/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((154 + 25/5) * 7) + 9^5 - log_4(4) + (-395 mod 6) + round(38/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 133
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((-12 + 297/9) * 1) + 8^2 - log_8(32768) + (-103 mod 3) + floor(19/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-12 + 297/9) * 1) + 8^2 - log_8(32768) + (-103 mod 3) + floor(19/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 134
} |
[
{
"role": "user",
"content": "Can you determine 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)... | {
"type": "trigonometry",
"seed": 1337,
"index": 135
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. -45x^2 - 110 + 169 = 62x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -45x^2 - 110 + 169 = 62x $\n\nMove all terms to the left (standard form):\n$ -45x^2 + -62x + 59 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 136
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -41x + 79 + 172 = -140x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -41x + 79 + 172 = -140x^2 $\n\nMove all terms to the left (standard form):\n$ 140x^2 + -41x + 251 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 137
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Find the modular inverse of 5 modulo 27, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{27}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 138
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 7 + 184x^2 + 21x = 18"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 7 + 184x^2 + 21x = 18 $\n\nMove all terms to the left (standard form):\n$ 184x^2 + 21x + -11 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 139
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Find the modular inverse of 21 modulo 26, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $21\\cdot a^{-1} \\equiv 1 \\pmod{26}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees i... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 140
} |
[
{
"role": "user",
"content": "Solve the equation shown 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{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 141
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((-26 + -216/9) * 11) + 12^5 - log_8(8) + (485 mod 18) + ceil(135/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-26 + -216/9) * 11) + 12^5 - log_8(8) + (485 mod 18) + ceil(135/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 142
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -15 - 91x^2 - 16 = -87x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15 - 91x^2 - 16 = -87x $\n\nMove all terms to the left (standard form):\n$ -91x^2 + 87x + -31 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 143
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Compute the determinant: $A=\\begin{pmatrix}4&-3\\\\5&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}4&-3\\\\\\5&-4\\end{pmatrix} $\n\nUse $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 144
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -985x - 952 = 258"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -985x - 952 = 258 $\n\nMove all terms to the left (standard form):\n$ -985x + -1210 = 0 $\n\nIsolate the $x$ term:\n$ -985x = 1210 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 145
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Differentiate with respect to $x$: $f(x) = -2e^{-3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2e^{-3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{6e^{-3x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 146
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Prove that $f(x,y)=\\frac12(9x^2+10y^2)+-1x+5y+-1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+10y^2)+-1x+5y+-1 $\n\n$ \\frac{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 147
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Compute the indefinite integral: $\\int \\ln(6x + 2)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(6x + 2)\\,dx $\n\nUse standard antiderivatives (and integration by parts if neede... | {
"type": "calculus",
"seed": 1337,
"index": 148
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 332x - 448 = 975"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 332x - 448 = 975 $\n\nMove all terms to the left (standard form):\n$ 332x + -1423 = 0 $\n\nIsolate the $x$ term:\n$ 332x = 1423 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 149
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Evaluate: ((49 + 132/4) * 20) + 4^3 - log_8(64) + (65 mod 6) + round(-78/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((49 + 132/4) * 20) + 4^3 - log_8(64) + (65 mod 6) + round(-78/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 150
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((95 + -539/11) * 14) + 11^4 - log_4(1024) + (-289 mod 25) + ceil(-47/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((95 + -539/11) * 14) + 11^4 - log_4(1024) + (-289 mod 25) + ceil(-47/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 151
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 10x - 181 - 20 = -85x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10x - 181 - 20 = -85x^2 $\n\nMove all terms to the left (standard form):\n$ 85x^2 + 10x + -201 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 152
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((-77 + -484/11) * 9) + 6^3 - log_3(243) + (-420 mod 19) + ceil(-101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-77 + -484/11) * 9) + 6^3 - log_3(243) + (-420 mod 19) + ceil(-101/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 153
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Prove that $f(x)=10x^2+2x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+2x+-9$.\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": 154
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}5&-8\\\\-4&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 5 & -8 \\\\ -4 & -8 \\end{pmatrix} $\n\nCompute th... | {
"type": "linear_algebra",
"seed": 1337,
"index": 155
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Evaluate: ((-90 + -690/23) * 15) + 6^3 - log_10(100000) + (36 mod 29) + floor(125/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-90 + -690/23) * 15) + 6^3 - log_10(100000) + (36 mod 29) + floor(125... | {
"type": "arithmetic",
"seed": 1337,
"index": 156
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute the indefinite integral: $\\int 1x^3 + -4x^2 + 10x + 12\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1x^3 + -4x^2 + 10x + 12\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 157
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Find the modular inverse of 11 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 158
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Evaluate: ((-189 + -135/15) * 3) + 6^5 - log_3(3) + (-414 mod 8) + ceil(96/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-189 + -135/15) * 3) + 6^5 - log_3(3) + (-414 mod 8) + ceil(96/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 159
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&7\\\\\\-3&5\\end{pmatrix},\\quad b=\\begin{pmatrix}-13\\\\\\43\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&7\\\\\\-3&5\\end{... | {
"type": "linear_algebra",
"seed": 1337,
"index": 160
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Evaluate: ((-111 + -54/3) * 8) + 3^2 - log_9(9) + (-324 mod 30) + round(-136/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-111 + -54/3) * 8) + 3^2 - log_9(9) + (-324 mod 30) + round(-136/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 161
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 17 + 157x = -418"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 17 + 157x = -418 $\n\nMove all terms to the left (standard form):\n$ 157x + 435 = 0 $\n\nIsolate the $x$ term:\n$ 157x = -435 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 162
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. -48 - 145x - 77 = -118x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48 - 145x - 77 = -118x^2 $\n\nMove all terms to the left (standard form):\n$ 118x^2 + -145x + -125 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 163
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Prove that $f(x,y)=\\frac12(3x^2+7y^2)+-5x+4y+2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+7y^2)+-5x+4y+2 $\n\n$ \\frac{\\partial^2 f... | {
"type": "optimization",
"seed": 1337,
"index": 164
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 50x - 127 - 37 = 175x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 50x - 127 - 37 = 175x^2 $\n\nMove all terms to the left (standard form):\n$ -175x^2 + 50x + -164 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 165
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((-101 + -518/14) * 20) + 8^3 - log_8(32768) + (334 mod 15) + floor(-187/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-101 + -518/14) * 20) + 8^3 - log_8(32768) + (334 mod 15) + floor(... | {
"type": "arithmetic",
"seed": 1337,
"index": 166
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Differentiate with respect to $x$: $f(x) = 6\\sin(7x) + 0\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6\\sin(7x) + 0\\cos(6x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\bo... | {
"type": "calculus",
"seed": 1337,
"index": 167
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute $(-4+-97) \\bmod 4$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-4+-97) \\bmod 4 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 168
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Compute the determinant: $A=\\begin{pmatrix}-8&9\\\\0&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-8&9\\\\\\0&-3\\end{pmatrix} $\n\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 169
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 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(\\fr... | {
"type": "trigonometry",
"seed": 1337,
"index": 170
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -3 - 167 - 152x = 24x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -3 - 167 - 152x = 24x^2 $\n\nMove all terms to the left (standard form):\n$ -24x^2 + -152x + -170 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 171
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 32x + 198x^2 + 139 = -30"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 32x + 198x^2 + 139 = -30 $\n\nMove all terms to the left (standard form):\n$ 198x^2 + 32x + 169 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 172
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Differentiate with respect to $x$: $f(x) = 1x^3 + -4x^2 + -4x + -1$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1x^3 + -4x^2 + -4x + -1 $\n\nApply the standard differentiation rules:\n$ f'(x) ... | {
"type": "calculus",
"seed": 1337,
"index": 173
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Differentiate with respect to $x$: $f(x) = 7e^{-4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7e^{-4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-28e^{-4x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 174
} |
[
{
"role": "user",
"content": "solve 18x^2 + 73x + 72 = -88"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 18x^2 + 73x + 72 = -88 $\n\nMove all terms to the left (standard form):\n$ 18x^2 + 73x + 160 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 175
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 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": 176
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the indefinite integral: $\\int -2x^3 + 1x^2 + -20x + 16\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2x^3 + 1x^2 + -20x + 16\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 177
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. 620x + 736 = -275"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 620x + 736 = -275 $\n\nMove all terms to the left (standard form):\n$ 620x + 1011 = 0 $\n\nIsolate the $x$ term:\n$ 620x = -1011 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 178
} |
[
{
"role": "user",
"content": "solve 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$ \\alpha = \\arctan(\\frac{\\sqrt{3}}{2}... | {
"type": "trigonometry",
"seed": 1337,
"index": 179
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. 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 value).\n$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 180
} |
[
{
"role": "user",
"content": "Can you compute this equation? 20 + 122 - 83x^2 = 171x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20 + 122 - 83x^2 = 171x $\n\nMove all terms to the left (standard form):\n$ -83x^2 + -171x + 142 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 181
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Prove that $(\\mathbb{Z}_19, +)$ is a group under addition modulo 19."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_19=\\{0,1,\\dots,18\\}$ with operation $+$ modulo $19$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 182
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((171 + 84/3) * 12) + 11^5 - log_10(1000) + (-253 mod 25) + ceil(166/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((171 + 84/3) * 12) + 11^5 - log_10(1000) + (-253 mod 25) + ce... | {
"type": "arithmetic",
"seed": 1337,
"index": 183
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-1&-5\\\\\\-4&0&3\\\\\\1&1&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-24\\\\\\12\\\\\\-8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=... | {
"type": "linear_algebra",
"seed": 1337,
"index": 184
} |
[
{
"role": "user",
"content": "Please evaluate and compute 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 185
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Compute the indefinite integral: $\\int (-3x + -3)e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + -3)e^{2x}\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 186
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Differentiate with respect to $x$: $f(x) = \\ln(2x + 3)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(2x + 3) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{2... | {
"type": "calculus",
"seed": 1337,
"index": 187
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. -5 + 67x - 54x^2 = -96"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -5 + 67x - 54x^2 = -96 $\n\nMove all terms to the left (standard form):\n$ -54x^2 + 67x + 91 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 188
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Differentiate with respect to $x$: $f(x) = -9\\sin(6x) + 0\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9\\sin(6x) + 0\\cos(1x) $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 189
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. 31x - 92 + 25x^2 = -84"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31x - 92 + 25x^2 = -84 $\n\nMove all terms to the left (standard form):\n$ 25x^2 + 31x + -8 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 190
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute the indefinite integral: $\\int -9e^{-4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -9e^{-4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if need... | {
"type": "calculus",
"seed": 1337,
"index": 191
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? -109x + 399 = 904"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -109x + 399 = 904 $\n\nMove all terms to the left (standard form):\n$ -109x + -505 = 0 $\n\nIsolate the $x$ term:\n$ -109x = 505 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 192
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 42x + 486 = 736"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 42x + 486 = 736 $\n\nMove all terms to the left (standard form):\n$ 42x + -250 = 0 $\n\nIsolate the $x$ term:\n$ 42x = 250 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 193
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute $(-191+72) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-191+72) \\bmod 8 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 194
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Find the modular inverse of 19 modulo 22, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{22}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 195
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-1&0\\\\\\-5&4&2\\\\\\3&-3&5\\end{pmatrix},\\quad b=\\begin{pmatrix}18\\\\\\-1\\\\\\-10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 196
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Prove that $(\\mathbb{Z}_4, +)$ is a group under addition modulo 4."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_4=\\{0,1,\\dots,3\\}$ with operation $+$ modulo $4$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then $(a... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 197
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Differentiate with respect to $x$: $f(x) = 2\\sin(9x) + 8\\cos(2x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2\\sin(9x) + 8\\cos(2x) $\n\nApply the standard differentiation rules:\n$ f'(x)... | {
"type": "calculus",
"seed": 1337,
"index": 198
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Prove that $f(x)=7x^2+-2x+10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+-2x+10$.\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": 199
} |
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