messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Resolve this equation and give the result. -34 + 115x + 37 = -109x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -34 + 115x + 37 = -109x^2 $\n\nMove all terms to the left (standard form):\n$ 109x^2 + 115x + 3 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8100
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&9\\\\\\-5&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-27\\\\\\51\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&9\\\\\\-5&3\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8101
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((-31 + -104/8) * 1) + 8^3 - log_10(10000) + (-452 mod 12) + floor(49/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-31 + -104/8) * 1) + 8^3 - log_10(10000) + (-452 mod 12) + floor(49/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 8102
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Compute the indefinite integral: $\\int (-1x + 3)e^{6x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-1x + 3)e^{6x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int (-1x... | {
"type": "calculus",
"seed": 1337,
"index": 8103
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&-5\\\\\\-6&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}-75\\\\\\-18\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&-5\\\\\\-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8104
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -22 + 183x^2 - 176x = -69"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -22 + 183x^2 - 176x = -69 $\n\nMove all terms to the left (standard form):\n$ 183x^2 + -176x + 47 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8105
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -15 - 103x + 126x^2 = 200"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15 - 103x + 126x^2 = 200 $\n\nMove all terms to the left (standard form):\n$ 126x^2 + -103x + -215 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8106
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 33 + 50x - 162x^2 = -107"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33 + 50x - 162x^2 = -107 $\n\nMove all terms to the left (standard form):\n$ -162x^2 + 50x + 140 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8107
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -31 + 57 - 49x^2 = -87x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -31 + 57 - 49x^2 = -87x $\n\nMove all terms to the left (standard form):\n$ -49x^2 + 87x + 26 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8108
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -22 - 133x - 198x^2 = 6"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -22 - 133x - 198x^2 = 6 $\n\nMove all terms to the left (standard form):\n$ -198x^2 + -133x + -28 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8109
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Prove that $f(x,y)=\\frac12(3x^2+8y^2)+-3x+3y+-3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+8y^2)+-3x+3y+-3 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 8110
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. -912 + 310 = 357x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -912 + 310 = 357x $\n\nMove all terms to the left (standard form):\n$ -357x + -602 = 0 $\n\nIsolate the $x$ term:\n$ -357x = 602 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 8111
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Prove that $f(x,y)=\\frac12(5x^2+2y^2)+-3x+4y+-6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+2y^2)+-3x+4y+-6 $\n\n$ \\frac{\\partial^... | {
"type": "optimization",
"seed": 1337,
"index": 8112
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. 46x - 26 + 36x^2 = 1"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 46x - 26 + 36x^2 = 1 $\n\nMove all terms to the left (standard form):\n$ 36x^2 + 46x + -27 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8113
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. -13x + 81 + 41x^2 = -41"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -13x + 81 + 41x^2 = -41 $\n\nMove all terms to the left (standard form):\n$ 41x^2 + -13x + 122 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8114
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\... | {
"type": "optimization",
"seed": 1337,
"index": 8115
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Compute the indefinite integral: $\\int 4x^3 + 6x^2 + 5x + -2\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4x^3 + 6x^2 + 5x + -2\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 8116
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Prove that $f(x)=3x^2+-5x+-3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+-5x+-3$.\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": 8117
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Compute $(130+144) \\bmod 22$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (130+144) \\bmod 22 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 8118
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 45x + 138x^2 + 17 = 184"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 45x + 138x^2 + 17 = 184 $\n\nMove all terms to the left (standard form):\n$ 138x^2 + 45x + -167 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8119
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-2&-5\\\\\\2&1&4\\\\\\-4&-5&3\\end{pmatrix},\\quad b=\\begin{pmatrix}26\\\\\\-13\\\\\\24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8120
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Differentiate with respect to $x$: $f(x) = 4e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{4e^{1x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 8121
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Differentiate with respect to $x$: $f(x) = -4x^3 + 4x^2 + -2x + 17$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4x^3 + 4x^2 + -2x + 17 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 8122
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 8123
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. 110 - 133x = 712"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 110 - 133x = 712 $\n\nMove all terms to the left (standard form):\n$ -133x + -602 = 0 $\n\nIsolate the $x$ term:\n$ -133x = 602 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 8124
} |
[
{
"role": "user",
"content": "solve Solve for $x$ (in radians): sin(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(\\frac{1}{2}) = 0.523599 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 8125
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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 $a,b\\in\\mathbb{Z}_n$, th... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 8126
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute the indefinite integral: $\\int -4\\sin(6x) + -7\\cos(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4\\sin(6x) + -7\\cos(1x)\\,dx $\n\nUse standard antiderivat... | {
"type": "calculus",
"seed": 1337,
"index": 8127
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Prove that $(\\mathbb{Z}_18, +)$ is a group under addition modulo 18."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_18=\\{0,1,\\dots,17\\}$ with operation $+$ modulo $18$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 8128
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Evaluate: ((176 + -247/13) * 6) + 3^5 - log_8(32768) + (372 mod 8) + floor(163/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((176 + -247/13) * 6) + 3^5 - log_8(32768) + (372 mod 8) + floor(163/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 8129
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Compute the indefinite integral: $\\int -5x^3 + 0x^2 + -2x + 4\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5x^3 + 0x^2 + -2x + 4\\,dx $\n\nUse standard antiderivatives (and integra... | {
"type": "calculus",
"seed": 1337,
"index": 8130
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Differentiate with respect to $x$: $f(x) = 4e^{-3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4e^{-3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-12e^{-3x}} $"
}... | {
"type": "calculus",
"seed": 1337,
"index": 8131
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 346 + 54 = -608x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 346 + 54 = -608x $\n\nMove all terms to the left (standard form):\n$ 608x + 400 = 0 $\n\nIsolate the $x$ term:\n$ 608x = -400 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 8132
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 78 + 591 = -133x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 78 + 591 = -133x $\n\nMove all terms to the left (standard form):\n$ 133x + 669 = 0 $\n\nIsolate the $x$ term:\n$ 133x = -669 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 8133
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((-164 + -630/21) * 5) + 5^2 - log_8(8) + (-272 mod 24) + floor(-168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-164 + -630/21) * 5) + 5^2 - log_8(8) + (-272 mod 24) + floor(-168/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 8134
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-... | {
"type": "optimization",
"seed": 1337,
"index": 8135
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. -13 + 152 + 13x^2 = 162x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -13 + 152 + 13x^2 = 162x $\n\nMove all terms to the left (standard form):\n$ 13x^2 + -162x + 139 = 0 $\n\nApply the quadr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8136
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Evaluate: ((166 + 112/16) * 8) + 5^5 - log_7(16807) + (412 mod 3) + ceil(81/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((166 + 112/16) * 8) + 5^5 - log_7(16807) + (412 mod 3) + ceil(81/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 8137
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. 115 + 740x = -443"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 115 + 740x = -443 $\n\nMove all terms to the left (standard form):\n$ 740x + 558 = 0 $\n\nIsolate the $x$ term:\n$ 740x = -558 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 8138
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 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$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 8139
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Differentiate with respect to $x$: $f(x) = -3x^3 + 5x^2 + -18x + -12$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + 5x^2 + -18x + -12 $\n\nApply the standard differentiation rules:\n$ f'... | {
"type": "calculus",
"seed": 1337,
"index": 8140
} |
[
{
"role": "user",
"content": "Can you compute this equation? Prove that $f(x)=1x^2+4x+-4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+4x+-4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 2x + 4 $\n... | {
"type": "optimization",
"seed": 1337,
"index": 8141
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Evaluate: ((-72 + 231/11) * 17) + 2^2 - log_7(343) + (96 mod 17) + floor(-165/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-72 + 231/11) * 17) + 2^2 - log_7(343) + (96 mod 17) + floor(-165/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 8142
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 16x + 19x^2 - 72 = -137"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 16x + 19x^2 - 72 = -137 $\n\nMove all terms to the left (standard form):\n$ 19x^2 + 16x + 65 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8143
} |
[
{
"role": "user",
"content": "Please work out this equation. Find the modular inverse of 11 modulo 20, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{20}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 8144
} |
[
{
"role": "user",
"content": "Please work out this equation. Compute the indefinite integral: $\\int 3\\sin(4x) + -7\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3\\sin(4x) + -7\\cos(2x)\\,dx $\n\nUse standard antiderivatives (and integration b... | {
"type": "calculus",
"seed": 1337,
"index": 8145
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Evaluate: ((161 + 70/10) * 14) + 4^5 - log_5(5) + (-74 mod 14) + ceil(199/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((161 + 70/10) * 14) + 4^5 - log_5(5) + (-74 mod 14) + ceil(199/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 8146
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 8147
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Evaluate: ((-18 + 425/17) * 2) + 9^4 - log_4(256) + (117 mod 7) + ceil(121/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-18 + 425/17) * 2) + 9^4 - log_4(256) + (117 mod 7) + ceil(121/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 8148
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Prove that $f(x,y)=\\frac12(10x^2+3y^2)+-6x+-6y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+3y^2)+-6x+-6y+4 $\n\n$ \\frac{\\partial^2 f... | {
"type": "optimization",
"seed": 1337,
"index": 8149
} |
[
{
"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": 8150
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Find $A^{-1}$ for $A=\\begin{pmatrix}-7&-3\\\\6&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -7 & -3 \\\\ 6 & 9 \\end{pmatrix} $\n\nCompute the determinant... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8151
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute the determinant: $A=\\begin{pmatrix}7&-3\\\\9&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&-3\\\\\\9&-7\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8152
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Evaluate: ((1 + 120/6) * 12) + 3^3 - log_8(512) + (-275 mod 29) + floor(152/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((1 + 120/6) * 12) + 3^3 - log_8(512) + (-275 mod 29) + floor(152/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 8153
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. -32 + 99x^2 - 169 = 116x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -32 + 99x^2 - 169 = 116x $\n\nMove all terms to the left (standard form):\n$ 99x^2 + -116x + -201 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8154
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 8155
} |
[
{
"role": "user",
"content": "Please compute the answer to 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$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 8156
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x)=5x^2+-6x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-6x+0$.\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": 8157
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Find $A^{-1}$ for $A=\\begin{pmatrix}-4&-1\\\\3&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -4 & -1 \\\\ 3 & -9 \\end{pmatrix} $\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8158
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Compute $(-61+192) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-61+192) \\bmod 13 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 8159
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Evaluate: ((172 + -448/16) * 13) + 8^3 - log_2(16) + (-173 mod 27) + floor(120/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((172 + -448/16) * 13) + 8^3 - log_2(16) + (-173 mod 27) + floor(120/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 8160
} |
[
{
"role": "user",
"content": "Solve the equation and state 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 $\n\nThe general ... | {
"type": "trigonometry",
"seed": 1337,
"index": 8161
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((100 + 400/8) * 8) + 5^5 - log_2(8) + (53 mod 26) + ceil(-33/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((100 + 400/8) * 8) + 5^5 - log_2(8) + (53 mod 26) + ceil(-33/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 8162
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 271 - 172 = 395x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 271 - 172 = 395x $\n\nMove all terms to the left (standard form):\n$ -395x + 99 = 0 $\n\nIsolate the $x$ term:\n$ -395x = -99 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 8163
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -38x - 106 = -707"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -38x - 106 = -707 $\n\nMove all terms to the left (standard form):\n$ -38x + 601 = 0 $\n\nIsolate the $x$ term:\n$ -38x = -601 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 8164
} |
[
{
"role": "user",
"content": "Determine the correct answer to 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 $a,b\\in\\mat... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 8165
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Evaluate: ((-74 + 410/10) * 3) + 8^5 - log_4(16) + (-494 mod 29) + round(6/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-74 + 410/10) * 3) + 8^5 - log_4(16) + (-494 mod 29) + round(6/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 8166
} |
[
{
"role": "user",
"content": "Find the value that satisfies this 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$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 8167
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 27 - 163x^2 + 139 = -82x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27 - 163x^2 + 139 = -82x $\n\nMove all terms to the left (standard form):\n$ -163x^2 + 82x + 166 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8168
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Compute the determinant: $A=\\begin{pmatrix}7&-1\\\\5&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&-1\\\\\\5&-7\\end{pmatrix} $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8169
} |
[
{
"role": "user",
"content": "solve: 7 + 167 + 110x = 21x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 7 + 167 + 110x = 21x^2 $\n\nMove all terms to the left (standard form):\n$ -21x^2 + 110x + 174 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4a... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8170
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute the determinant: $A=\\begin{pmatrix}6&3\\\\2&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&3\\\\\\2&-5\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8171
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&7\\\\\\-7&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-31\\\\\\17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&7\\\\\\-7&6\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8172
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&1&2\\\\\\5&2&-1\\\\\\-1&-5&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\6\\\\\\34\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by G... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8173
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((154 + 98/2) * 14) + 10^5 - log_6(36) + (-42 mod 5) + ceil(178/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((154 + 98/2) * 14) + 10^5 - log_6(36) + (-42 mod 5) + ceil(178/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 8174
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&0\\\\\\-5&9\\end{pmatrix},\\quad b=\\begin{pmatrix}-72\\\\\\31\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&0\\\\\\-5&9\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8175
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}6&-7\\\\4&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 6 & -7 \\\\ 4 & -8 \\end{pmatrix} $\n\nCompute the dete... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8176
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Evaluate: ((-165 + 324/18) * 10) + 2^4 - log_6(216) + (-237 mod 14) + ceil(-35/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-165 + 324/18) * 10) + 2^4 - log_6(216) + (-237 mod 14) + ceil(-35/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 8177
} |
[
{
"role": "user",
"content": "Please find the solution of this 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 value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 8178
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Prove that $f(x,y)=\\frac12(4x^2+8y^2)+4x+-4y+5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+8y^2)+4x+-4y+5 $\n\n$ \\frac{\\partial^2 f}{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 8179
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -617 - 622x = -763"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -617 - 622x = -763 $\n\nMove all terms to the left (standard form):\n$ -622x + 146 = 0 $\n\nIsolate the $x$ term:\n$ -622x = -146 $\n\... | {
"type": "linear_equation",
"seed": 1337,
"index": 8180
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? -188 - 21x = -685"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -188 - 21x = -685 $\n\nMove all terms to the left (standard form):\n$ -21x + 497 = 0 $\n\nIsolate the $x$ term:\n$ -21x = -497 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 8181
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Differentiate with respect to $x$: $f(x) = -1\\sin(9x) + 0\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1\\sin(9x) + 0\\cos(7x) $\n\nApply the standard differentiation rules... | {
"type": "calculus",
"seed": 1337,
"index": 8182
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((-133 + 132/22) * 18) + 6^4 - log_10(10000) + (333 mod 12) + round(-65/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-133 + 132/22) * 18) + 6^4 - log_10(10000) + (333 mod 12) + round(-65... | {
"type": "arithmetic",
"seed": 1337,
"index": 8183
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 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": 8184
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. -22 - 199 - 95x^2 = -94x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -22 - 199 - 95x^2 = -94x $\n\nMove all terms to the left (standard form):\n$ -95x^2 + 94x + -221 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8185
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute the indefinite integral: $\\int \\ln(2x + -9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + -9)\\,dx $\n\nUse standard antiderivatives (and integration by parts ... | {
"type": "calculus",
"seed": 1337,
"index": 8186
} |
[
{
"role": "user",
"content": "Evaluate the following 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": 8187
} |
[
{
"role": "user",
"content": "Determine the correct answer 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 $\... | {
"type": "trigonometry",
"seed": 1337,
"index": 8188
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&-3&-1\\\\\\0&-2&1\\\\\\4&3&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-7\\\\\\-2\\\\\\-20\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8189
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Evaluate: ((-112 + -25/25) * 3) + 4^5 - log_8(64) + (-320 mod 15) + ceil(-94/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-112 + -25/25) * 3) + 4^5 - log_8(64) + (-320 mod 15) + ceil(-94/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 8190
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 945x - 536 = -255"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 945x - 536 = -255 $\n\nMove all terms to the left (standard form):\n$ 945x + -281 = 0 $\n\nIsolate the $x$ term:\n$ 945x = 281 $\n\nDivide both sides by the coefficient o... | {
"type": "linear_equation",
"seed": 1337,
"index": 8191
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Compute the indefinite integral: $\\int -3\\sin(1x) + -5\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3\\sin(1x) + -5\\cos(5x)\\,dx $\n\nUse standard antiderivat... | {
"type": "calculus",
"seed": 1337,
"index": 8192
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Evaluate: ((132 + 0/17) * 13) + 5^5 - log_8(512) + (-119 mod 30) + round(-107/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((132 + 0/17) * 13) + 5^5 - log_8(512) + (-119 mod 30) + round(-107/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 8193
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -205 + 250x = 318"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -205 + 250x = 318 $\n\nMove all terms to the left (standard form):\n$ 250x + -523 = 0 $\n\nIsolate the $x$ term:\n$ 250x = 523 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 8194
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Compute the determinant: $A=\\begin{pmatrix}-3&-2\\\\-7&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&-2\\\\\\-7&-1\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8195
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((27 + -130/10) * 1) + 5^2 - log_10(100000) + (495 mod 10) + round(-164/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((27 + -130/10) * 1) + 5^2 - log_10(100000) + (495 mod 10) + round(-16... | {
"type": "arithmetic",
"seed": 1337,
"index": 8196
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-170 + 792/24) * 15) + 6^4 - log_3(81) + (158 mod 25) + floor(56/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-170 + 792/24) * 15) + 6^4 - log_3(81) + (158 mod 25) + floor(... | {
"type": "arithmetic",
"seed": 1337,
"index": 8197
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&5&0\\\\\\1&-5&1\\\\\\-4&-2&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-2\\\\\\16\\\\\\-20\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Sol... | {
"type": "linear_algebra",
"seed": 1337,
"index": 8198
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -20 - 177 + 60x^2 = -114x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20 - 177 + 60x^2 = -114x $\n\nMove all terms to the left (standard form):\n$ 60x^2 + 114x + -197 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 8199
} |
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