messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the equation shown below. -456 - 585x = -855"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -456 - 585x = -855 $\n\nMove all terms to the left (standard form):\n$ -585x + 399 = 0 $\n\nIsolate the $x$ term:\n$ -585x = -399 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2500
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((-116 + 836/19) * 11) + 10^3 - log_7(2401) + (-154 mod 22) + round(-29/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-116 + 836/19) * 11) + 10^3 - log_7(2401) + (-154 mod 22) + round(... | {
"type": "arithmetic",
"seed": 1337,
"index": 2501
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((31 + 276/6) * 1) + 12^5 - log_5(15625) + (58 mod 15) + floor(-5/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((31 + 276/6) * 1) + 12^5 - log_5(15625) + (58 mod 15) + floor(-5/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 2502
} |
[
{
"role": "user",
"content": "solve: 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 gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 2503
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the determinant: $A=\\begin{pmatrix}-6&-1\\\\-4&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-6&-1\\\\\\-4&9\\end{pmatrix} $\n\nUse $\\det(A)... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2504
} |
[
{
"role": "user",
"content": "solve Evaluate: ((-165 + -16/16) * 5) + 3^3 - log_6(6) + (241 mod 22) + round(42/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-165 + -16/16) * 5) + 3^3 - log_6(6) + (241 mod 22) + round(42/2) $\n\nCompute each component:\n$ -16/16 = -1 $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2505
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Prove that $f(x)=10x^2+-3x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-3x+-6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $... | {
"type": "optimization",
"seed": 1337,
"index": 2506
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Evaluate: ((47 + -23/23) * 10) + 12^4 - log_5(625) + (484 mod 26) + floor(-101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((47 + -23/23) * 10) + 12^4 - log_5(625) + (484 mod 26) + floor(-101/... | {
"type": "arithmetic",
"seed": 1337,
"index": 2507
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -36x + 139x^2 + 134 = -142"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x + 139x^2 + 134 = -142 $\n\nMove all terms to the left (standard form):\n$ 139x^2 + -36x + 276 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2508
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 38 - 16 + 80x = -82x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38 - 16 + 80x = -82x^2 $\n\nMove all terms to the left (standard form):\n$ 82x^2 + 80x + 22 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2509
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 50 + 20 + 106x^2 = -153x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 50 + 20 + 106x^2 = -153x $\n\nMove all terms to the left (standard form):\n$ 106x^2 + 153x + 70 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2510
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 532 - 542x = -367"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 532 - 542x = -367 $\n\nMove all terms to the left (standard form):\n$ -542x + 899 = 0 $\n\nIsolate the $x$ term:\n$ -542x = -899 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 2511
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Compute the indefinite integral: $\\int 2\\sin(3x) + 5\\cos(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2\\sin(3x) + 5\\cos(3x)\\,dx $\n\nUse standard antiderivatives (and integration by... | {
"type": "calculus",
"seed": 1337,
"index": 2512
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Find the modular inverse of 15 modulo 34, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $15\\cdot a^{-1} \\equiv 1 \\pmod{34}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2513
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Differentiate with respect to $x$: $f(x) = (3x + 3)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (3x + 3)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{3... | {
"type": "calculus",
"seed": 1337,
"index": 2514
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&0&5\\\\\\1&-5&0\\\\\\-5&0&4\\end{pmatrix},\\quad b=\\begin{pmatrix}1\\\\\\7\\\\\\11\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2515
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((191 + -81/3) * 3) + 6^5 - log_4(256) + (107 mod 29) + round(113/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((191 + -81/3) * 3) + 6^5 - log_4(256) + (107 mod 29) + round(113/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2516
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 625x - 18 = -923"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 625x - 18 = -923 $\n\nMove all terms to the left (standard form):\n$ 625x + 905 = 0 $\n\nIsolate the $x$ term:\n$ 625x = -905 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2517
} |
[
{
"role": "user",
"content": "Solve the following math 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:\n$ 4x(x... | {
"type": "optimization",
"seed": 1337,
"index": 2518
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 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 va... | {
"type": "trigonometry",
"seed": 1337,
"index": 2519
} |
[
{
"role": "user",
"content": "Solve the following math equation. -2x^2 + 147x - 186 = 138"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2x^2 + 147x - 186 = 138 $\n\nMove all terms to the left (standard form):\n$ -2x^2 + 147x + -324 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2520
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Differentiate with respect to $x$: $f(x) = -6x^3 + 4x^2 + 17x + -2$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + 4x^2 + 17x + -2 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-18x^2 + 8x + ... | {
"type": "calculus",
"seed": 1337,
"index": 2521
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Compute the indefinite integral: $\\int -3e^{-3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3e^{-3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int ... | {
"type": "calculus",
"seed": 1337,
"index": 2522
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. -23x^2 + 169x + 67 = 137"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23x^2 + 169x + 67 = 137 $\n\nMove all terms to the left (standard form):\n$ -23x^2 + 169x + -70 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2523
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Evaluate: ((-46 + -296/8) * 10) + 9^2 - log_6(7776) + (-412 mod 25) + round(-11/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-46 + -296/8) * 10) + 9^2 - log_6(7776) + (-412 mod 25) + round(-11... | {
"type": "arithmetic",
"seed": 1337,
"index": 2524
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-1&-3\\\\\\9&5\\end{pmatrix},\\quad b=\\begin{pmatrix}-15\\\\\\69\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-1&-3\\\\\\9&5\\end{pmatri... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2525
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Find the modular inverse of 13 modulo 22, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{22}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2526
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Prove that $f(x)=5x^2+-1x+8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-1x+8$.\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": 2527
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. -544 + 923x = -730"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -544 + 923x = -730 $\n\nMove all terms to the left (standard form):\n$ 923x + 186 = 0 $\n\nIsolate the $x$ term:\n$ 923x = -186 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 2528
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Differentiate with respect to $x$: $f(x) = 4x^3 + -7x^2 + 5x + -20$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4x^3 + -7x^2 + 5x + -20 $\n\nApply the standard differentiation rules:\n$ f'(x) =... | {
"type": "calculus",
"seed": 1337,
"index": 2529
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 2530
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((-85 + 180/9) * 16) + 2^3 - log_10(100000) + (214 mod 9) + floor(-138/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-85 + 180/9) * 16) + 2^3 - log_10(100000) + (214 mod 9) + floor(-1... | {
"type": "arithmetic",
"seed": 1337,
"index": 2531
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 493x - 140 = -544"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 493x - 140 = -544 $\n\nMove all terms to the left (standard form):\n$ 493x + 404 = 0 $\n\nIsolate the $x$ term:\n$ 493x = -404 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 2532
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((119 + 152/19) * 20) + 10^4 - log_5(15625) + (169 mod 11) + ceil(34/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((119 + 152/19) * 20) + 10^4 - log_5(15625) + (169 mod 11) + ceil(34/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2533
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 38 + 132 - 99x = 43x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38 + 132 - 99x = 43x^2 $\n\nMove all terms to the left (standard form):\n$ -43x^2 + -99x + 170 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2534
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Compute the indefinite integral: $\\int (-4x + 3)e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-4x + 3)e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by p... | {
"type": "calculus",
"seed": 1337,
"index": 2535
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -50 + 124x - 32 = -154x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50 + 124x - 32 = -154x^2 $\n\nMove all terms to the left (standard form):\n$ 154x^2 + 124x + -82 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2536
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((-149 + -81/3) * 19) + 10^3 - log_2(32) + (135 mod 5) + round(166/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-149 + -81/3) * 19) + 10^3 - log_2(32) + (135 mod 5) + round(166/2) $\n\nCompute each component:\n$ -81/3... | {
"type": "arithmetic",
"seed": 1337,
"index": 2537
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((143 + 400/16) * 13) + 5^3 - log_4(64) + (253 mod 19) + floor(154/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((143 + 400/16) * 13) + 5^3 - log_4(64) + (253 mod 19) + floor(15... | {
"type": "arithmetic",
"seed": 1337,
"index": 2538
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. -17 - 122x + 119 = 102x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17 - 122x + 119 = 102x^2 $\n\nMove all terms to the left (standard form):\n$ -102x^2 + -122x + 102 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2539
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. -202 + 205 = 296x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -202 + 205 = 296x $\n\nMove all terms to the left (standard form):\n$ -296x + 3 = 0 $\n\nIsolate the $x$ term:\n$ -296x = -3 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 2540
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. 48x^2 - 139 + 148x = -126"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 48x^2 - 139 + 148x = -126 $\n\nMove all terms to the left (standard form):\n$ 48x^2 + 148x + -13 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2541
} |
[
{
"role": "user",
"content": "solve: \n\n Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&3&-1\\\\\\-3&3&4\\\\\\5&-2&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-13\\\\\\5\\\\\\-8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by Gaussian elimination)... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2542
} |
[
{
"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": 2543
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Compute the indefinite integral: $\\int -7e^{-3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -7e^{-3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int ... | {
"type": "calculus",
"seed": 1337,
"index": 2544
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 328 - 937 = -597x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 328 - 937 = -597x $\n\nMove all terms to the left (standard form):\n$ 597x + -609 = 0 $\n\nIsolate the $x$ term:\n$ 597x = 609 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 2545
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 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": 2546
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 2547
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Evaluate: ((-183 + 45/15) * 20) + 4^3 - log_2(4) + (-440 mod 27) + ceil(25/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-183 + 45/15) * 20) + 4^3 - log_2(4) + (-440 mod 27) + ceil(25/2) $\n\nCompute each com... | {
"type": "arithmetic",
"seed": 1337,
"index": 2548
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 943 - 661x = -377"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 943 - 661x = -377 $\n\nMove all terms to the left (standard form):\n$ -661x + 1320 = 0 $\n\nIsolate the $x$ term:\n$ -661x = -1320 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 2549
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 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 general ... | {
"type": "trigonometry",
"seed": 1337,
"index": 2550
} |
[
{
"role": "user",
"content": "Can you compute this equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&-3\\\\\\2&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-42\\\\\\20\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&-3\\\\\\2&4\\end{pmatrix} ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2551
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -787 + 189 = 582x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -787 + 189 = 582x $\n\nMove all terms to the left (standard form):\n$ -582x + -598 = 0 $\n\nIsolate the $x$ term:\n$ -582x = 598 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 2552
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the indefinite integral: $\\int 4\\sin(5x) + -2\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4\\sin(5x) + -2\\cos(2x)\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 2553
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&4&-4\\\\\\5&-3&-2\\\\\\0&4&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-13\\\\\\-9\\\\\\0\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2554
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Prove that $f(x,y)=\\frac12(3x^2+4y^2)+4x+5y+-1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+4y^2)+4x+5y+-1 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 2555
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. -4x - 106 + 146x^2 = -96"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4x - 106 + 146x^2 = -96 $\n\nMove all terms to the left (standard form):\n$ 146x^2 + -4x + -10 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2556
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 17 + 14 - 131x = 12x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 17 + 14 - 131x = 12x^2 $\n\nMove all terms to the left (standard form):\n$ -12x^2 + -131x + 31 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2557
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. -36 + 4x^2 - 39 = -163x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36 + 4x^2 - 39 = -163x $\n\nMove all terms to the left (standard form):\n$ 4x^2 + 163x + -75 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2558
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((-45 + 248/8) * 19) + 7^2 - log_2(8) + (-286 mod 20) + round(31/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-45 + 248/8) * 19) + 7^2 - log_2(8) + (-286 mod 20) + round(31/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2559
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Compute $(124+-182) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (124+-182) \\bmod 15 $\n\nUse the rule that addition is compatible with reduc... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2560
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 38x - 38 - 94x^2 = -166"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38x - 38 - 94x^2 = -166 $\n\nMove all terms to the left (standard form):\n$ -94x^2 + 38x + 128 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2561
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute the determinant: $A=\\begin{pmatrix}-8&-9\\\\2&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-8&-9\\\\\\2&-9\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2562
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 40 + 17x - 12 = -21x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 40 + 17x - 12 = -21x^2 $\n\nMove all terms to the left (standard form):\n$ 21x^2 + 17x + 28 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2563
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 613x + 424 = 211"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 613x + 424 = 211 $\n\nMove all terms to the left (standard form):\n$ 613x + 213 = 0 $\n\nIsolate the $x$ term:\n$ 613x = -213 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 2564
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -23x - 39 + 114x^2 = 168"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23x - 39 + 114x^2 = 168 $\n\nMove all terms to the left (standard form):\n$ 114x^2 + -23x + -207 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2565
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Evaluate: ((-117 + -114/6) * 20) + 9^2 - log_10(100) + (-255 mod 30) + floor(-27/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-117 + -114/6) * 20) + 9^2 - log_10(100) + (-255 mod 30) + floor(-27/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 2566
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -35 - 120x + 79x^2 = 9"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35 - 120x + 79x^2 = 9 $\n\nMove all terms to the left (standard form):\n$ 79x^2 + -120x + -44 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2567
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Differentiate with respect to $x$: $f(x) = 7\\sin(4x) + 0\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7\\sin(4x) + 0\\cos(6x) $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 2568
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Compute the determinant: $A=\\begin{pmatrix}0&7\\\\-5&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}0&7\\\\\\-5&8\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2569
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((61 + 390/13) * 18) + 3^5 - log_8(64) + (-71 mod 29) + ceil(-29/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((61 + 390/13) * 18) + 3^5 - log_8(64) + (-71 mod 29) + ceil(-29/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 2570
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&8\\\\\\4&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}52\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&8\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2571
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 12x^2 - 93 - 30 = 27x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 12x^2 - 93 - 30 = 27x $\n\nMove all terms to the left (standard form):\n$ 12x^2 + -27x + -123 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2572
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Evaluate: ((-125 + -750/15) * 19) + 11^5 - log_2(16) + (-366 mod 22) + round(-83/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-125 + -750/15) * 19) + 11^5 - log_2(16) + (-366 mod 22) + round(-83... | {
"type": "arithmetic",
"seed": 1337,
"index": 2573
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. -28x + 3 - 106 = 191x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -28x + 3 - 106 = 191x^2 $\n\nMove all terms to the left (standard form):\n$ -191x^2 + -28x + -103 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2574
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&3&3\\\\\\-1&2&-1\\\\\\5&3&2\\end{pmatrix},\\quad b=\\begin{pmatrix}9\\\\\\-6\\\\\\5\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solv... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2575
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Compute the determinant: $A=\\begin{pmatrix}8&-3\\\\-6&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}8&-3\\\\\\-6&4\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2576
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -41 + 162x + 111x^2 = -38"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -41 + 162x + 111x^2 = -38 $\n\nMove all terms to the left (standard form):\n$ 111x^2 + 162x + -3 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2577
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. -335x + 720 = 443"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -335x + 720 = 443 $\n\nMove all terms to the left (standard form):\n$ -335x + 277 = 0 $\n\nIsolate the $x$ term:\n$ -335x = -277 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 2578
} |
[
{
"role": "user",
"content": "Compute the solution to this 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\\mathbb{Z}_n... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2579
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 2580
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Compute the determinant: $A=\\begin{pmatrix}-4&9\\\\-5&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&9\\\\\\-5&-1\\end{pmatrix} $\n\nUse $\\det(... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2581
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((105 + -304/16) * 5) + 11^4 - log_3(729) + (94 mod 15) + ceil(150/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((105 + -304/16) * 5) + 11^4 - log_3(729) + (94 mod 15) + ceil(150... | {
"type": "arithmetic",
"seed": 1337,
"index": 2582
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Find the modular inverse of 3 modulo 20, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{20}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees in... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2583
} |
[
{
"role": "user",
"content": "Please calculate this 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 $a,b\\in\\mathbb{Z}_n$, then... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2584
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Compute $(118+75) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (118+75) \\bmod 12 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2585
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 3x^2 - 192 + 184 = 183x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 3x^2 - 192 + 184 = 183x $\n\nMove all terms to the left (standard form):\n$ 3x^2 + -183x + -8 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2586
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-3&3\\\\5&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -3 & 3 \\\\ 5 & 6 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2587
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = 2x^3 + 6x^2 + 11x + 13$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + 6x^2 + 11x + 13 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\... | {
"type": "calculus",
"seed": 1337,
"index": 2588
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -16x^2 - 136 + 64x = 102"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -16x^2 - 136 + 64x = 102 $\n\nMove all terms to the left (standard form):\n$ -16x^2 + 64x + -238 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2589
} |
[
{
"role": "user",
"content": "Solve the equation and state 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 2590
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Differentiate with respect to $x$: $f(x) = -6x^3 + 4x^2 + -10x + -15$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + 4x^2 + -10x + -15 $\n\nApply the standard differentiation rules:\n... | {
"type": "calculus",
"seed": 1337,
"index": 2591
} |
[
{
"role": "user",
"content": "Please determine the solution to 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": 2592
} |
[
{
"role": "user",
"content": "Solve the following math equation. -5x^2 + 170 - 18 = 118x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -5x^2 + 170 - 18 = 118x $\n\nMove all terms to the left (standard form):\n$ -5x^2 + -118x + 152 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2593
} |
[
{
"role": "user",
"content": "Please find the value of this math 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\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2594
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Find the modular inverse of 7 modulo 10, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{10}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2595
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n -11 - 66x^2 + 104 = 79x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -11 - 66x^2 + 104 = 79x $\n\nMove all terms to the left (standard form):\n$ -66x^2 + -79x + 93 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2596
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((16 + 748/22) * 13) + 4^5 - log_6(216) + (354 mod 22) + round(-20/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((16 + 748/22) * 13) + 4^5 - log_6(216) + (354 mod 22) + round(-20/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2597
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 588 + 869 = -30x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 588 + 869 = -30x $\n\nMove all terms to the left (standard form):\n$ 30x + 1457 = 0 $\n\nIsolate the $x$ term:\n$ 30x = -1457 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 2598
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. -13x^2 - 180 - 199 = -200x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -13x^2 - 180 - 199 = -200x $\n\nMove all terms to the left (standard form):\n$ -13x^2 + 200x + -379 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2599
} |
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