messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((142 + -329/7) * 2) + 2^4 - log_5(5) + (325 mod 27) + ceil(-142/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((142 + -329/7) * 2) + 2^4 - log_5(5) + (325 mod 27) + ceil(-142/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 6500
} |
[
{
"role": "user",
"content": "Find the final answer to 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) = 0 $\n\nThe gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 6501
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Prove that $f(x)=4x^2+-3x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+-3x+-9$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 8... | {
"type": "optimization",
"seed": 1337,
"index": 6502
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Differentiate with respect to $x$: $f(x) = -1x^3 + -7x^2 + -19x + 13$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1x^3 + -7x^2 + -19x + 13 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 6503
} |
[
{
"role": "user",
"content": "Please evaluate and solve 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{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 6504
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Prove that $(\\mathbb{Z}_13, +)$ is a group under addition modulo 13."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_13=\\{0,1,\\dots,12\\}$ with operation $+$ modulo $13$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6505
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Differentiate with respect to $x$: $f(x) = (1x + -8)\\sin(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + -8)\\sin(3x) $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 6506
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 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\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 6507
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Prove that $f(x,y)=\\frac12(3x^2+4y^2)+3x+-3y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+4y^2)+3x+-3y+4 $\n\n$ \\frac{\\partial^2 f... | {
"type": "optimization",
"seed": 1337,
"index": 6508
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -431 + 795x = -235"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -431 + 795x = -235 $\n\nMove all terms to the left (standard form):\n$ 795x + -196 = 0 $\n\nIsolate the $x$ term:\n$ 795x = 196 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6509
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Find the modular inverse of 10 modulo 13, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $10\\cdot a^{-1} \\equiv 1 \\pmod{13}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6510
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((57 + 507/13) * 20) + 7^4 - log_4(4) + (-327 mod 11) + floor(-69/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((57 + 507/13) * 20) + 7^4 - log_4(4) + (-327 mod 11) + floor(-69/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6511
} |
[
{
"role": "user",
"content": "Determine the solution of the given 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": 6512
} |
[
{
"role": "user",
"content": "Find the solution to 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$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 6513
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Find the modular inverse of 7 modulo 17, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{17}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6514
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -982 + 479 = 547x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -982 + 479 = 547x $\n\nMove all terms to the left (standard form):\n$ -547x + -503 = 0 $\n\nIsolate the $x$ term:\n$ -547x = 503 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 6515
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find the modular inverse of 24 modulo 35, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $24\\cdot a^{-1} \\equiv 1 \\pmod{35}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees inte... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6516
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-1&0\\\\\\1&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}3\\\\\\33\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-1&0\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6517
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&1\\\\\\3&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\-14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&1\\\\\\3&-5\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6518
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Differentiate with respect to $x$: $f(x) = (3x + 0)\\sin(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (3x + 0)\\sin(3x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 6519
} |
[
{
"role": "user",
"content": "Please solve this math problem. 553 - 349x = -362"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 553 - 349x = -362 $\n\nMove all terms to the left (standard form):\n$ -349x + 915 = 0 $\n\nIsolate the $x$ term:\n$ -349x = -915 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 6520
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Evaluate: ((-35 + 630/14) * 8) + 6^3 - log_8(262144) + (-202 mod 19) + ceil(192/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-35 + 630/14) * 8) + 6^3 - log_8(262144) + (-202 mod 19) + ceil(192/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 6521
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 199x - 173 = 800"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 199x - 173 = 800 $\n\nMove all terms to the left (standard form):\n$ 199x + -973 = 0 $\n\nIsolate the $x$ term:\n$ 199x = 973 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 6522
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. 307x + 316 = -333"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 307x + 316 = -333 $\n\nMove all terms to the left (standard form):\n$ 307x + 649 = 0 $\n\nIsolate the $x$ term:\n$ 307x = -649 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6523
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 18 + 125x^2 + 181x = 139"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 18 + 125x^2 + 181x = 139 $\n\nMove all terms to the left (standard form):\n$ 125x^2 + 181x + -121 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6524
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Prove that $f(x,y)=\\frac12(9x^2+7y^2)+-2x+3y+-9$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+7y^2)+-2x+3y+-9 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 6525
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -13x^2 - 164x + 169 = 116"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -13x^2 - 164x + 169 = 116 $\n\nMove all terms to the left (standard form):\n$ -13x^2 + -164x + 53 = 0 $\n\nApply the quadrat... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6526
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Compute the determinant: $A=\\begin{pmatrix}6&7\\\\-3&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&7\\\\\\-3&-4\\end{pmatrix... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6527
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. 39 + 27x^2 + 164 = -190x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 39 + 27x^2 + 164 = -190x $\n\nMove all terms to the left (standard form):\n$ 27x^2 + 190x + 203 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6528
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Differentiate with respect to $x$: $f(x) = -9\\sin(2x) + 8\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9\\sin(2x) + 8\\cos(6x) $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 6529
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 640 - 786x = -14"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 640 - 786x = -14 $\n\nMove all terms to the left (standard form):\n$ -786x + 654 = 0 $\n\nIsolate the $x$ term:\n$ -786x = -654 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6530
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Compute the indefinite integral: $\\int 5e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int 5e^{3x}\\,dx = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 6531
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Find $A^{-1}$ for $A=\\begin{pmatrix}0&5\\\\-5&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 0 & 5 \\\\ -5 & -7 \\end{pmatrix} $\n\nComput... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6532
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Evaluate: ((37 + 78/2) * 2) + 12^2 - log_3(729) + (63 mod 23) + floor(71/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((37 + 78/2) * 2) + 12^2 - log_3(729) + (63 mod 23) + floor(71/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 6533
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Find the modular inverse of 9 modulo 20, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{20}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6534
} |
[
{
"role": "user",
"content": "Find the final answer to the given 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 = \\arcco... | {
"type": "trigonometry",
"seed": 1337,
"index": 6535
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Compute the determinant: $A=\\begin{pmatrix}-4&-3\\\\-5&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&-3\\\\\\-5&-4\\end{pmatrix} $\n\nUse $\\det(A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6536
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((-66 + 70/2) * 10) + 9^2 - log_8(262144) + (391 mod 28) + floor(35/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-66 + 70/2) * 10) + 9^2 - log_8(262144) + (391 mod 28) + floor(35/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 6537
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Evaluate: ((-111 + -24/6) * 18) + 5^4 - log_5(3125) + (488 mod 22) + ceil(-94/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-111 + -24/6) * 18) + 5^4 - log_5(3125) + (488 mod 22) + ceil(-94/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 6538
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((90 + -114/3) * 10) + 12^3 - log_4(64) + (-212 mod 25) + ceil(143/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((90 + -114/3) * 10) + 12^3 - log_4(64) + (-212 mod 25) + ceil(143/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 6539
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Prove that $f(x)=2x^2+-3x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+-3x+6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 4x + -3 $... | {
"type": "optimization",
"seed": 1337,
"index": 6540
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 4x^2 + 44 + 25 = -116x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 4x^2 + 44 + 25 = -116x $\n\nMove all terms to the left (standard form):\n$ 4x^2 + 116x + 69 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6541
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute the indefinite integral: $\\int (-3x + -8)\\sin(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + -8)\\sin(5x)\\,dx $\n\nUse standard antiderivatives (and integrati... | {
"type": "calculus",
"seed": 1337,
"index": 6542
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Find the modular inverse of 29 modulo 36, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $29\\cdot a^{-1} \\equiv 1 \\pmod{36}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6543
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 143x - 616 = -572"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 143x - 616 = -572 $\n\nMove all terms to the left (standard form):\n$ 143x + -44 = 0 $\n\nIsolate the $x$ term:\n$ 143x = 44 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 6544
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Compute $(-158+162) \\bmod 16$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-158+162) \\bmod 16 $\n\nUse the rule that addition is compatible with reduction modulo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6545
} |
[
{
"role": "user",
"content": "Please work out this equation. Prove that $f(x)=9x^2+-3x+3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-3x+3$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x + -3 $... | {
"type": "optimization",
"seed": 1337,
"index": 6546
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Prove that $(\\mathbb{Z}_26, +)$ is a group under addition modulo 26."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_26=\\{0,1,\\dots,25\\}$ with operation $+$ modulo $26$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6547
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((-119 + 760/20) * 17) + 7^4 - log_7(16807) + (-7 mod 29) + round(96/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-119 + 760/20) * 17) + 7^4 - log_7(16807) + (-7 mod 29) + round(96/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 6548
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. 20 - 110x^2 - 74x = 107"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20 - 110x^2 - 74x = 107 $\n\nMove all terms to the left (standard form):\n$ -110x^2 + -74x + -87 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6549
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((3 + 203/7) * 1) + 12^4 - log_6(36) + (-26 mod 12) + floor(-2/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((3 + 203/7) * 1) + 12^4 - log_6(36) + (-26 mod 12) + floor(-2/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 6550
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}6&2\\\\-8&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 6 & 2 \\\\ -8 & 5 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6551
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute the determinant: $A=\\begin{pmatrix}7&-1\\\\-5&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&-1\\\\\\-5&8\\end{pmatrix... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6552
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((-56 + -740/20) * 14) + 4^2 - log_10(1000) + (33 mod 4) + round(172/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-56 + -740/20) * 14) + 4^2 - log_10(1000) + (33 mod 4) + round(172/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 6553
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Evaluate: ((92 + 64/16) * 14) + 3^3 - log_6(7776) + (-431 mod 5) + floor(-156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((92 + 64/16) * 14) + 3^3 - log_6(7776) + (-431 mod 5) + floor(-156/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 6554
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Compute the indefinite integral: $\\int (-3x + 5)e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + 5)e^{5x}\\,dx $\n\nUse standard antiderivatives (and integration by... | {
"type": "calculus",
"seed": 1337,
"index": 6555
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. -20 - 175x + 136 = 10x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20 - 175x + 136 = 10x^2 $\n\nMove all terms to the left (standard form):\n$ -10x^2 + -175x + 116 = 0 $\n\nApply the quadrat... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6556
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Find the modular inverse of 6 modulo 23, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $6\\cdot a^{-1} \\equiv 1 \\pmod{23}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6557
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. -41 + 59x = -682"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -41 + 59x = -682 $\n\nMove all terms to the left (standard form):\n$ 59x + 641 = 0 $\n\nIsolate the $x$ term:\n$ 59x = -641 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6558
} |
[
{
"role": "user",
"content": "solve: \n\n 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 = \\arccos(\\frac{1}{2}) = 1.0472 $\n\nThe... | {
"type": "trigonometry",
"seed": 1337,
"index": 6559
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? -48 + 14x - 19 = 11x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48 + 14x - 19 = 11x^2 $\n\nMove all terms to the left (standard form):\n$ -11x^2 + 14x + -67 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6560
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -32 + 50x + 77 = 168x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -32 + 50x + 77 = 168x^2 $\n\nMove all terms to the left (standard form):\n$ -168x^2 + 50x + 45 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6561
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&-4&0\\\\\\5&-4&-4\\\\\\0&-5&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\16\\\\\\17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6562
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. -9 - 192x^2 - 53x = -75"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -9 - 192x^2 - 53x = -75 $\n\nMove all terms to the left (standard form):\n$ -192x^2 + -53x + 66 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6563
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&-3\\\\\\-5&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-72\\\\\\-45\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&-3... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6564
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 15x - 333 = 377"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 15x - 333 = 377 $\n\nMove all terms to the left (standard form):\n$ 15x + -710 = 0 $\n\nIsolate the $x$ term:\n$ 15x = 710 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 6565
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Compute $(97+78) \\bmod 11$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (97+78) \\bmod 11 $\n\nUse the rule that addition is compatible with reduction mo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6566
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 36x - 4 - 155 = 15x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36x - 4 - 155 = 15x^2 $\n\nMove all terms to the left (standard form):\n$ -15x^2 + 36x + -159 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6567
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((-188 + -312/24) * 7) + 6^3 - log_9(729) + (-491 mod 23) + ceil(-150/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-188 + -312/24) * 7) + 6^3 - log_9(729) + (-491 mod 23) + ceil(-150/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 6568
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -56x - 136 = 349"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -56x - 136 = 349 $\n\nMove all terms to the left (standard form):\n$ -56x + -485 = 0 $\n\nIsolate the $x$ term:\n$ -56x = 485 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 6569
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Differentiate with respect to $x$: $f(x) = (-6x + 5)e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-6x + 5)e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-... | {
"type": "calculus",
"seed": 1337,
"index": 6570
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Prove that $f(x,y)=\\frac12(1x^2+4y^2)+1x+5y+-7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+4y^2)+1x+5y+-7 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 6571
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((-181 + -805/23) * 5) + 6^4 - log_7(16807) + (355 mod 3) + ceil(142/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-181 + -805/23) * 5) + 6^4 - log_7(16807) + (355 mod 3) + ceil(142/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 6572
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. -31 + 191x + 49x^2 = -4"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -31 + 191x + 49x^2 = -4 $\n\nMove all terms to the left (standard form):\n$ 49x^2 + 191x + -27 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6573
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Prove that $f(x)=1x^2+7x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+7x+6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 2x... | {
"type": "optimization",
"seed": 1337,
"index": 6574
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -207 - 309x = 861"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -207 - 309x = 861 $\n\nMove all terms to the left (standard form):\n$ -309x + -1068 = 0 $\n\nIsolate the $x$ term:\n$ -309x = 1068 $\n\... | {
"type": "linear_equation",
"seed": 1337,
"index": 6575
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -200x + 476 = -198"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -200x + 476 = -198 $\n\nMove all terms to the left (standard form):\n$ -200x + 674 = 0 $\n\nIsolate the $x$ term:\n$ -200x = -674 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 6576
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. -18 - 124x = 51"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -18 - 124x = 51 $\n\nMove all terms to the left (standard form):\n$ -124x + -69 = 0 $\n\nIsolate the $x$ term:\n$ -124x = 69 $\n\nDivide both sides by th... | {
"type": "linear_equation",
"seed": 1337,
"index": 6577
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Compute the determinant: $A=\\begin{pmatrix}2&-3\\\\-7&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&-3\\\\\\-7&1\\end{pmatrix} $\n\nUse $\\det(A)=... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6578
} |
[
{
"role": "user",
"content": "Find the answer to the following 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\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 6579
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 6580
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Compute the determinant: $A=\\begin{pmatrix}9&9\\\\1&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}9&9\\\\\\1&-7\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6581
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Compute $(110+123) \\bmod 24$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (110+123) \\bmod 24 $\n\nUse the rule that addition is compatible with redu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6582
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 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": 6583
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&5\\\\\\-5&7\\end{pmatrix},\\quad b=\\begin{pmatrix}-13\\\\\\37\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&5\\\\\\-5&7\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6584
} |
[
{
"role": "user",
"content": "solve Evaluate: ((-75 + -750/25) * 13) + 10^3 - log_7(117649) + (138 mod 20) + ceil(-158/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-75 + -750/25) * 13) + 10^3 - log_7(117649) + (138 mod 20) + ceil(-158/2) $\n\nCompute each component:\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6585
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. -393 + 952x = -969"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -393 + 952x = -969 $\n\nMove all terms to the left (standard form):\n$ 952x + 576 = 0 $\n\nIsolate the $x$ term:\n$ 952x = -576 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6586
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Prove that $(\\mathbb{Z}_3, +)$ is a group under addition modulo 3."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_3=\\{0,1,\\dots,2\\}$ with operation $+$ modulo $3$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6587
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 34 + 397 = -226x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 34 + 397 = -226x $\n\nMove all terms to the left (standard form):\n$ 226x + 431 = 0 $\n\nIsolate the $x$ term:\n$ 226x = -431 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 6588
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 129 - 326 = -551x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 129 - 326 = -551x $\n\nMove all terms to the left (standard form):\n$ 551x + -197 = 0 $\n\nIsolate the $x$ term:\n$ 551x = 197 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6589
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -38 + 88 + 149x = -74x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -38 + 88 + 149x = -74x^2 $\n\nMove all terms to the left (standard form):\n$ 74x^2 + 149x + 50 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6590
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 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 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 6591
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. 338 - 839x = 473"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 338 - 839x = 473 $\n\nMove all terms to the left (standard form):\n$ -839x + -135 = 0 $\n\nIsolate the $x$ term:\n$ -839x = 135 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 6592
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Compute $(-88+45) \\bmod 20$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-88+45) \\bmod 20 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6593
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&-3&1\\\\\\-1&-4&2\\\\\\0&2&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}6\\\\\\0\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.,... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6594
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Find $A^{-1}$ for $A=\\begin{pmatrix}4&0\\\\2&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 4 & 0 \\\\ 2 & 5 \\end{pmatrix} $\n\nCompute the d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6595
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in 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": 6596
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 35 + 20x^2 + 3x = 120"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 35 + 20x^2 + 3x = 120 $\n\nMove all terms to the left (standard form):\n$ 20x^2 + 3x + -85 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6597
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. -607x + 84 = -19"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -607x + 84 = -19 $\n\nMove all terms to the left (standard form):\n$ -607x + 103 = 0 $\n\nIsolate the $x$ term:\n$ -607x = -103 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6598
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 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": 6599
} |
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