messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Can you find the solution to this equation? 706 + 210 = 423x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 706 + 210 = 423x $\n\nMove all terms to the left (standard form):\n$ -423x + 916 = 0 $\n\nIsolate the $x$ term:\n$ -423x = -916 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4500
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 533 + 682 = -880x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 533 + 682 = -880x $\n\nMove all terms to the left (standard form):\n$ 880x + 1215 = 0 $\n\nIsolate the $x$ term:\n$ 880x = -1215 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4501
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Prove that $(\\mathbb{Z}_4, +)$ is a group under addition modulo 4."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_4=\\{0,1,\\dots,3\\}$ with operation $+$ modulo $4$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, t... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4502
} |
[
{
"role": "user",
"content": "Resolve the equation provided. - 81 + 27x = 70x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ - 81 + 27x = 70x^2 $\n\nMove all terms to the left (standard form):\n$ -70x^2 + 27x + -81 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4503
} |
[
{
"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 = \\arccos... | {
"type": "trigonometry",
"seed": 1337,
"index": 4504
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((-10 + 92/2) * 4) + 4^5 - log_3(27) + (-327 mod 17) + floor(193/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-10 + 92/2) * 4) + 4^5 - log_3(27) + (-327 mod 17) + floor(193/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 4505
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Prove that $f(x)=8x^2+2x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+2x+-9$.\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": 4506
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 598 - 133 = 943x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 598 - 133 = 943x $\n\nMove all terms to the left (standard form):\n$ -943x + 465 = 0 $\n\nIsolate the $x$ term:\n$ -943x = -465 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4507
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((164 + -240/12) * 9) + 12^2 - log_8(64) + (321 mod 23) + ceil(-143/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((164 + -240/12) * 9) + 12^2 - log_8(64) + (321 mod 23) + ceil(-143/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 4508
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Differentiate with respect to $x$: $f(x) = (2x + 0)e^{6x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (2x + 0)e^{6x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{2e^{... | {
"type": "calculus",
"seed": 1337,
"index": 4509
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Find the modular inverse of 7 modulo 32, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{32}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4510
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((12 + 32/8) * 14) + 7^5 - log_10(10) + (-7 mod 24) + round(-199/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((12 + 32/8) * 14) + 7^5 - log_10(10) + (-7 mod 24) + round(-199/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 4511
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Solve for $x$ (in radians): sin(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-1) = -1.5708 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 4512
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&7\\\\\\-9&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}27\\\\\\-69\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&7\\\\\\-9&-1\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4513
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Differentiate with respect to $x$: $f(x) = \\ln(7x + 5)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(7x + 5) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{7}{7x... | {
"type": "calculus",
"seed": 1337,
"index": 4514
} |
[
{
"role": "user",
"content": "Please calculate this equation. -26 - 645 = 964x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -26 - 645 = 964x $\n\nMove all terms to the left (standard form):\n$ -964x + -671 = 0 $\n\nIsolate the $x$ term:\n$ -964x = 671 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 4515
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -28 + 91x - 75x^2 = 30"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -28 + 91x - 75x^2 = 30 $\n\nMove all terms to the left (standard form):\n$ -75x^2 + 91x + -58 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4516
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Differentiate with respect to $x$: $f(x) = (2x + 6)\\sin(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (2x + 6)\\sin(1x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\bo... | {
"type": "calculus",
"seed": 1337,
"index": 4517
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{... | {
"type": "optimization",
"seed": 1337,
"index": 4518
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 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\... | {
"type": "trigonometry",
"seed": 1337,
"index": 4519
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Compute the indefinite integral: $\\int -2\\sin(4x) + 0\\cos(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2\\sin(4x) + 0\\cos(1x)\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 4520
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Evaluate: ((-107 + -84/4) * 6) + 9^5 - log_4(4096) + (223 mod 20) + round(50/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-107 + -84/4) * 6) + 9^5 - log_4(4096) + (223 mod 20) + round(50/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4521
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 46 - 38 + 67x = -11x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 46 - 38 + 67x = -11x^2 $\n\nMove all terms to the left (standard form):\n$ 11x^2 + 67x + 8 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4522
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute the determinant: $A=\\begin{pmatrix}2&-2\\\\7&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&-2\\\\\\7&-3\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4523
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute the indefinite integral: $\\int \\ln(5x + -4)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + -4)\\,dx $\n\nUse standard antiderivatives (and integration by part... | {
"type": "calculus",
"seed": 1337,
"index": 4524
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-107 + -145/5) * 11) + 7^2 - log_9(81) + (496 mod 15) + floor(-154/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-107 + -145/5) * 11) + 7^2 - log_9(81) + (496 mod 15) + floor(-154/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4525
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the determinant: $A=\\begin{pmatrix}-9&3\\\\6&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-9&3\\\\\\6&9\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4526
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&-8\\\\\\-8&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\54\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&-8\\\\\\-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4527
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Differentiate with respect to $x$: $f(x) = 7\\sin(4x) + 2\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7\\sin(4x) + 2\\cos(1x) $\n\nApply the standard differentiation rules:\n$... | {
"type": "calculus",
"seed": 1337,
"index": 4528
} |
[
{
"role": "user",
"content": "Please determine the outcome of 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 = \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 4529
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Differentiate with respect to $x$: $f(x) = -8e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -8e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-16e^{2x}}... | {
"type": "calculus",
"seed": 1337,
"index": 4530
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((-69 + 240/8) * 2) + 7^4 - log_7(7) + (122 mod 27) + ceil(119/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-69 + 240/8) * 2) + 7^4 - log_7(7) + (122 mod 27) + ceil(119/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 4531
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 45x - 180x^2 - 78 = 67"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 45x - 180x^2 - 78 = 67 $\n\nMove all terms to the left (standard form):\n$ -180x^2 + 45x + -145 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4532
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Evaluate: ((-4 + 527/17) * 19) + 2^4 - log_3(729) + (-16 mod 15) + ceil(-38/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-4 + 527/17) * 19) + 2^4 - log_3(729) + (-16 mod 15) + ceil(-38/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4533
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Prove that $f(x)=1x^2+-4x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+-4x+-9$.\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": 4534
} |
[
{
"role": "user",
"content": "Find the numerical solution to this 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 $a,b\\in\\math... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4535
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((31 + -768/24) * 13) + 9^5 - log_5(125) + (-481 mod 8) + floor(52/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((31 + -768/24) * 13) + 9^5 - log_5(125) + (-481 mod 8) + floor(52/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4536
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -478 + 135x = -216"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -478 + 135x = -216 $\n\nMove all terms to the left (standard form):\n$ 135x + -262 = 0 $\n\nIsolate the $x$ term:\n$ 135x = 262 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4537
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -529 + 520 = 950x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -529 + 520 = 950x $\n\nMove all terms to the left (standard form):\n$ -950x + -9 = 0 $\n\nIsolate the $x$ term:\n$ -950x = 9 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4538
} |
[
{
"role": "user",
"content": "Determine the value produced by 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 = \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 4539
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((186 + 384/12) * 18) + 5^2 - log_3(243) + (473 mod 23) + ceil(-9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((186 + 384/12) * 18) + 5^2 - log_3(243) + (473 mod 23) + ceil(-9/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 4540
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 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^2-... | {
"type": "optimization",
"seed": 1337,
"index": 4541
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute the indefinite integral: $\\int \\ln(4x + -8)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(4x + -8)\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 4542
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Solve for $x$ (in radians): sin(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(1) = 1.5708 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 4543
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&-4\\\\\\8&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-50\\\\\\-45\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&-4\\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4544
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Prove that $f(x)=9x^2+8x+-3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+8x+-3$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x + ... | {
"type": "optimization",
"seed": 1337,
"index": 4545
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Solve for $x$ (in radians): sin(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 4546
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Find $A^{-1}$ for $A=\\begin{pmatrix}9&8\\\\9&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 9 & 8 \\\\ 9 & -6 \\end{pmatrix} $\n\nCompute the deter... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4547
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. -14 - 755 = -841x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -14 - 755 = -841x $\n\nMove all terms to the left (standard form):\n$ 841x + -769 = 0 $\n\nIsolate the $x$ term:\n$ 841x = 769 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 4548
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 384 - 310x = 27"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 384 - 310x = 27 $\n\nMove all terms to the left (standard form):\n$ -310x + 357 = 0 $\n\nIsolate the $x$ term:\n$ -310x = -357 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4549
} |
[
{
"role": "user",
"content": "solve: Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2 f}{\\partial x\\partial y} ... | {
"type": "optimization",
"seed": 1337,
"index": 4550
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((148 + 36/3) * 18) + 5^4 - log_7(2401) + (-199 mod 15) + ceil(-98/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((148 + 36/3) * 18) + 5^4 - log_7(2401) + (-199 mod 15) + ceil(-98/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4551
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -597 - 629 = 212x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -597 - 629 = 212x $\n\nMove all terms to the left (standard form):\n$ -212x + -1226 = 0 $\n\nIsolate the $x$ term:\n$ -212x = 1226 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4552
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 512 + 5 = 872x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 512 + 5 = 872x $\n\nMove all terms to the left (standard form):\n$ -872x + 517 = 0 $\n\nIsolate the $x$ term:\n$ -872x = -517 $\n\nDivide both sides by the ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4553
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&2\\\\-6&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & 2 \\\\ -6 & 3 \\end{pmatrix} $\n\nCompute the... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4554
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 37 + 168x - 132x^2 = 99"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 + 168x - 132x^2 = 99 $\n\nMove all terms to the left (standard form):\n$ -132x^2 + 168x + -62 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4555
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((-123 + 490/14) * 20) + 9^3 - log_7(117649) + (374 mod 30) + round(-27/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-123 + 490/14) * 20) + 9^3 - log_7(117649) + (374 mod 30) + round(-27/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4556
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -50x + 130 - 98 = 92x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50x + 130 - 98 = 92x^2 $\n\nMove all terms to the left (standard form):\n$ -92x^2 + -50x + 32 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4557
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Solve for $x$ (in radians): sin(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 4558
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Prove that $f(x)=4x^2+3x+-8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+3x+-8$.\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": 4559
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -42 + 286x = -658"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -42 + 286x = -658 $\n\nMove all terms to the left (standard form):\n$ 286x + 616 = 0 $\n\nIsolate the $x$ term:\n$ 286x = -616 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 4560
} |
[
{
"role": "user",
"content": "Solve the following math equation. -36x^2 + 65 + 43x = -77"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x^2 + 65 + 43x = -77 $\n\nMove all terms to the left (standard form):\n$ -36x^2 + 43x + 142 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4561
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4... | {
"type": "optimization",
"seed": 1337,
"index": 4562
} |
[
{
"role": "user",
"content": "Determine the solution of the given 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": 4563
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((-59 + -360/18) * 2) + 3^5 - log_3(27) + (482 mod 26) + round(-108/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-59 + -360/18) * 2) + 3^5 - log_3(27) + (482 mod 26) + round(-108/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 4564
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Evaluate: ((-150 + 1000/25) * 8) + 11^4 - log_8(8) + (-51 mod 16) + round(-118/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-150 + 1000/25) * 8) + 11^4 - log_8(8) + (-51 mod 16) + round(-118/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 4565
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((-82 + 392/8) * 3) + 8^5 - log_6(7776) + (-363 mod 25) + round(189/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-82 + 392/8) * 3) + 8^5 - log_6(7776) + (-363 mod 25) + round(189... | {
"type": "arithmetic",
"seed": 1337,
"index": 4566
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 17x + 58x^2 - 128 = 26"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 17x + 58x^2 - 128 = 26 $\n\nMove all terms to the left (standard form):\n$ 58x^2 + 17x + -154 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4567
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 11 + 181 - x = -175x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11 + 181 - x = -175x^2 $\n\nMove all terms to the left (standard form):\n$ 175x^2 + -1x + 192 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4568
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Solve for $x$ (in radians): cos(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(1) = 0 $\n\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 4569
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 4570
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Prove that $(\\mathbb{Z}_7, +)$ is a group under addition modulo 7."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_7=\\{0,1,\\dots,6\\}$ with operation $+$ modulo $7$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$,... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4571
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Compute $(142+80) \\bmod 11$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (142+80) \\bmod 11 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4572
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Find the modular inverse of 3 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4573
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. -48x^2 + 20 - 159x = 49"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48x^2 + 20 - 159x = 49 $\n\nMove all terms to the left (standard form):\n$ -48x^2 + -159x + -29 = 0 $\n\nApply the quadrat... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4574
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-3&-1\\\\\\-5&0&4\\\\\\1&5&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}36\\\\\\4\\\\\\-16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4575
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Find $A^{-1}$ for $A=\\begin{pmatrix}3&2\\\\0&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & 2 \\\\ 0 & 6 \\end{pmatrix} $\n\nCompute ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4576
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 27x + 79 - 29x^2 = 34"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27x + 79 - 29x^2 = 34 $\n\nMove all terms to the left (standard form):\n$ -29x^2 + 27x + 45 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4577
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 9x^2 + 127 + 37x = 143"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 9x^2 + 127 + 37x = 143 $\n\nMove all terms to the left (standard form):\n$ 9x^2 + 37x + -16 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4578
} |
[
{
"role": "user",
"content": "Please solve this math problem. Prove that $f(x)=2x^2+-9x+10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+-9x+10$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 4x + -9... | {
"type": "optimization",
"seed": 1337,
"index": 4579
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute the indefinite integral: $\\int -6x^3 + -4x^2 + -5x + 2\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -6x^3 + -4x^2 + -5x + 2\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 4580
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Differentiate with respect to $x$: $f(x) = -6e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-24e^{4x... | {
"type": "calculus",
"seed": 1337,
"index": 4581
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Differentiate with respect to $x$: $f(x) = -9\\sin(2x) + 3\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9\\sin(2x) + 3\\cos(8x) $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 4582
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -40x^2 + 97 + 126 = -190x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40x^2 + 97 + 126 = -190x $\n\nMove all terms to the left (standard form):\n$ -40x^2 + 190x + 223 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4583
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Evaluate: ((114 + -246/6) * 16) + 8^5 - log_10(100) + (-29 mod 25) + round(-73/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((114 + -246/6) * 16) + 8^5 - log_10(100) + (-29 mod 25) + round(-73... | {
"type": "arithmetic",
"seed": 1337,
"index": 4584
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((-147 + 95/5) * 6) + 9^4 - log_5(3125) + (-335 mod 27) + ceil(28/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-147 + 95/5) * 6) + 9^4 - log_5(3125) + (-335 mod 27) + ceil(28/2) $\n\nCompute each co... | {
"type": "arithmetic",
"seed": 1337,
"index": 4585
} |
[
{
"role": "user",
"content": "Please calculate this equation. -882x + 737 = 855"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -882x + 737 = 855 $\n\nMove all terms to the left (standard form):\n$ -882x + -118 = 0 $\n\nIsolate the $x$ term:\n$ -882x = 118 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 4586
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 818 - 155x = -600"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 818 - 155x = -600 $\n\nMove all terms to the left (standard form):\n$ -155x + 1418 = 0 $\n\nIsolate the $x$ term:\n$ -155x = -1418 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 4587
} |
[
{
"role": "user",
"content": "Please evaluate and compute 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{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 4588
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Differentiate with respect to $x$: $f(x) = 9\\sin(7x) + -1\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 9\\sin(7x) + -1\\cos(1x) $\n\nApply the standard differentiation rules:\n... | {
"type": "calculus",
"seed": 1337,
"index": 4589
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&-3\\\\\\-5&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}-21\\\\\\23\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&-3\\\\\\-5&-8\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4590
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 340 - 463 = 460x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 340 - 463 = 460x $\n\nMove all terms to the left (standard form):\n$ -460x + -123 = 0 $\n\nIsolate the $x$ term:\n$ -460x = 123 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 4591
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((-136 + 120/20) * 10) + 9^2 - log_8(8) + (106 mod 8) + round(73/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-136 + 120/20) * 10) + 9^2 - log_8(8) + (106 mod 8) + round(73/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4592
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute the determinant: $A=\\begin{pmatrix}5&7\\\\8&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}5&7\\\\\\8&-9\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4593
} |
[
{
"role": "user",
"content": "solve: \n\n -515 - 337 = 686x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -515 - 337 = 686x $\n\nMove all terms to the left (standard form):\n$ -686x + -852 = 0 $\n\nIsolate the $x$ term:\n$ -686x = 852 $\n\nDivide both sides by the coefficient of ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4594
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Evaluate: ((-198 + 533/13) * 9) + 10^4 - log_4(64) + (-24 mod 7) + ceil(-181/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-198 + 533/13) * 9) + 10^4 - log_4(64) + (-24 mod 7) + ceil(-181/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4595
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Compute the indefinite integral: $\\int (1x + -5)e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + -5)e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by pa... | {
"type": "calculus",
"seed": 1337,
"index": 4596
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((-122 + 145/5) * 5) + 8^3 - log_2(4) + (123 mod 16) + floor(157/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-122 + 145/5) * 5) + 8^3 - log_2(4) + (123 mod 16) + floor(157/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4597
} |
[
{
"role": "user",
"content": "Compute and 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} & \... | {
"type": "optimization",
"seed": 1337,
"index": 4598
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -526x - 952 = -326"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -526x - 952 = -326 $\n\nMove all terms to the left (standard form):\n$ -526x + -626 = 0 $\n\nIsolate the $x$ term:\n$ -526x = 626 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4599
} |
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