messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Compute the outcome of this equation. -2x^2 + 0 + 86x = 28"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2x^2 + 0 + 86x = 28 $\n\nMove all terms to the left (standard form):\n$ -2x^2 + 86x + -28 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6400
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Compute the indefinite integral: $\\int 2x^3 + 0x^2 + 4x + 16\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2x^3 + 0x^2 + 4x + 16\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 6401
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. 33x + 157 + 148 = -12x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33x + 157 + 148 = -12x^2 $\n\nMove all terms to the left (standard form):\n$ 12x^2 + 33x + 305 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6402
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&1\\\\\\7&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}49\\\\\\-28\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&1\\\\\\7&-3\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6403
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute $(195+-85) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (195+-85) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6404
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the determinant: $A=\\begin{pmatrix}-7&5\\\\2&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&5\\\\\\2&1\\end{pmatrix} $\n\nUse $\\det(A)=ad-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6405
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 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": 6406
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute the determinant: $A=\\begin{pmatrix}3&-4\\\\7&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&-4\\\\\\7&-3\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6407
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-168 + 506/22) * 16) + 7^2 - log_4(4096) + (18 mod 12) + round(147/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-168 + 506/22) * 16) + 7^2 - log_4(4096) + (18 mod 12) + rou... | {
"type": "arithmetic",
"seed": 1337,
"index": 6408
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Find the modular inverse of 11 modulo 35, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{35}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6409
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute the determinant: $A=\\begin{pmatrix}-6&-6\\\\4&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-6&-6\\\\\\4&7\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6410
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Find the modular inverse of 4 modulo 5, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{5}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6411
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Compute the determinant: $A=\\begin{pmatrix}3&-9\\\\1&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&-9\\\\\\1&8\\end{pmatrix} $\n\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6412
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the determinant: $A=\\begin{pmatrix}-6&8\\\\2&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-6&8\\\\\\2&6\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6413
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-148 + -45/5) * 13) + 6^4 - log_10(1000) + (-150 mod 19) + floor(124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-148 + -45/5) * 13) + 6^4 - log_10(1000) + (-150 mod 19) + floor(124/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6414
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&3\\\\-4&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & 3 \\\\ -4 & 4 \\end{pmatrix} $\n\nCompute ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6415
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Differentiate with respect to $x$: $f(x) = 2\\sin(1x) + -8\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2\\sin(1x) + -8\\cos(8x) $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 6416
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find the modular inverse of 7 modulo 24, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{24}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6417
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. -115 + 972x = 612"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -115 + 972x = 612 $\n\nMove all terms to the left (standard form):\n$ 972x + -727 = 0 $\n\nIsolate the $x$ term:\n$ 972x = 727 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6418
} |
[
{
"role": "user",
"content": "Can you find 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{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 6419
} |
[
{
"role": "user",
"content": "solve: 42x + 142 + 14x^2 = 73"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 42x + 142 + 14x^2 = 73 $\n\nMove all terms to the left (standard form):\n$ 14x^2 + 42x + 69 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6420
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&4&-3\\\\\\-3&5&-2\\\\\\-5&-1&0\\end{pmatrix},\\quad b=\\begin{pmatrix}1\\\\\\-10\\\\\\-2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6421
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the determinant: $A=\\begin{pmatrix}-6&-2\\\\9&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-6&-2\\\\\\9&6\\end{pmatrix} $\n\nUse $\\det(A)... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6422
} |
[
{
"role": "user",
"content": "solve Prove that $f(x)=9x^2+-4x+-10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-4x+-10$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x + -4 $\n$ f''(x) = 18 $\n\... | {
"type": "optimization",
"seed": 1337,
"index": 6423
} |
[
{
"role": "user",
"content": "Please determine the outcome 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 6424
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((-158 + 690/15) * 15) + 6^3 - log_5(125) + (356 mod 20) + round(-70/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-158 + 690/15) * 15) + 6^3 - log_5(125) + (356 mod 20) + round(-70/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6425
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 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$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 6426
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan... | {
"type": "trigonometry",
"seed": 1337,
"index": 6427
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x,y)=\\frac12(1x^2+5y^2)+1x+-4y+6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+5y^2)+1x+-4y+6 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 6428
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute $(-2+-198) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-2+-198) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6429
} |
[
{
"role": "user",
"content": "Find the solution to the following 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": 6430
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((156 + -172/4) * 7) + 12^5 - log_7(49) + (228 mod 22) + round(-64/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((156 + -172/4) * 7) + 12^5 - log_7(49) + (228 mod 22) + round(-64/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 6431
} |
[
{
"role": "user",
"content": "Compute the solution for 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{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 6432
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-3&3\\\\\\5&-2&0\\\\\\2&2&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-14\\\\\\-1\\\\\\8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6433
} |
[
{
"role": "user",
"content": "Solve the given equation and provide 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 $f'(x)=0$... | {
"type": "optimization",
"seed": 1337,
"index": 6434
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute the indefinite integral: $\\int -3x^3 + 2x^2 + 20x + 20\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3x^3 + 2x^2 + 20x + 20\\,dx $\n\nUse standard antiderivatives (and integration by... | {
"type": "calculus",
"seed": 1337,
"index": 6435
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $(\\mathbb{Z}_20, +)$ is a group under addition modulo 20."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_20=\\{0,1,\\dots,19\\}$ with operation $+$ modulo $20$.\n\n**Closure:** If $a,b\\in\\mathbb{... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6436
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((-27 + -660/20) * 9) + 11^3 - log_9(729) + (-440 mod 10) + round(196/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-27 + -660/20) * 9) + 11^3 - log_9(729) + (-440 mod 10) + round(196/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 6437
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Evaluate: ((-47 + -874/23) * 16) + 4^4 - log_10(100000) + (196 mod 3) + round(-13/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-47 + -874/23) * 16) + 4^4 - log_10(100000) + (196 mod 3) + round(-13... | {
"type": "arithmetic",
"seed": 1337,
"index": 6438
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -30 - 57 - 183x^2 = -75x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -30 - 57 - 183x^2 = -75x $\n\nMove all terms to the left (standard form):\n$ -183x^2 + 75x + -87 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6439
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 237 + 253x = -661"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 237 + 253x = -661 $\n\nMove all terms to the left (standard form):\n$ 253x + 898 = 0 $\n\nIsolate the $x$ term:\n$ 253x = -898 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 6440
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Compute the determinant: $A=\\begin{pmatrix}3&6\\\\3&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&6\\\\\\3&2\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6441
} |
[
{
"role": "user",
"content": "solve: 441 + 399 = -499x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 441 + 399 = -499x $\n\nMove all terms to the left (standard form):\n$ 499x + 840 = 0 $\n\nIsolate the $x$ term:\n$ 499x = -840 $\n\nDivide both sides by the coefficient of $x$:\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 6442
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute the determinant: $A=\\begin{pmatrix}-3&7\\\\7&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&7\\\\\\7&8\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6443
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 441 + 780x = 375"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 441 + 780x = 375 $\n\nMove all terms to the left (standard form):\n$ 780x + 66 = 0 $\n\nIsolate the $x$ term:\n$ 780x = -66 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 6444
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((40 + 242/22) * 12) + 8^4 - log_7(7) + (-436 mod 18) + floor(-125/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((40 + 242/22) * 12) + 8^4 - log_7(7) + (-436 mod 18) + floor(-125/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 6445
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Compute the indefinite integral: $\\int 3\\sin(2x) + 8\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3\\sin(2x) + 8\\cos(5x)\\,dx $\n\nUse standard antiderivatives (and integra... | {
"type": "calculus",
"seed": 1337,
"index": 6446
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha... | {
"type": "trigonometry",
"seed": 1337,
"index": 6447
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 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 = \\arcc... | {
"type": "trigonometry",
"seed": 1337,
"index": 6448
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Solve for $x$ (in radians): tan(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(-1) = -0.785398 $... | {
"type": "trigonometry",
"seed": 1337,
"index": 6449
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute the indefinite integral: $\\int \\ln(7x + 9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(7x + 9)\\,dx $\n\nUse standard antiderivatives (and integration by... | {
"type": "calculus",
"seed": 1337,
"index": 6450
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Evaluate: ((-111 + 473/11) * 12) + 6^5 - log_3(3) + (96 mod 11) + ceil(172/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-111 + 473/11) * 12) + 6^5 - log_3(3) + (96 mod 11) + ceil(172/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 6451
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((55 + -1100/25) * 1) + 8^3 - log_9(59049) + (-398 mod 7) + floor(-143/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((55 + -1100/25) * 1) + 8^3 - log_9(59049) + (-398 mod 7) + floor(-14... | {
"type": "arithmetic",
"seed": 1337,
"index": 6452
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 6453
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Evaluate: ((-47 + 138/3) * 10) + 8^3 - log_8(262144) + (-155 mod 6) + ceil(82/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-47 + 138/3) * 10) + 8^3 - log_8(262144) + (-155 mod 6) + ceil(82/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 6454
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Differentiate with respect to $x$: $f(x) = 6\\sin(8x) + -7\\cos(2x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6\\sin(8x) + -7\\cos(2x) $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 6455
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-6&1\\\\\\1&4\\end{pmatrix},\\quad b=\\begin{pmatrix}39\\\\\\31\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-6&1\\\\\\1&4\\end{pmatrix... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6456
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 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$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 6457
} |
[
{
"role": "user",
"content": "Please resolve 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) = 0 $\n\nThe general s... | {
"type": "trigonometry",
"seed": 1337,
"index": 6458
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Differentiate with respect to $x$: $f(x) = 1\\sin(2x) + -6\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1\\sin(2x) + -6\\cos(7x) $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 6459
} |
[
{
"role": "user",
"content": "Find the correct solution for this 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": 6460
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 48 + 137x^2 - 56x = -199"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 48 + 137x^2 - 56x = -199 $\n\nMove all terms to the left (standard form):\n$ 137x^2 + -56x + 247 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6461
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-188 + -456/24) * 14) + 5^4 - log_4(4) + (-361 mod 6) + ceil(20/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-188 + -456/24) * 14) + 5^4 - log_4(4) + (-361 mod 6) + ceil(20/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 6462
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-7&7\\\\\\3&3\\end{pmatrix},\\quad b=\\begin{pmatrix}21\\\\\\3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-7&7\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6463
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((-101 + 414/23) * 4) + 2^5 - log_6(216) + (-262 mod 30) + ceil(-187/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-101 + 414/23) * 4) + 2^5 - log_6(216) + (-262 mod 30) + ceil(-187/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6464
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 26 - 72 - 152x = -6x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 26 - 72 - 152x = -6x^2 $\n\nMove all terms to the left (standard form):\n$ 6x^2 + -152x + -46 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6465
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 6466
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Find the modular inverse of 6 modulo 13, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $6\\cdot a^{-1} \\equiv 1 \\pmod{13}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarante... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6467
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-2&1\\\\-6&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -2 & 1 \\\\ -6 & -6 \\end{pmatrix} $\n\nCompu... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6468
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Prove that $f(x,y)=\\frac12(3x^2+9y^2)+1x+4y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+9y^2)+1x+4y+4 $\n\n$ \\frac{\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 6469
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 48 - 85x + 185x^2 = 21"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 48 - 85x + 185x^2 = 21 $\n\nMove all terms to the left (standard form):\n$ 185x^2 + -85x + 27 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6470
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the determinant: $A=\\begin{pmatrix}4&6\\\\3&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}4&6\\\\\\3&5\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6471
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Find the modular inverse of 4 modulo 9, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{9}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $x... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6472
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute $(-65+22) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-65+22) \\bmod 8 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6473
} |
[
{
"role": "user",
"content": "Can you compute this equation? -30 - 154x^2 + 2x = 168"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -30 - 154x^2 + 2x = 168 $\n\nMove all terms to the left (standard form):\n$ -154x^2 + 2x + -198 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6474
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -64x - 376 = -924"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -64x - 376 = -924 $\n\nMove all terms to the left (standard form):\n$ -64x + 548 = 0 $\n\nIsolate the $x$ term:\n$ -64x = -548 $\n\nDivide both sides by th... | {
"type": "linear_equation",
"seed": 1337,
"index": 6475
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((188 + -256/8) * 18) + 6^3 - log_7(343) + (301 mod 8) + round(89/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((188 + -256/8) * 18) + 6^3 - log_7(343) + (301 mod 8) + round(89/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6476
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 22x + 48 + 63x^2 = -136"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 22x + 48 + 63x^2 = -136 $\n\nMove all terms to the left (standard form):\n$ 63x^2 + 22x + 184 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6477
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Compute the indefinite integral: $\\int \\ln(9x + -2)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(9x + -2)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\... | {
"type": "calculus",
"seed": 1337,
"index": 6478
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Find the modular inverse of 8 modulo 9, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $8\\cdot a^{-1} \\equiv 1 \\pmod{9}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees int... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6479
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. -40 + 95x - 200 = -127x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40 + 95x - 200 = -127x^2 $\n\nMove all terms to the left (standard form):\n$ 127x^2 + 95x + -240 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6480
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Evaluate: ((-185 + 120/8) * 11) + 6^3 - log_10(100) + (-167 mod 3) + round(99/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-185 + 120/8) * 11) + 6^3 - log_10(100) + (-167 mod 3) + round(99/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 6481
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Find the modular inverse of 5 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6482
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Differentiate with respect to $x$: $f(x) = -9e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-9e^{1x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 6483
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. -328 + 247x = 558"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -328 + 247x = 558 $\n\nMove all terms to the left (standard form):\n$ 247x + -886 = 0 $\n\nIsolate the $x$ term:\n$ 247x = 886 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 6484
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute $(-13+-122) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-13+-122) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6485
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Compute the indefinite integral: $\\int \\ln(5x + 4)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + 4)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int \\ln(5x + ... | {
"type": "calculus",
"seed": 1337,
"index": 6486
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. -920 - 589 = 145x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -920 - 589 = 145x $\n\nMove all terms to the left (standard form):\n$ -145x + -1509 = 0 $\n\nIsolate the $x$ term:\n$ -145x = 1509 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 6487
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $f(x,y)=\\frac12(5x^2+3y^2)+4x+1y+7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+3y^2)+4x+1y+7 $\n\n$ \\frac{\\partial^2 f}{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 6488
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -957 + 549x = -537"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -957 + 549x = -537 $\n\nMove all terms to the left (standard form):\n$ 549x + -420 = 0 $\n\nIsolate the $x$ term:\n$ 549x = 420 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6489
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Prove that $f(x,y)=\\frac12(1x^2+1y^2)+6x+-6y+-3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+1y^2)+6x+-6y+-3 $\n\n$ \\frac{\\partial^2 f}{\\partial x^... | {
"type": "optimization",
"seed": 1337,
"index": 6490
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 14x^2 - 179 - 98 = -76x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 14x^2 - 179 - 98 = -76x $\n\nMove all terms to the left (standard form):\n$ 14x^2 + 76x + -277 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6491
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -70 + 404x = -166"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -70 + 404x = -166 $\n\nMove all terms to the left (standard form):\n$ 404x + 96 = 0 $\n\nIsolate the $x$ term:\n$ 404x = -96 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 6492
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((-75 + -594/18) * 11) + 4^3 - log_10(1000000) + (355 mod 3) + round(170/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-75 + -594/18) * 11) + 4^3 - log_10(1000000) + (355 mod 3) + round(170... | {
"type": "arithmetic",
"seed": 1337,
"index": 6493
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((-162 + 850/17) * 7) + 6^2 - log_9(531441) + (-298 mod 11) + round(-88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-162 + 850/17) * 7) + 6^2 - log_9(531441) + (-298 mod 11) + round(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 6494
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 15 + 9 - 186x = 56x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15 + 9 - 186x = 56x^2 $\n\nMove all terms to the left (standard form):\n$ -56x^2 + -186x + 24 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6495
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 927 + 157 = 372x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 927 + 157 = 372x $\n\nMove all terms to the left (standard form):\n$ -372x + 1084 = 0 $\n\nIsolate the $x$ term:\n$ -372x = -1084 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 6496
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. 70 + 537x = -285"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 70 + 537x = -285 $\n\nMove all terms to the left (standard form):\n$ 537x + 355 = 0 $\n\nIsolate the $x$ term:\n$ 537x = -355 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 6497
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&3\\\\\\-3&0\\end{pmatrix},\\quad b=\\begin{pmatrix}45\\\\\\24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&3\\\\\\-3&0\\en... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6498
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Prove that $f(x)=3x^2+4x+-4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+4x+-4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(... | {
"type": "optimization",
"seed": 1337,
"index": 6499
} |
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