messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please work out this equation. -47x^2 + 168 + 89 = 185x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47x^2 + 168 + 89 = 185x $\n\nMove all terms to the left (standard form):\n$ -47x^2 + -185x + 257 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6100
} |
[
{
"role": "user",
"content": "Please solve this math problem. -50x^2 + 133 + 139 = 46x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50x^2 + 133 + 139 = 46x $\n\nMove all terms to the left (standard form):\n$ -50x^2 + -46x + 272 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6101
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&1&3\\\\\\0&-1&2\\\\\\1&-4&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}2\\\\\\3\\\\\\-1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6102
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac... | {
"type": "optimization",
"seed": 1337,
"index": 6103
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 832 - 542 = 277x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 832 - 542 = 277x $\n\nMove all terms to the left (standard form):\n$ -277x + 290 = 0 $\n\nIsolate the $x$ term:\n$ -277x = -290 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 6104
} |
[
{
"role": "user",
"content": "solve -941x + 654 = -220"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -941x + 654 = -220 $\n\nMove all terms to the left (standard form):\n$ -941x + 874 = 0 $\n\nIsolate the $x$ term:\n$ -941x = -874 $\n\nDivide both sides by the coefficient of $x$... | {
"type": "linear_equation",
"seed": 1337,
"index": 6105
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Find the modular inverse of 13 modulo 24, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{24}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6106
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((199 + -246/6) * 17) + 5^4 - log_5(3125) + (96 mod 4) + ceil(155/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((199 + -246/6) * 17) + 5^4 - log_5(3125) + (96 mod 4) + ceil(155/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6107
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 6108
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 6109
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Compute the indefinite integral: $\\int -6\\sin(4x) + -5\\cos(7x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -6\\sin(4x) + -5\\cos(7x)\\,dx $\n\nUse standard antiderivatives... | {
"type": "calculus",
"seed": 1337,
"index": 6110
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. 853 + 200 = 909x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 853 + 200 = 909x $\n\nMove all terms to the left (standard form):\n$ -909x + 1053 = 0 $\n\nIsolate the $x$ term:\n$ -909x = -1053 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6111
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. -187 - 273x = 435"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -187 - 273x = 435 $\n\nMove all terms to the left (standard form):\n$ -273x + -622 = 0 $\n\nIsolate the $x$ term:\n$ -273x = 622 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6112
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -37x + 113x^2 - 11 = -110"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37x + 113x^2 - 11 = -110 $\n\nMove all terms to the left (standard form):\n$ 113x^2 + -37x + 99 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6113
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 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 general s... | {
"type": "trigonometry",
"seed": 1337,
"index": 6114
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Find the modular inverse of 5 modulo 7, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{7}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity g... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6115
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Compute $(-26+0) \\bmod 20$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-26+0) \\bmod 20 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6116
} |
[
{
"role": "user",
"content": "Please evaluate and compute 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": 6117
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Differentiate with respect to $x$: $f(x) = -9e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-45e^{5x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 6118
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 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 gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 6119
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}7&-2\\\\3&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 7 & -2 \\\\ 3 & -5 \\end{pmatrix} $\n\nC... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6120
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Find the modular inverse of 7 modulo 11, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{11}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees int... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6121
} |
[
{
"role": "user",
"content": "Please solve this math problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&5\\\\\\8&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-20\\\\\\-17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&5\\\\\\8&3\\end{pmatrix} ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6122
} |
[
{
"role": "user",
"content": "Evaluate and solve the given 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(-\... | {
"type": "trigonometry",
"seed": 1337,
"index": 6123
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 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 $\n\nThe genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 6124
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((-49 + 45/5) * 17) + 2^4 - log_8(8) + (-38 mod 21) + round(54/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-49 + 45/5) * 17) + 2^4 - log_8(8) + (-38 mod 21) + round(54/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6125
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((54 + 285/15) * 18) + 2^5 - log_9(6561) + (-369 mod 4) + ceil(-47/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((54 + 285/15) * 18) + 2^5 - log_9(6561) + (-369 mod 4) + ceil(-47/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 6126
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the indefinite integral: $\\int (-1x + -9)e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-1x + -9)e^{5x}\\,dx $\n\nUse standard antiderivatives (and integration by p... | {
"type": "calculus",
"seed": 1337,
"index": 6127
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Solve for $x$ (in radians): cos(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(1) = 0 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 6128
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Evaluate: ((-146 + 198/22) * 10) + 6^3 - log_3(9) + (-380 mod 16) + round(-3/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-146 + 198/22) * 10) + 6^3 - log_3(9) + (-380 mod 16) + round(-3/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 6129
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Solve for $x$ (in radians): tan(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(-1) = -0.785398 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 6130
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the indefinite integral: $\\int \\ln(8x + -7)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + -7)\\,dx $\n\nUse standard antiderivatives (and integration by parts i... | {
"type": "calculus",
"seed": 1337,
"index": 6131
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Evaluate: ((-88 + 200/25) * 20) + 6^5 - log_5(15625) + (329 mod 16) + round(85/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-88 + 200/25) * 20) + 6^5 - log_5(15625) + (329 mod 16) + round(85/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 6132
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 17 - 37x^2 - 26x = 129"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 17 - 37x^2 - 26x = 129 $\n\nMove all terms to the left (standard form):\n$ -37x^2 + -26x + -112 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6133
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 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) = -0.785... | {
"type": "trigonometry",
"seed": 1337,
"index": 6134
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -27x - 65 + 170x^2 = -80"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -27x - 65 + 170x^2 = -80 $\n\nMove all terms to the left (standard form):\n$ 170x^2 + -27x + 15 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6135
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((-28 + -703/19) * 10) + 11^4 - log_8(4096) + (-350 mod 20) + ceil(170/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-28 + -703/19) * 10) + 11^4 - log_8(4096) + (-350 mod 20) + ceil(170/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 6136
} |
[
{
"role": "user",
"content": "solve: \n\n Compute $(88+-38) \\bmod 18$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (88+-38) \\bmod 18 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$ (a+b)\\bmod n = ((a... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6137
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. 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 = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 6138
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. + 89x + 93x^2 = 30"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ + 89x + 93x^2 = 30 $\n\nMove all terms to the left (standard form):\n$ 93x^2 + 89x + -30 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6139
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. -146x - 502 = 822"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -146x - 502 = 822 $\n\nMove all terms to the left (standard form):\n$ -146x + -1324 = 0 $\n\nIsolate the $x$ term:\n$ -146x = 1324 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 6140
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Prove that $(\\mathbb{Z}_20, +)$ is a group under addition modulo 20."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_20=\\{0,1,\\dots,19\\}$ with operation $+$ modulo $20$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6141
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Prove that $f(x,y)=\\frac12(8x^2+6y^2)+2x+-6y+8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(8x^2+6y^2)+2x+-6y+8 $\n\n$ \\frac{\\partial^2 f... | {
"type": "optimization",
"seed": 1337,
"index": 6142
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Prove that $f(x,y)=\\frac12(10x^2+8y^2)+-4x+1y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+8y^2)+-4x+1y+-5 $\n\n$ \\frac{\\partial^2 f... | {
"type": "optimization",
"seed": 1337,
"index": 6143
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute $(-156+48) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-156+48) \\bmod 2 $\n\nUse the rule that addition is compatible with redu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6144
} |
[
{
"role": "user",
"content": "Please find the value of this math 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 6145
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((-191 + -360/8) * 19) + 8^4 - log_7(7) + (202 mod 23) + round(-31/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-191 + -360/8) * 19) + 8^4 - log_7(7) + (202 mod 23) + round(-31... | {
"type": "arithmetic",
"seed": 1337,
"index": 6146
} |
[
{
"role": "user",
"content": "Compute the correct solution for 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 $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 6147
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. 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 ... | {
"type": "trigonometry",
"seed": 1337,
"index": 6148
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Compute the determinant: $A=\\begin{pmatrix}-3&6\\\\7&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&6\\\\\\7&8\\end{pmatrix} $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6149
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -4 + 149x^2 + 20x = -167"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4 + 149x^2 + 20x = -167 $\n\nMove all terms to the left (standard form):\n$ 149x^2 + 20x + 163 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6150
} |
[
{
"role": "user",
"content": "Compute the solution to 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 gener... | {
"type": "trigonometry",
"seed": 1337,
"index": 6151
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute the indefinite integral: $\\int -7e^{-4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -7e^{-4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if neede... | {
"type": "calculus",
"seed": 1337,
"index": 6152
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((95 + -408/12) * 18) + 6^2 - log_7(117649) + (63 mod 10) + round(-29/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((95 + -408/12) * 18) + 6^2 - log_7(117649) + (63 mod 10) + round(-29/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 6153
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -3 - 56 + 86x = 42x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -3 - 56 + 86x = 42x^2 $\n\nMove all terms to the left (standard form):\n$ -42x^2 + 86x + -59 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6154
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Compute $(170+167) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (170+167) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction modu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6155
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 6156
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Differentiate with respect to $x$: $f(x) = -2e^{-4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2e^{-4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{8e^{-4x}} ... | {
"type": "calculus",
"seed": 1337,
"index": 6157
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-88 + -15/3) * 18) + 5^2 - log_8(32768) + (295 mod 6) + round(-196/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-88 + -15/3) * 18) + 5^2 - log_8(32768) + (295 mod 6) + round(-196/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 6158
} |
[
{
"role": "user",
"content": "Compute the result for the following 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 6159
} |
[
{
"role": "user",
"content": "Please calculate this equation. 3 + 172x + 167 = 88x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 3 + 172x + 167 = 88x^2 $\n\nMove all terms to the left (standard form):\n$ -88x^2 + 172x + 170 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6160
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-2&1\\\\\\-3&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-6\\\\\\27\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-2&1\\\\\\-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6161
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute $(194+17) \\bmod 7$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (194+17) \\bmod 7 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6162
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 486 - 302 = -671x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 486 - 302 = -671x $\n\nMove all terms to the left (standard form):\n$ 671x + 184 = 0 $\n\nIsolate the $x$ term:\n$ 671x = -184 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6163
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Compute the indefinite integral: $\\int \\ln(4x + -9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(4x + -9)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 6164
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 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(-... | {
"type": "trigonometry",
"seed": 1337,
"index": 6165
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Differentiate with respect to $x$: $f(x) = -6\\sin(6x) + 8\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6\\sin(6x) + 8\\cos(1x) $\n\nApply the standard differentiation rules... | {
"type": "calculus",
"seed": 1337,
"index": 6166
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the indefinite integral: $\\int 2x^3 + 9x^2 + 1x + -10\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2x^3 + 9x^2 + 1x + -10\\,dx $\n\nUse standard antiderivatives (and int... | {
"type": "calculus",
"seed": 1337,
"index": 6167
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 512 - 806x = 211"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 512 - 806x = 211 $\n\nMove all terms to the left (standard form):\n$ -806x + 301 = 0 $\n\nIsolate the $x$ term:\n$ -806x = -301 $\n\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 6168
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. -25 - 94x^2 - 163x = -141"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -25 - 94x^2 - 163x = -141 $\n\nMove all terms to the left (standard form):\n$ -94x^2 + -163x + 116 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6169
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute the determinant: $A=\\begin{pmatrix}4&2\\\\4&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}4&2\\\\\\4&-2\\end{pmatrix} $\n\nUse $\\d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6170
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -140 + 348x = 29"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -140 + 348x = 29 $\n\nMove all terms to the left (standard form):\n$ 348x + -169 = 0 $\n\nIsolate the $x$ term:\n$ 348x = 169 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6171
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. -2 + 98 + 83x^2 = -70x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2 + 98 + 83x^2 = -70x $\n\nMove all terms to the left (standard form):\n$ 83x^2 + 70x + 96 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6172
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = 2x^3 + 2x^2 + -14x + -5$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + 2x^2 + -14x + -5 $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 6173
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((139 + 1056/22) * 15) + 3^5 - log_4(4096) + (-366 mod 9) + floor(162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((139 + 1056/22) * 15) + 3^5 - log_4(4096) + (-366 mod 9) + floor(162/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6174
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? 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 = \... | {
"type": "trigonometry",
"seed": 1337,
"index": 6175
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((71 + -850/25) * 20) + 11^2 - log_9(6561) + (32 mod 10) + round(103/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((71 + -850/25) * 20) + 11^2 - log_9(6561) + (32 mod 10) + round(103/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 6176
} |
[
{
"role": "user",
"content": "Can you compute this equation? Compute the indefinite integral: $\\int \\ln(1x + 8)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + 8)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \... | {
"type": "calculus",
"seed": 1337,
"index": 6177
} |
[
{
"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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 6178
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((126 + -377/13) * 12) + 7^4 - log_2(8) + (453 mod 20) + floor(-143/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((126 + -377/13) * 12) + 7^4 - log_2(8) + (453 mod 20) + floor(-143/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 6179
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Differentiate with respect to $x$: $f(x) = -4x^3 + -3x^2 + 16x + -1$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4x^3 + -3x^2 + 16x + -1 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\... | {
"type": "calculus",
"seed": 1337,
"index": 6180
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 9x + 54 + 89 = 126x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 9x + 54 + 89 = 126x^2 $\n\nMove all terms to the left (standard form):\n$ -126x^2 + 9x + 143 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6181
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Differentiate with respect to $x$: $f(x) = \\ln(7x + -9)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(7x + -9) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\... | {
"type": "calculus",
"seed": 1337,
"index": 6182
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. -37x^2 + 146 + 21x = 153"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37x^2 + 146 + 21x = 153 $\n\nMove all terms to the left (standard form):\n$ -37x^2 + 21x + -7 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6183
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. 838x + 959 = -746"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 838x + 959 = -746 $\n\nMove all terms to the left (standard form):\n$ 838x + 1705 = 0 $\n\nIsolate the $x$ term:\n$ 838x = -1705 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 6184
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. 16x - 32 - 118x^2 = -176"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 16x - 32 - 118x^2 = -176 $\n\nMove all terms to the left (standard form):\n$ -118x^2 + 16x + 144 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6185
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Compute $(104+-51) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (104+-51) \\bmod 12 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6186
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 998x - 129 = 752"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 998x - 129 = 752 $\n\nMove all terms to the left (standard form):\n$ 998x + -881 = 0 $\n\nIsolate the $x$ term:\n$ 998x = 881 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 6187
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&0\\\\\\-6&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-27\\\\\\18\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&0\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6188
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 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\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6189
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Prove that $f(x)=5x^2+-6x+8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-6x+8$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n... | {
"type": "optimization",
"seed": 1337,
"index": 6190
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Differentiate with respect to $x$: $f(x) = 1e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{1e^{1x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 6191
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((-130 + -378/14) * 20) + 7^5 - log_9(59049) + (-2 mod 22) + ceil(-88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-130 + -378/14) * 20) + 7^5 - log_9(59049) + (-2 mod 22) + ceil(-88... | {
"type": "arithmetic",
"seed": 1337,
"index": 6192
} |
[
{
"role": "user",
"content": "Can you compute this equation? Prove that $f(x,y)=\\frac12(6x^2+1y^2)+-3x+1y+-8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+1y^2)+-3x+1y+-8 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2... | {
"type": "optimization",
"seed": 1337,
"index": 6193
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Prove that $(\\mathbb{Z}_25, +)$ is a group under addition modulo 25."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_25=\\{0,1,\\dots,24\\}$ with operation $+$ modulo $25$.\n\n**Closure:** If $a,b\\in\\mathbb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6194
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve for $x$ (in radians): cos(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-1) = 3.14159 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 6195
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the indefinite integral: $\\int -2e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 6196
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Prove that $f(x)=7x^2+1x+-7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+1x+-7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 14x... | {
"type": "optimization",
"seed": 1337,
"index": 6197
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 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 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 6198
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 33x + 133 - 173 = -71x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33x + 133 - 173 = -71x^2 $\n\nMove all terms to the left (standard form):\n$ 71x^2 + 33x + -40 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6199
} |
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