messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n -47x^2 - 68 + 25x = 125"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47x^2 - 68 + 25x = 125 $\n\nMove all terms to the left (standard form):\n$ -47x^2 + 25x + -193 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3500
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. -2x^2 - 75x + 166 = -7"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2x^2 - 75x + 166 = -7 $\n\nMove all terms to the left (standard form):\n$ -2x^2 + -75x + 173 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3501
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Differentiate with respect to $x$: $f(x) = 3\\sin(3x) + 6\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3\\sin(3x) + 6\\cos(1x) $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 3502
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -23x + 126x^2 - 157 = 4"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23x + 126x^2 - 157 = 4 $\n\nMove all terms to the left (standard form):\n$ 126x^2 + -23x + -161 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3503
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 18x^2 - 101x + 47 = 15"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 18x^2 - 101x + 47 = 15 $\n\nMove all terms to the left (standard form):\n$ 18x^2 + -101x + 32 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3504
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}7&-6\\\\7&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 7 & -6 \\\\ 7 & 8 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3505
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. -525x + 682 = 784"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -525x + 682 = 784 $\n\nMove all terms to the left (standard form):\n$ -525x + -102 = 0 $\n\nIsolate the $x$ term:\n$ -525x = 102 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3506
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 976 + 72x = -289"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 976 + 72x = -289 $\n\nMove all terms to the left (standard form):\n$ 72x + 1265 = 0 $\n\nIsolate the $x$ term:\n$ 72x = -1265 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 3507
} |
[
{
"role": "user",
"content": "Compute the final answer to 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 $f'(x)=0$, hence:... | {
"type": "optimization",
"seed": 1337,
"index": 3508
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 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\\math... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3509
} |
[
{
"role": "user",
"content": "solve Prove that $f(x)=6x^2+-8x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+-8x+4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 12x + -8 $\n$ f''(x) = 12 $\n\nSin... | {
"type": "optimization",
"seed": 1337,
"index": 3510
} |
[
{
"role": "user",
"content": "Find the solution to the following 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 $\n\nThe... | {
"type": "trigonometry",
"seed": 1337,
"index": 3511
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 13x^2 + 153 - 191 = 148x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13x^2 + 153 - 191 = 148x $\n\nMove all terms to the left (standard form):\n$ 13x^2 + -148x + -38 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3512
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal val... | {
"type": "trigonometry",
"seed": 1337,
"index": 3513
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Differentiate with respect to $x$: $f(x) = -6\\sin(4x) + -9\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6\\sin(4x) + -9\\cos(7x) $\n\nApply the standard differentiation rules:\n$ f'... | {
"type": "calculus",
"seed": 1337,
"index": 3514
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-1&-1\\\\\\1&-5&0\\\\\\3&5&5\\end{pmatrix},\\quad b=\\begin{pmatrix}2\\\\\\-18\\\\\\46\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3515
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find the modular inverse of 11 modulo 18, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{18}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3516
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((185 + -368/23) * 6) + 10^2 - log_8(8) + (-255 mod 22) + floor(58/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((185 + -368/23) * 6) + 10^2 - log_8(8) + (-255 mod 22) + floor(58/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3517
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. -2x - 68x^2 - 123 = 87"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2x - 68x^2 - 123 = 87 $\n\nMove all terms to the left (standard form):\n$ -68x^2 + -2x + -210 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3518
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 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 $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 3519
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-24 + 374/17) * 2) + 6^3 - log_2(64) + (-69 mod 5) + ceil(107/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-24 + 374/17) * 2) + 6^3 - log_2(64) + (-69 mod 5) + ceil(107/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 3520
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((92 + 374/22) * 8) + 8^2 - log_5(15625) + (-231 mod 2) + round(-164/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((92 + 374/22) * 8) + 8^2 - log_5(15625) + (-231 mod 2) + round(-164/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 3521
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((-185 + 323/17) * 19) + 5^4 - log_2(4) + (171 mod 29) + floor(102/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-185 + 323/17) * 19) + 5^4 - log_2(4) + (171 mod 29) + floor(102/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3522
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 3523
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Differentiate with respect to $x$: $f(x) = \\ln(8x + -3)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(8x + -3) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{8}... | {
"type": "calculus",
"seed": 1337,
"index": 3524
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 153 - 709x = -792"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 153 - 709x = -792 $\n\nMove all terms to the left (standard form):\n$ -709x + 945 = 0 $\n\nIsolate the $x$ term:\n$ -709x = -945 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 3525
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 684x - 808 = 513"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 684x - 808 = 513 $\n\nMove all terms to the left (standard form):\n$ 684x + -1321 = 0 $\n\nIsolate the $x$ term:\n$ 684x = 1321 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3526
} |
[
{
"role": "user",
"content": "Find the answer to the following 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": 3527
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Compute the indefinite integral: $\\int -5x^3 + -9x^2 + -6x + -12\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5x^3 + -9x^2 + -6x + -12\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 3528
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Evaluate: ((31 + 124/4) * 11) + 9^3 - log_3(243) + (41 mod 7) + floor(-156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((31 + 124/4) * 11) + 9^3 - log_3(243) + (41 mod 7) + floor(-156/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 3529
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 9 + 26x + 164 = -100x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 9 + 26x + 164 = -100x^2 $\n\nMove all terms to the left (standard form):\n$ 100x^2 + 26x + 173 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3530
} |
[
{
"role": "user",
"content": "Please work out this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&-9\\\\\\7&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-57\\\\\\-47\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&-9\\\\\\7&-1\\end{pmatri... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3531
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Prove that $f(x,y)=\\frac12(2x^2+5y^2)+-5x+2y+-9$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+5y^2)+-5x+2y+-9 $\n\n$ \\frac{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 3532
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. -11 + 97x = -564"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -11 + 97x = -564 $\n\nMove all terms to the left (standard form):\n$ 97x + 553 = 0 $\n\nIsolate the $x$ term:\n$ 97x = -553 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3533
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute the determinant: $A=\\begin{pmatrix}-5&3\\\\5&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&3\\\\\\5&-2\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3534
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 908 - 554 = -250x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 908 - 554 = -250x $\n\nMove all terms to the left (standard form):\n$ 250x + 354 = 0 $\n\nIsolate the $x$ term:\n$ 250x = -354 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 3535
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -40 - 64x^2 + 71 = -84x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40 - 64x^2 + 71 = -84x $\n\nMove all terms to the left (standard form):\n$ -64x^2 + 84x + 31 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3536
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((49 + 570/19) * 5) + 11^3 - log_6(46656) + (120 mod 26) + ceil(80/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((49 + 570/19) * 5) + 11^3 - log_6(46656) + (120 mod 26) + ceil(80/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 3537
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 15x^2 + 134 + 71 = 65x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15x^2 + 134 + 71 = 65x $\n\nMove all terms to the left (standard form):\n$ 15x^2 + -65x + 205 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3538
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Find $A^{-1}$ for $A=\\begin{pmatrix}9&-4\\\\-9&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 9 & -4 \\\\ -9 & -5 \\end{pmatrix} $\n\nComput... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3539
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. 296x + 816 = -13"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 296x + 816 = -13 $\n\nMove all terms to the left (standard form):\n$ 296x + 829 = 0 $\n\nIsolate the $x$ term:\n$ 296x = -829 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 3540
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((55 + 228/19) * 10) + 6^5 - log_7(117649) + (283 mod 8) + floor(-113/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((55 + 228/19) * 10) + 6^5 - log_7(117649) + (283 mod 8) + floor(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 3541
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 433 - 626x = 50"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 433 - 626x = 50 $\n\nMove all terms to the left (standard form):\n$ -626x + 383 = 0 $\n\nIsolate the $x$ term:\n$ -626x = -383 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 3542
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}1&5\\\\\\3&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-2\\\\\\12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}1&5\\\\\\3&-3\\end{p... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3543
} |
[
{
"role": "user",
"content": "Please determine the outcome of 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": 3544
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Differentiate with respect to $x$: $f(x) = (3x + 2)e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (3x + 2)e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{3e^{5x} + (3x ... | {
"type": "calculus",
"seed": 1337,
"index": 3545
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\... | {
"type": "optimization",
"seed": 1337,
"index": 3546
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Evaluate: ((-149 + -64/2) * 15) + 9^5 - log_5(125) + (121 mod 25) + ceil(11/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-149 + -64/2) * 15) + 9^5 - log_5(125) + (121 mod 25) + ceil(11/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 3547
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute the indefinite integral: $\\int \\ln(9x + -8)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(9x + -8)\\,dx $\n\nUse standard antiderivatives (and integration b... | {
"type": "calculus",
"seed": 1337,
"index": 3548
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 29x^2 - 169 - 16x = 164"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 29x^2 - 169 - 16x = 164 $\n\nMove all terms to the left (standard form):\n$ 29x^2 + -16x + -333 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3549
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 279 - 379x = -102"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 279 - 379x = -102 $\n\nMove all terms to the left (standard form):\n$ -379x + 381 = 0 $\n\nIsolate the $x$ term:\n$ -379x = -381 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3550
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((-183 + 234/18) * 20) + 11^2 - log_6(7776) + (-221 mod 3) + ceil(-150/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-183 + 234/18) * 20) + 11^2 - log_6(7776) + (-221 mod 3) + ceil(-150/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3551
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Differentiate with respect to $x$: $f(x) = 3x^3 + -5x^2 + -4x + 0$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3x^3 + -5x^2 + -4x + 0 $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 3552
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&-5\\\\\\-7&3\\end{pmatrix},\\quad b=\\begin{pmatrix}76\\\\\\37\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&-5\\\\\\-7&3\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3553
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. -22 + 19x^2 + 72 = -112x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -22 + 19x^2 + 72 = -112x $\n\nMove all terms to the left (standard form):\n$ 19x^2 + 112x + 50 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3554
} |
[
{
"role": "user",
"content": "Solve the following math equation. Prove that $f(x)=9x^2+-8x+7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-8x+7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x + ... | {
"type": "optimization",
"seed": 1337,
"index": 3555
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -13x^2 + 85 - 80x = -1"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -13x^2 + 85 - 80x = -1 $\n\nMove all terms to the left (standard form):\n$ -13x^2 + -80x + 86 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3556
} |
[
{
"role": "user",
"content": "solve: \n\n Differentiate with respect to $x$: $f(x) = (-3x + -10)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-3x + -10)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-3e^{2x} + (-3x + -10)\\cdot 2... | {
"type": "calculus",
"seed": 1337,
"index": 3557
} |
[
{
"role": "user",
"content": "Find the value that satisfies 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 $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 3558
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Find the modular inverse of 13 modulo 35, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{35}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3559
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&5&2\\\\\\-4&-1&-3\\\\\\5&-2&2\\end{pmatrix},\\quad b=\\begin{pmatrix}2\\\\\\7\\\\\\-9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3560
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -21 + 154 - 187x = 64x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21 + 154 - 187x = 64x^2 $\n\nMove all terms to the left (standard form):\n$ -64x^2 + -187x + 133 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3561
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 359x - 704 = 565"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 359x - 704 = 565 $\n\nMove all terms to the left (standard form):\n$ 359x + -1269 = 0 $\n\nIsolate the $x$ term:\n$ 359x = 1269 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 3562
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Compute $(192+-180) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (192+-180) \\bmod 17 $\n\nUse the rule that addition is compatible wit... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3563
} |
[
{
"role": "user",
"content": "Please work out this equation. Differentiate with respect to $x$: $f(x) = -7e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -7e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-28e^{4x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 3564
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Prove that $(\\mathbb{Z}_9, +)$ is a group under addition modulo 9."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_9=\\{0,1,\\dots,8\\}$ with operation $+$ modulo $9$.\n\n**Closure:** If $a,b\\in\\mathbb{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3565
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Differentiate with respect to $x$: $f(x) = 1x^3 + -8x^2 + -20x + 20$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1x^3 + -8x^2 + -20x + 20 $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 3566
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&4&-1\\\\\\0&-1&-2\\\\\\5&-2&1\\end{pmatrix},\\quad b=\\begin{pmatrix}6\\\\\\-1\\\\\\8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.,... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3567
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute $(-50+107) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-50+107) \\bmod 12 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3568
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -448x + 110 = -133"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -448x + 110 = -133 $\n\nMove all terms to the left (standard form):\n$ -448x + 243 = 0 $\n\nIsolate the $x$ term:\n$ -448x = -243 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 3569
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -19x + 147 - 84 = 94x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -19x + 147 - 84 = 94x^2 $\n\nMove all terms to the left (standard form):\n$ -94x^2 + -19x + 63 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3570
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&-3&-4\\\\\\-4&3&4\\\\\\4&0&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}6\\\\\\-20\\\\\\8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3571
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((-162 + -759/23) * 9) + 10^5 - log_10(100) + (-144 mod 26) + ceil(-43/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-162 + -759/23) * 9) + 10^5 - log_10(100) + (-144 mod 26) + ceil(-4... | {
"type": "arithmetic",
"seed": 1337,
"index": 3572
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -732 - 193x = 757"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -732 - 193x = 757 $\n\nMove all terms to the left (standard form):\n$ -193x + -1489 = 0 $\n\nIsolate the $x$ term:\n$ -193x = 1489 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3573
} |
[
{
"role": "user",
"content": "Evaluate 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{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 3574
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 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 $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 3575
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. -35 - 64x - 147x^2 = -134"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35 - 64x - 147x^2 = -134 $\n\nMove all terms to the left (standard form):\n$ -147x^2 + -64x + 99 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3576
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. 910 - 946 = -423x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 910 - 946 = -423x $\n\nMove all terms to the left (standard form):\n$ 423x + -36 = 0 $\n\nIsolate the $x$ term:\n$ 423x = 36 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3577
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. -394x - 284 = 473"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -394x - 284 = 473 $\n\nMove all terms to the left (standard form):\n$ -394x + -757 = 0 $\n\nIsolate the $x$ term:\n$ -394x = 757 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3578
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 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": 3579
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -684 + 115 = 259x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -684 + 115 = 259x $\n\nMove all terms to the left (standard form):\n$ -259x + -569 = 0 $\n\nIsolate the $x$ term:\n$ -259x = 569 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3580
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 607 - 224 = -843x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 607 - 224 = -843x $\n\nMove all terms to the left (standard form):\n$ 843x + 383 = 0 $\n\nIsolate the $x$ term:\n$ 843x = -383 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 3581
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute $(-156+-147) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-156+-147) \\bmod 13 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3582
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Find the modular inverse of 31 modulo 32, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $31\\cdot a^{-1} \\equiv 1 \\pmod{32}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3583
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Find $A^{-1}$ for $A=\\begin{pmatrix}8&6\\\\-4&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 8 & 6 \\\\ -4 & -8 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3584
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Evaluate: ((0 + 26/2) * 2) + 3^3 - log_4(1024) + (-154 mod 14) + round(42/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((0 + 26/2) * 2) + 3^3 - log_4(1024) + (-154 mod 14) + round(42/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 3585
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 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 $\n\nThe general so... | {
"type": "trigonometry",
"seed": 1337,
"index": 3586
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((174 + -658/14) * 15) + 3^2 - log_10(100) + (36 mod 7) + round(86/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((174 + -658/14) * 15) + 3^2 - log_10(100) + (36 mod 7) + round(86/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3587
} |
[
{
"role": "user",
"content": "solve: Evaluate: ((71 + 312/8) * 7) + 3^2 - log_4(1024) + (466 mod 15) + ceil(182/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((71 + 312/8) * 7) + 3^2 - log_4(1024) + (466 mod 15) + ceil(182/2) $\n\nCompute each component:\n$ 312/8 = 39 $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3588
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 3589
} |
[
{
"role": "user",
"content": "Find the correct answer to the 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 = \\arc... | {
"type": "trigonometry",
"seed": 1337,
"index": 3590
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute the indefinite integral: $\\int -3e^{-4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3e^{-4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if neede... | {
"type": "calculus",
"seed": 1337,
"index": 3591
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&3&4\\\\\\4&2&5\\\\\\1&-4&4\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\5\\\\\\4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by G... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3592
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((197 + -235/5) * 8) + 10^4 - log_2(4) + (-484 mod 9) + floor(122/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((197 + -235/5) * 8) + 10^4 - log_2(4) + (-484 mod 9) + floor(122... | {
"type": "arithmetic",
"seed": 1337,
"index": 3593
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -775 + 572x = 908"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -775 + 572x = 908 $\n\nMove all terms to the left (standard form):\n$ 572x + -1683 = 0 $\n\nIsolate the $x$ term:\n$ 572x = 1683 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3594
} |
[
{
"role": "user",
"content": "Find the value that satisfies 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 $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 3595
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-2&-1\\\\\\0&5\\end{pmatrix},\\quad b=\\begin{pmatrix}17\\\\\\-5\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-2&-1\\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3596
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. 843 + 764 = 328x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 843 + 764 = 328x $\n\nMove all terms to the left (standard form):\n$ -328x + 1607 = 0 $\n\nIsolate the $x$ term:\n$ -328x = -1607 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 3597
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -37x - 42 - 60 = 5x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37x - 42 - 60 = 5x^2 $\n\nMove all terms to the left (standard form):\n$ -5x^2 + -37x + -102 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3598
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Evaluate: ((-143 + -204/12) * 20) + 10^4 - log_7(343) + (-432 mod 13) + floor(-79/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-143 + -204/12) * 20) + 10^4 - log_7(343) + (-432 mod 13) + floor(... | {
"type": "arithmetic",
"seed": 1337,
"index": 3599
} |
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