messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve this equation accurately. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3100
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((35 + 138/6) * 10) + 10^2 - log_8(8) + (288 mod 23) + round(-109/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((35 + 138/6) * 10) + 10^2 - log_8(8) + (288 mod 23) + round(-109/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 3101
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((86 + -357/21) * 14) + 5^3 - log_2(16) + (-222 mod 11) + ceil(139/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((86 + -357/21) * 14) + 5^3 - log_2(16) + (-222 mod 11) + ceil(139/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 3102
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 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": 3103
} |
[
{
"role": "user",
"content": "Solve the math equation and present 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": 3104
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 40x - 33 + 32 = -90x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 40x - 33 + 32 = -90x^2 $\n\nMove all terms to the left (standard form):\n$ 90x^2 + 40x + -1 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3105
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -28x - 65 - 64x^2 = -133"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -28x - 65 - 64x^2 = -133 $\n\nMove all terms to the left (standard form):\n$ -64x^2 + -28x + 68 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3106
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical 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) = -1.57... | {
"type": "trigonometry",
"seed": 1337,
"index": 3107
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((164 + -259/7) * 3) + 7^5 - log_9(6561) + (124 mod 22) + round(8/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((164 + -259/7) * 3) + 7^5 - log_9(6561) + (124 mod 22) + round(8/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 3108
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((-72 + -336/7) * 7) + 3^4 - log_4(1024) + (112 mod 22) + round(-8/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-72 + -336/7) * 7) + 3^4 - log_4(1024) + (112 mod 22) + round(-8/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 3109
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -11x - 109 + 143x^2 = -5"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -11x - 109 + 143x^2 = -5 $\n\nMove all terms to the left (standard form):\n$ 143x^2 + -11x + -104 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3110
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 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 $\n\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 3111
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 343x - 638 = 108"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 343x - 638 = 108 $\n\nMove all terms to the left (standard form):\n$ 343x + -746 = 0 $\n\nIsolate the $x$ term:\n$ 343x = 746 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 3112
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. -10x^2 - 24 - 194 = 18x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -10x^2 - 24 - 194 = 18x $\n\nMove all terms to the left (standard form):\n$ -10x^2 + -18x + -218 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3113
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&-9\\\\6&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & -9 \\\\ 6 & -9 \\end{pmatrix} $\n\nCompu... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3114
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute $(143+-27) \\bmod 4$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (143+-27) \\bmod 4 $\n\nUse the rule that addition is compatible with redu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3115
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the determinant: $A=\\begin{pmatrix}-3&-2\\\\6&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&-2\\\\\\6&-8\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3116
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. -46x^2 - 90x + 42 = -106"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -46x^2 - 90x + 42 = -106 $\n\nMove all terms to the left (standard form):\n$ -46x^2 + -90x + 148 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3117
} |
[
{
"role": "user",
"content": "Solve the equation shown below. -804x + 779 = -26"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -804x + 779 = -26 $\n\nMove all terms to the left (standard form):\n$ -804x + 805 = 0 $\n\nIsolate the $x$ term:\n$ -804x = -805 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 3118
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. -27x - 47 - 52x^2 = -101"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -27x - 47 - 52x^2 = -101 $\n\nMove all terms to the left (standard form):\n$ -52x^2 + -27x + 54 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3119
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute the determinant: $A=\\begin{pmatrix}-8&-2\\\\8&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-8&-2\\\\\\8&-4\\end{pmatrix} $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3120
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&-1&0\\\\\\4&5&-3\\\\\\-5&-2&0\\end{pmatrix},\\quad b=\\begin{pmatrix}0\\\\\\-3\\\\\\-1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3121
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 49x^2 - 8 + 100x = 62"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 49x^2 - 8 + 100x = 62 $\n\nMove all terms to the left (standard form):\n$ 49x^2 + 100x + -70 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3122
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Prove that $(\\mathbb{Z}_6, +)$ is a group under addition modulo 6."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_6=\\{0,1,\\dots,5\\}$ with operation $+$ modulo $6$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3123
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Compute the indefinite integral: $\\int 3x^3 + 4x^2 + 4x + -12\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3x^3 + 4x^2 + 4x + -12\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 3124
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 13 + 3x^2 - 136x = 133"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13 + 3x^2 - 136x = 133 $\n\nMove all terms to the left (standard form):\n$ 3x^2 + -136x + -120 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3125
} |
[
{
"role": "user",
"content": "Please solve this math problem. 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$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3126
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 447x + 908 = -124"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 447x + 908 = -124 $\n\nMove all terms to the left (standard form):\n$ 447x + 1032 = 0 $\n\nIsolate the $x$ term:\n$ 447x = -1032 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3127
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Compute the indefinite integral: $\\int \\ln(7x + -3)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(7x + -3)\\,dx $\n\nUse standard antiderivatives (and integration by parts if n... | {
"type": "calculus",
"seed": 1337,
"index": 3128
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. -159x + 312 = -330"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -159x + 312 = -330 $\n\nMove all terms to the left (standard form):\n$ -159x + 642 = 0 $\n\nIsolate the $x$ term:\n$ -159x = -642 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 3129
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 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} & \\f... | {
"type": "optimization",
"seed": 1337,
"index": 3130
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Differentiate with respect to $x$: $f(x) = -8e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -8e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-8e^{1x}} $... | {
"type": "calculus",
"seed": 1337,
"index": 3131
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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 $a,b\\in\\mathbb{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3132
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((-199 + 238/7) * 16) + 12^4 - log_9(531441) + (63 mod 17) + floor(-193/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-199 + 238/7) * 16) + 12^4 - log_9(531441) + (63 mod 17) + floor(... | {
"type": "arithmetic",
"seed": 1337,
"index": 3133
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((-194 + 1225/25) * 6) + 11^4 - log_4(16) + (-43 mod 19) + ceil(188/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-194 + 1225/25) * 6) + 11^4 - log_4(16) + (-43 mod 19) + ceil(188/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3134
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 280x + 755 = -239"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 280x + 755 = -239 $\n\nMove all terms to the left (standard form):\n$ 280x + 994 = 0 $\n\nIsolate the $x$ term:\n$ 280x = -994 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3135
} |
[
{
"role": "user",
"content": "Work out the result of this equation. -936 + 725 = 433x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -936 + 725 = 433x $\n\nMove all terms to the left (standard form):\n$ -433x + -211 = 0 $\n\nIsolate the $x$ term:\n$ -433x = 211 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 3136
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((-100 + 486/18) * 1) + 5^2 - log_9(81) + (-9 mod 17) + round(-107/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-100 + 486/18) * 1) + 5^2 - log_9(81) + (-9 mod 17) + round(-107/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3137
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 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": 3138
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 3139
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute the indefinite integral: $\\int 6e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int 6e^{... | {
"type": "calculus",
"seed": 1337,
"index": 3140
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Compute the indefinite integral: $\\int -3x^3 + 2x^2 + -10x + 10\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3x^3 + 2x^2 + -10x + 10\\,dx $\n\nUse standard antiderivatives (... | {
"type": "calculus",
"seed": 1337,
"index": 3141
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Evaluate: ((77 + -405/15) * 6) + 4^4 - log_6(1296) + (-148 mod 22) + floor(193/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((77 + -405/15) * 6) + 4^4 - log_6(1296) + (-148 mod 22) + floor(193/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 3142
} |
[
{
"role": "user",
"content": "Compute and determine the solution 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 va... | {
"type": "trigonometry",
"seed": 1337,
"index": 3143
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha... | {
"type": "trigonometry",
"seed": 1337,
"index": 3144
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Prove that $f(x)=1x^2+1x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+1x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 2... | {
"type": "optimization",
"seed": 1337,
"index": 3145
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((23 + 782/23) * 14) + 2^4 - log_5(25) + (-414 mod 7) + round(17/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((23 + 782/23) * 14) + 2^4 - log_5(25) + (-414 mod 7) + round(17/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3146
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((140 + -115/5) * 20) + 3^4 - log_2(4) + (204 mod 17) + ceil(-104/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((140 + -115/5) * 20) + 3^4 - log_2(4) + (204 mod 17) + ceil(-104/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 3147
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Find the modular inverse of 11 modulo 12, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{12}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees i... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3148
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -39 - 159 + 128x^2 = 41x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -39 - 159 + 128x^2 = 41x $\n\nMove all terms to the left (standard form):\n$ 128x^2 + -41x + -198 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3149
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 18x^2 - 126 + 24 = -190x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 18x^2 - 126 + 24 = -190x $\n\nMove all terms to the left (standard form):\n$ 18x^2 + 190x + -102 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3150
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal val... | {
"type": "trigonometry",
"seed": 1337,
"index": 3151
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 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{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 3152
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute the determinant: $A=\\begin{pmatrix}6&3\\\\1&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&3\\\\\\1&-9\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3153
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((123 + -52/4) * 13) + 8^4 - log_6(36) + (-380 mod 30) + round(-46/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((123 + -52/4) * 13) + 8^4 - log_6(36) + (-380 mod 30) + round(-46/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3154
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&-3&2\\\\\\-5&1&-1\\\\\\0&-5&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}13\\\\\\-21\\\\\\16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3155
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Differentiate with respect to $x$: $f(x) = \\ln(5x + 6)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(5x + 6) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{... | {
"type": "calculus",
"seed": 1337,
"index": 3156
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -102 + 839x = 602"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -102 + 839x = 602 $\n\nMove all terms to the left (standard form):\n$ 839x + -704 = 0 $\n\nIsolate the $x$ term:\n$ 839x = 704 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 3157
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -147x + 500 = 478"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -147x + 500 = 478 $\n\nMove all terms to the left (standard form):\n$ -147x + 22 = 0 $\n\nIsolate the $x$ term:\n$ -147x = -22 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3158
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((-51 + -36/12) * 5) + 4^5 - log_9(9) + (-364 mod 10) + round(179/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-51 + -36/12) * 5) + 4^5 - log_9(9) + (-364 mod 10) + round(179/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 3159
} |
[
{
"role": "user",
"content": "Find the value that satisfies 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 $\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3160
} |
[
{
"role": "user",
"content": "Please solve this math problem. Differentiate with respect to $x$: $f(x) = \\ln(3x + -2)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(3x + -2) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{3}{3x + -2}... | {
"type": "calculus",
"seed": 1337,
"index": 3161
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Differentiate with respect to $x$: $f(x) = 4x^3 + 3x^2 + 14x + 12$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4x^3 + 3x^2 + 14x + 12 $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 3162
} |
[
{
"role": "user",
"content": "Work out the result of this equation. -26x + 18 + 171 = -46x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -26x + 18 + 171 = -46x^2 $\n\nMove all terms to the left (standard form):\n$ 46x^2 + -26x + 189 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3163
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Prove that $f(x,y)=\\frac12(3x^2+6y^2)+-2x+5y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+6y^2)+-2x+5y+-2 $\n\n$ \\frac{\\partial^2 f}{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 3164
} |
[
{
"role": "user",
"content": "solve: Prove that $f(x,y)=\\frac12(4x^2+3y^2)+-5x+6y+10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+3y^2)+-5x+6y+10 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 4,\\quad \\frac{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 3165
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe general s... | {
"type": "trigonometry",
"seed": 1337,
"index": 3166
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -878 + 364x = -329"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -878 + 364x = -329 $\n\nMove all terms to the left (standard form):\n$ 364x + -549 = 0 $\n\nIsolate the $x$ term:\n$ 364x = 549 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 3167
} |
[
{
"role": "user",
"content": "solve: -36x - 64 - 85x^2 = -170"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x - 64 - 85x^2 = -170 $\n\nMove all terms to the left (standard form):\n$ -85x^2 + -36x + 106 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3168
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -894x + 782 = -453"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -894x + 782 = -453 $\n\nMove all terms to the left (standard form):\n$ -894x + 1235 = 0 $\n\nIsolate the $x$ term:\n$ -894x = -1235 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 3169
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Prove that $f(x,y)=\\frac12(5x^2+3y^2)+5x+-5y+-7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+3y^2)+5x+-5y+-7 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 3170
} |
[
{
"role": "user",
"content": "Find the correct solution for 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 = \\arcsi... | {
"type": "trigonometry",
"seed": 1337,
"index": 3171
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&1\\\\\\2&2\\end{pmatrix},\\quad b=\\begin{pmatrix}-30\\\\\\4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&1\\\\\\2&2\\end{pmatrix} ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3172
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Find the modular inverse of 3 modulo 10, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{10}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarante... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3173
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 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 gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 3174
} |
[
{
"role": "user",
"content": "Determine the result of the 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... | {
"type": "optimization",
"seed": 1337,
"index": 3175
} |
[
{
"role": "user",
"content": "solve: Solve for $x$ (in radians): tan(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(-\\frac{1}{2}) = -0.463648 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 3176
} |
[
{
"role": "user",
"content": "Can you compute this equation? Find $A^{-1}$ for $A=\\begin{pmatrix}7&-7\\\\0&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 7 & -7 \\\\ 0 & 4 \\end{pmatrix} $\n\nCompute the determinant: $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3177
} |
[
{
"role": "user",
"content": "Work out the result of this equation. 953x - 282 = -765"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 953x - 282 = -765 $\n\nMove all terms to the left (standard form):\n$ 953x + 483 = 0 $\n\nIsolate the $x$ term:\n$ 953x = -483 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 3178
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Find the modular inverse of 2 modulo 5, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $2\\cdot a^{-1} \\equiv 1 \\pmod{5}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3179
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Evaluate: ((-153 + -42/21) * 19) + 8^4 - log_3(3) + (184 mod 23) + floor(15/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-153 + -42/21) * 19) + 8^4 - log_3(3) + (184 mod 23) + floor(15/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 3180
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-39 + -147/21) * 6) + 3^4 - log_5(3125) + (241 mod 3) + round(-155/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-39 + -147/21) * 6) + 3^4 - log_5(3125) + (241 mod 3) + round(-155/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 3181
} |
[
{
"role": "user",
"content": "Please work out this equation. 24 + 12 - 51x^2 = -72x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 24 + 12 - 51x^2 = -72x $\n\nMove all terms to the left (standard form):\n$ -51x^2 + 72x + 36 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3182
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Prove that $(\\mathbb{Z}_21, +)$ is a group under addition modulo 21."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_21=\\{0,1,\\dots,20\\}$ with operation $+$ modulo $21$.\n\n**Closure:** If $a,b\\in\\mathbb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3183
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? 29 + 44x^2 - 200 = 97x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 29 + 44x^2 - 200 = 97x $\n\nMove all terms to the left (standard form):\n$ 44x^2 + -97x + -171 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3184
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Find the modular inverse of 4 modulo 13, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{13}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3185
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((-172 + -102/17) * 6) + 2^2 - log_10(10000) + (416 mod 8) + floor(-124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-172 + -102/17) * 6) + 2^2 - log_10(10000) + (416 mod 8) + floor(-124/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3186
} |
[
{
"role": "user",
"content": "solve: \n\n Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&-4&-5\\\\\\-3&-2&-3\\\\\\4&-1&3\\end{pmatrix},\\quad b=\\begin{pmatrix}2\\\\\\11\\\\\\-20\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by Gaussian eliminatio... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3187
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Compute the determinant: $A=\\begin{pmatrix}-7&7\\\\-4&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&7\\\\\\-4&9\\end{pmatrix}... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3188
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-1&7\\\\\\7&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}9\\\\\\-63\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-1&7\\\\\\7... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3189
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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$ \\alpha = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 3190
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 44x^2 + 141 - 166x = 133"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 44x^2 + 141 - 166x = 133 $\n\nMove all terms to the left (standard form):\n$ 44x^2 + -166x + 8 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3191
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute the indefinite integral: $\\int \\ln(1x + -9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + -9)\\,dx $\n\nUse standard antiderivatives (and integration... | {
"type": "calculus",
"seed": 1337,
"index": 3192
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 411 - 393 = 380x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 411 - 393 = 380x $\n\nMove all terms to the left (standard form):\n$ -380x + 18 = 0 $\n\nIsolate the $x$ term:\n$ -380x = -18 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 3193
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Evaluate: ((-198 + 55/11) * 19) + 12^3 - log_9(531441) + (-9 mod 30) + ceil(134/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-198 + 55/11) * 19) + 12^3 - log_9(531441) + (-9 mod 30) + ceil(134/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3194
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 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": 3195
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Differentiate with respect to $x$: $f(x) = 4\\sin(9x) + 5\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4\\sin(9x) + 5\\cos(4x) $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 3196
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 38 + 174x^2 + 45x = -125"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38 + 174x^2 + 45x = -125 $\n\nMove all terms to the left (standard form):\n$ 174x^2 + 45x + 163 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3197
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((9 + 132/11) * 19) + 11^3 - log_2(64) + (-50 mod 2) + floor(114/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((9 + 132/11) * 19) + 11^3 - log_2(64) + (-50 mod 2) + floor(114/2) $\n\nCompute each comp... | {
"type": "arithmetic",
"seed": 1337,
"index": 3198
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((-141 + 391/17) * 1) + 12^2 - log_5(25) + (184 mod 18) + round(-195/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-141 + 391/17) * 1) + 12^2 - log_5(25) + (184 mod 18) + round(-195/2) $\n\nCompute each component:\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3199
} |
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