messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Determine the solution for this math problem. 118x - 654 = -588"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 118x - 654 = -588 $\n\nMove all terms to the left (standard form):\n$ 118x + -66 = 0 $\n\nIsolate the $x$ term:\n$ 118x = 66 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 1400
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical 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 $a,b\\in\\mat... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1401
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Evaluate: ((-184 + -902/22) * 17) + 11^2 - log_8(32768) + (459 mod 17) + ceil(101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-184 + -902/22) * 17) + 11^2 - log_8(32768) + (459 mod 17) +... | {
"type": "arithmetic",
"seed": 1337,
"index": 1402
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Prove that $f(x,y)=\\frac12(9x^2+7y^2)+1x+1y+-7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+7y^2)+1x+1y+-7 $\n\n$ \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 1403
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Compute the indefinite integral: $\\int -9e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -9e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 1404
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Prove that $(\\mathbb{Z}_16, +)$ is a group under addition modulo 16."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_16=\\{0,1,\\dots,15\\}$ with operation $+$ modulo $16$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1405
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Prove that $(\\mathbb{Z}_24, +)$ is a group under addition modulo 24."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_24=\\{0,1,\\dots,23\\}$ with operation $+$ modulo $24$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1406
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Find the modular inverse of 32 modulo 39, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $32\\cdot a^{-1} \\equiv 1 \\pmod{39}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1407
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Compute $(187+-197) \\bmod 5$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (187+-197) \\bmod 5 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1408
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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$ \\alpha = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 1409
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 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 + 7 $\n... | {
"type": "optimization",
"seed": 1337,
"index": 1410
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. 203 - 779 = 950x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 203 - 779 = 950x $\n\nMove all terms to the left (standard form):\n$ -950x + -576 = 0 $\n\nIsolate the $x$ term:\n$ -950x = 576 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1411
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\nThe gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 1412
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -28x + 421 = -728"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -28x + 421 = -728 $\n\nMove all terms to the left (standard form):\n$ -28x + 1149 = 0 $\n\nIsolate the $x$ term:\n$ -28x = -1149 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1413
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. 394x - 328 = -962"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 394x - 328 = -962 $\n\nMove all terms to the left (standard form):\n$ 394x + 634 = 0 $\n\nIsolate the $x$ term:\n$ 394x = -634 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 1414
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-164 + 990/22) * 2) + 3^4 - log_5(15625) + (-208 mod 25) + floor(-181/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-164 + 990/22) * 2) + 3^4 - log_5(15625) + (-208 mod 25) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1415
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal v... | {
"type": "trigonometry",
"seed": 1337,
"index": 1416
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Evaluate: ((-120 + -756/18) * 13) + 10^5 - log_6(7776) + (-153 mod 25) + floor(99/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-120 + -756/18) * 13) + 10^5 - log_6(7776) + (-153 mod 25) + floor(99/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1417
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 14 + 116 + 33x^2 = 179x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 14 + 116 + 33x^2 = 179x $\n\nMove all terms to the left (standard form):\n$ 33x^2 + -179x + 130 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1418
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((-6 + 925/25) * 6) + 11^3 - log_5(625) + (-314 mod 18) + ceil(128/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-6 + 925/25) * 6) + 11^3 - log_5(625) + (-314 mod 18) + ceil(128/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 1419
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha... | {
"type": "trigonometry",
"seed": 1337,
"index": 1420
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((-185 + 592/16) * 10) + 11^3 - log_9(531441) + (-16 mod 5) + floor(6/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-185 + 592/16) * 10) + 11^3 - log_9(531441) + (-16 mod 5) + floor(6/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1421
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&0&-3\\\\\\3&4&0\\\\\\1&5&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-10\\\\\\18\\\\\\17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1422
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-164 + 506/22) * 17) + 8^4 - log_6(216) + (473 mod 5) + floor(-18/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-164 + 506/22) * 17) + 8^4 - log_6(216) + (473 mod 5) + floor(-18/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1423
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. -886x + 745 = -689"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -886x + 745 = -689 $\n\nMove all terms to the left (standard form):\n$ -886x + 1434 = 0 $\n\nIsolate the $x$ term:\n$ -886x = -1434 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1424
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Evaluate: ((-102 + -252/14) * 1) + 4^5 - log_9(6561) + (-57 mod 7) + round(88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-102 + -252/14) * 1) + 4^5 - log_9(6561) + (-57 mod 7) + round(8... | {
"type": "arithmetic",
"seed": 1337,
"index": 1425
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Compute the indefinite integral: $\\int (1x + 5)e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + 5)e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration b... | {
"type": "calculus",
"seed": 1337,
"index": 1426
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 949 + 758 = 239x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 949 + 758 = 239x $\n\nMove all terms to the left (standard form):\n$ -239x + 1707 = 0 $\n\nIsolate the $x$ term:\n$ -239x = -1707 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1427
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute the indefinite integral: $\\int 6\\sin(3x) + -8\\cos(9x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6\\sin(3x) + -8\\cos(9x)\\,dx $\n\nUse standard antiderivatives (and in... | {
"type": "calculus",
"seed": 1337,
"index": 1428
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -663 + 32x = 181"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -663 + 32x = 181 $\n\nMove all terms to the left (standard form):\n$ 32x + -844 = 0 $\n\nIsolate the $x$ term:\n$ 32x = 844 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 1429
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Solve for $x$ (in radians): cos(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-1) = 3.14159 $\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 1430
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 49x + 28x^2 + 119 = 58"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 49x + 28x^2 + 119 = 58 $\n\nMove all terms to the left (standard form):\n$ 28x^2 + 49x + 61 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1431
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 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\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 1432
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Compute the indefinite integral: $\\int 1e^{-2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1e^{-2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed)... | {
"type": "calculus",
"seed": 1337,
"index": 1433
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute the indefinite integral: $\\int 1\\sin(9x) + 8\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1\\sin(9x) + 8\\cos(6x)\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 1434
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 836 - 539 = 706x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 836 - 539 = 706x $\n\nMove all terms to the left (standard form):\n$ -706x + 297 = 0 $\n\nIsolate the $x$ term:\n$ -706x = -297 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1435
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Prove that $f(x)=3x^2+-4x+10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+-4x+10$.\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": 1436
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}1&0\\\\\\9&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-7\\\\\\-75\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}1&0\\\\\\9&-4\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1437
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 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... | {
"type": "calculus",
"seed": 1337,
"index": 1438
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Differentiate with respect to $x$: $f(x) = 6x^3 + 4x^2 + -8x + 11$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6x^3 + 4x^2 + -8x + 11 $\n\nApply the standard differentiation rules:\n$ f'(x) =... | {
"type": "calculus",
"seed": 1337,
"index": 1439
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 1440
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -243 - 361 = -863x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -243 - 361 = -863x $\n\nMove all terms to the left (standard form):\n$ 863x + -604 = 0 $\n\nIsolate the $x$ term:\n$ 863x = 604 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1441
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Compute $(-23+40) \\bmod 22$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-23+40) \\bmod 22 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1442
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -836 + 793 = 375x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -836 + 793 = 375x $\n\nMove all terms to the left (standard form):\n$ -375x + -43 = 0 $\n\nIsolate the $x$ term:\n$ -375x = 43 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1443
} |
[
{
"role": "user",
"content": "solve: Compute the indefinite integral: $\\int 7\\sin(9x) + 1\\cos(7x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 7\\sin(9x) + 1\\cos(7x)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\... | {
"type": "calculus",
"seed": 1337,
"index": 1444
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 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$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 1445
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Prove that $f(x,y)=\\frac12(10x^2+3y^2)+0x+-2y+-3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+3y^2)+0x+-2y+-3 $\n\n$ \\frac{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 1446
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 177x - 787 = 559"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 177x - 787 = 559 $\n\nMove all terms to the left (standard form):\n$ 177x + -1346 = 0 $\n\nIsolate the $x$ term:\n$ 177x = 1346 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 1447
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the indefinite integral: $\\int \\ln(5x + 6)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + 6)\\,dx $\n\nUse standard antiderivatives (and integration by parts if ... | {
"type": "calculus",
"seed": 1337,
"index": 1448
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute the determinant: $A=\\begin{pmatrix}1&3\\\\5&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}1&3\\\\\\5&-8\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1449
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Evaluate: ((14 + -195/5) * 5) + 11^2 - log_5(125) + (-244 mod 16) + floor(-17/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((14 + -195/5) * 5) + 11^2 - log_5(125) + (-244 mod 16) + floor(-17/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1450
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 4x + 85x^2 + 187 = 54"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 4x + 85x^2 + 187 = 54 $\n\nMove all terms to the left (standard form):\n$ 85x^2 + 4x + 133 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1451
} |
[
{
"role": "user",
"content": "Solve the following math equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha =... | {
"type": "trigonometry",
"seed": 1337,
"index": 1452
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. -20 - 115x^2 - 5 = 5x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20 - 115x^2 - 5 = 5x $\n\nMove all terms to the left (standard form):\n$ -115x^2 + -5x + -25 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1453
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Compute the indefinite integral: $\\int -4x^3 + 9x^2 + -16x + 9\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4x^3 + 9x^2 + -16x + 9\\,dx $\n\nUse standard antiderivatives (a... | {
"type": "calculus",
"seed": 1337,
"index": 1454
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Prove that $f(x)=1x^2+-10x+1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+-10x+1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$... | {
"type": "optimization",
"seed": 1337,
"index": 1455
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 1456
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Find the modular inverse of 3 modulo 37, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{37}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees i... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1457
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -108x + 854 = 354"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -108x + 854 = 354 $\n\nMove all terms to the left (standard form):\n$ -108x + 500 = 0 $\n\nIsolate the $x$ term:\n$ -108x = -500 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1458
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Differentiate with respect to $x$: $f(x) = (-1x + 7)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-1x + 7)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) =... | {
"type": "calculus",
"seed": 1337,
"index": 1459
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&-4&4\\\\\\-4&-3&5\\\\\\3&-5&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-29\\\\\\-11\\\\\\-2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1460
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Prove that $f(x,y)=\\frac12(2x^2+4y^2)+-1x+0y+-8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+4y^2)+-1x+0y+-8 $\n\n$ \\frac{\\partial^2 f... | {
"type": "optimization",
"seed": 1337,
"index": 1461
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 505x + 903 = 411"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 505x + 903 = 411 $\n\nMove all terms to the left (standard form):\n$ 505x + 492 = 0 $\n\nIsolate the $x$ term:\n$ 505x = -492 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 1462
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&-7\\\\\\2&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}43\\\\\\37\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&-7\\\\\\2&... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1463
} |
[
{
"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": 1464
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Prove that $f(x,y)=\\frac12(2x^2+1y^2)+0x+2y+-8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+1y^2)+0x+2y+-8 $\n\n$ \\frac{\\partial^2 f}{\\partial x... | {
"type": "optimization",
"seed": 1337,
"index": 1465
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&0\\\\\\8&9\\end{pmatrix},\\quad b=\\begin{pmatrix}32\\\\\\100\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&0\\\\\\8&9\\end{pm... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1466
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Find the modular inverse of 17 modulo 39, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{39}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1467
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Find the modular inverse of 21 modulo 38, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $21\\cdot a^{-1} \\equiv 1 \\pmod{38}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1468
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Differentiate with respect to $x$: $f(x) = \\ln(1x + -5)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(1x + -5) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\fra... | {
"type": "calculus",
"seed": 1337,
"index": 1469
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 12x^2 - 183 + 145 = -142x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 12x^2 - 183 + 145 = -142x $\n\nMove all terms to the left (standard form):\n$ 12x^2 + 142x + -38 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1470
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Find the modular inverse of 11 modulo 31, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{31}$.\n\nSince $\\gcd(a,m)=1$, Bézout's iden... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1471
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 688 - 633 = -49x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 688 - 633 = -49x $\n\nMove all terms to the left (standard form):\n$ 49x + 55 = 0 $\n\nIsolate the $x$ term:\n$ 49x = -55 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 1472
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -227 + 683x = -484"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -227 + 683x = -484 $\n\nMove all terms to the left (standard form):\n$ 683x + 257 = 0 $\n\nIsolate the $x$ term:\n$ 683x = -257 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 1473
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}1&1\\\\\\-6&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-8\\\\\\49\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}1&1\\\\\\-6... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1474
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Compute the indefinite integral: $\\int 4\\sin(6x) + 4\\cos(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4\\sin(6x) + 4\\cos(3x)\\,dx $\n\nUse standard antiderivatives (and integration by... | {
"type": "calculus",
"seed": 1337,
"index": 1475
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Find $A^{-1}$ for $A=\\begin{pmatrix}-4&0\\\\-2&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -4 & 0 \\\\ -2 & -6 \\end{pmatrix} $\n\nCo... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1476
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((-6 + -432/18) * 1) + 10^2 - log_8(32768) + (499 mod 27) + floor(45/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-6 + -432/18) * 1) + 10^2 - log_8(32768) + (499 mod 27) + floor(45/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 1477
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -435 - 34x = -400"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -435 - 34x = -400 $\n\nMove all terms to the left (standard form):\n$ -34x + -35 = 0 $\n\nIsolate the $x$ term:\n$ -34x = 35 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1478
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 368 + 666x = -315"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 368 + 666x = -315 $\n\nMove all terms to the left (standard form):\n$ 666x + 683 = 0 $\n\nIsolate the $x$ term:\n$ 666x = -683 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1479
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((47 + 748/22) * 7) + 3^3 - log_9(81) + (464 mod 19) + ceil(179/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((47 + 748/22) * 7) + 3^3 - log_9(81) + (464 mod 19) + ceil(179/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 1480
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -46x^2 - 98 - 167x = 107"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -46x^2 - 98 - 167x = 107 $\n\nMove all terms to the left (standard form):\n$ -46x^2 + -167x + -205 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1481
} |
[
{
"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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 1482
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Differentiate with respect to $x$: $f(x) = -2x^3 + -7x^2 + 16x + -4$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2x^3 + -7x^2 + 16x + -4 $\n\nApply the standard differentiation rules... | {
"type": "calculus",
"seed": 1337,
"index": 1483
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Differentiate with respect to $x$: $f(x) = -3x^3 + -2x^2 + -7x + 3$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + -2x^2 + -7x + 3 $\n\nApply the standard differentiation rules:\n$ f'(x) =... | {
"type": "calculus",
"seed": 1337,
"index": 1484
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 13 - 97x^2 + 79 = 191x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13 - 97x^2 + 79 = 191x $\n\nMove all terms to the left (standard form):\n$ -97x^2 + -191x + 92 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1485
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Prove that $(\\mathbb{Z}_15, +)$ is a group under addition modulo 15."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_15=\\{0,1,\\dots,14\\}$ with operation $+$ modulo $15$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1486
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((-199 + 357/21) * 16) + 2^5 - log_8(64) + (-425 mod 18) + ceil(89/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-199 + 357/21) * 16) + 2^5 - log_8(64) + (-425 mod 18) + ceil(89/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1487
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 43x + 195 - 38x^2 = -66"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 43x + 195 - 38x^2 = -66 $\n\nMove all terms to the left (standard form):\n$ -38x^2 + 43x + 261 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1488
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Evaluate: ((111 + -325/13) * 7) + 11^2 - log_5(625) + (341 mod 13) + ceil(60/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((111 + -325/13) * 7) + 11^2 - log_5(625) + (341 mod 13) + ceil(60/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 1489
} |
[
{
"role": "user",
"content": "Please solve this mathematical 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 $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1490
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((9 + -456/12) * 16) + 7^5 - log_5(125) + (-311 mod 10) + floor(-113/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((9 + -456/12) * 16) + 7^5 - log_5(125) + (-311 mod 10) + floor(-113/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1491
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in\\mathbb{... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1492
} |
[
{
"role": "user",
"content": "Please compute the answer 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{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 1493
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Find the modular inverse of 7 modulo 15, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{15}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1494
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 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$... | {
"type": "optimization",
"seed": 1337,
"index": 1495
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Compute the determinant: $A=\\begin{pmatrix}5&4\\\\7&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}5&4\\\\\\7&2\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1496
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. -368x - 211 = -241"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -368x - 211 = -241 $\n\nMove all terms to the left (standard form):\n$ -368x + 30 = 0 $\n\nIsolate the $x$ term:\n$ -368x = -30 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1497
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 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).... | {
"type": "trigonometry",
"seed": 1337,
"index": 1498
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 19x^2 - 69x - 48 = -135"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19x^2 - 69x - 48 = -135 $\n\nMove all terms to the left (standard form):\n$ 19x^2 + -69x + 87 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1499
} |
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