messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Provide the solution to the following equation. -357 + 777x = -233"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -357 + 777x = -233 $\n\nMove all terms to the left (standard form):\n$ 777x + -124 = 0 $\n\nIsolate the $x$ term:\n$ 777x = 124 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4400
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Compute the indefinite integral: $\\int \\ln(3x + -2)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(3x + -2)\\,dx $\n\nUse standard antiderivatives (and integration by parts if ne... | {
"type": "calculus",
"seed": 1337,
"index": 4401
} |
[
{
"role": "user",
"content": "Compute the correct solution for 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).... | {
"type": "trigonometry",
"seed": 1337,
"index": 4402
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. -38 + 50 - 7x^2 = 161x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -38 + 50 - 7x^2 = 161x $\n\nMove all terms to the left (standard form):\n$ -7x^2 + -161x + 12 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4403
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Compute the indefinite integral: $\\int (-4x + -10)e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-4x + -10)e^{2x}\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 4404
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the indefinite integral: $\\int (2x + -9)e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (2x + -9)e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 4405
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 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\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4406
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Compute the determinant: $A=\\begin{pmatrix}-9&-6\\\\3&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-9&-6\\\\\\3&-8\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4407
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((56 + -48/4) * 17) + 10^4 - log_3(3) + (-10 mod 5) + round(-171/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((56 + -48/4) * 17) + 10^4 - log_3(3) + (-10 mod 5) + round(-171/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4408
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. 46x - 1 + 43x^2 = -58"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 46x - 1 + 43x^2 = -58 $\n\nMove all terms to the left (standard form):\n$ 43x^2 + 46x + 57 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4409
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((50 + 360/18) * 13) + 7^4 - log_2(4) + (294 mod 13) + floor(-138/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((50 + 360/18) * 13) + 7^4 - log_2(4) + (294 mod 13) + floor(-138/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4410
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 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": 4411
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 986 - 384x = -684"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 986 - 384x = -684 $\n\nMove all terms to the left (standard form):\n$ -384x + 1670 = 0 $\n\nIsolate the $x$ term:\n$ -384x = -1670 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4412
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Differentiate with respect to $x$: $f(x) = (5x + -3)\\sin(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (5x + -3)\\sin(1x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 4413
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Evaluate: ((-4 + 231/11) * 7) + 8^5 - log_7(2401) + (-290 mod 17) + ceil(-145/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-4 + 231/11) * 7) + 8^5 - log_7(2401) + (-290 mod 17) + ceil(-145/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 4414
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Compute the indefinite integral: $\\int 2\\sin(2x) + 0\\cos(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2\\sin(2x) + 0\\cos(1x)\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 4415
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute the determinant: $A=\\begin{pmatrix}-1&-3\\\\-8&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&-3\\\\\\-8&1\\end{pmatrix} $\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4416
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 46 - 188x + 49 = 39x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 46 - 188x + 49 = 39x^2 $\n\nMove all terms to the left (standard form):\n$ -39x^2 + -188x + 95 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4417
} |
[
{
"role": "user",
"content": "Please calculate this equation. 33x^2 - 150 - 103x = -84"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33x^2 - 150 - 103x = -84 $\n\nMove all terms to the left (standard form):\n$ 33x^2 + -103x + -66 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4418
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Differentiate with respect to $x$: $f(x) = (4x + -9)\\sin(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (4x + -9)\\sin(4x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 4419
} |
[
{
"role": "user",
"content": "solve: Evaluate: ((-146 + 175/5) * 18) + 10^4 - log_6(6) + (-101 mod 10) + ceil(28/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-146 + 175/5) * 18) + 10^4 - log_6(6) + (-101 mod 10) + ceil(28/2) $\n\nCompute each component:\n$ 175/5 = 35 ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4420
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. 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": 4421
} |
[
{
"role": "user",
"content": "solve Prove that $f(x)=2x^2+2x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+2x+-2$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 4x + 2 $\n$ f''(x) = 4 $\n\nSince ... | {
"type": "optimization",
"seed": 1337,
"index": 4422
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 909 - 588x = 302"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 909 - 588x = 302 $\n\nMove all terms to the left (standard form):\n$ -588x + 607 = 0 $\n\nIsolate the $x$ term:\n$ -588x = -607 $\n\... | {
"type": "linear_equation",
"seed": 1337,
"index": 4423
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 34x - 65 - 44 = 134x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 34x - 65 - 44 = 134x^2 $\n\nMove all terms to the left (standard form):\n$ -134x^2 + 34x + -109 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4424
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the determinant: $A=\\begin{pmatrix}4&-4\\\\4&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}4&-4\\\\\\4&8\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4425
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Evaluate: ((94 + 48/6) * 10) + 12^5 - log_3(729) + (-142 mod 22) + round(120/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((94 + 48/6) * 10) + 12^5 - log_3(729) + (-142 mod 22) + round(120/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4426
} |
[
{
"role": "user",
"content": "Please calculate and resolve 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 = \\arct... | {
"type": "trigonometry",
"seed": 1337,
"index": 4427
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Compute the indefinite integral: $\\int \\ln(2x + -4)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + -4)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 4428
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 34 - 110x - 51 = 39x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 34 - 110x - 51 = 39x^2 $\n\nMove all terms to the left (standard form):\n$ -39x^2 + -110x + -17 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4429
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Find the modular inverse of 15 modulo 31, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $15\\cdot a^{-1} \\equiv 1 \\pmod{31}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4430
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((38 + -85/5) * 10) + 11^4 - log_5(15625) + (475 mod 23) + round(6/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((38 + -85/5) * 10) + 11^4 - log_5(15625) + (475 mod 23) + round(... | {
"type": "arithmetic",
"seed": 1337,
"index": 4431
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 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 $\n\nThe general... | {
"type": "trigonometry",
"seed": 1337,
"index": 4432
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((-68 + -256/16) * 2) + 4^4 - log_7(49) + (194 mod 5) + floor(-74/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-68 + -256/16) * 2) + 4^4 - log_7(49) + (194 mod 5) + floor(-74/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4433
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Differentiate with respect to $x$: $f(x) = (-3x + 5)e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-3x + 5)e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-3e^{4... | {
"type": "calculus",
"seed": 1337,
"index": 4434
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Compute the indefinite integral: $\\int 7e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 7e^{2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\... | {
"type": "calculus",
"seed": 1337,
"index": 4435
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -270 - 973 = -927x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -270 - 973 = -927x $\n\nMove all terms to the left (standard form):\n$ 927x + -1243 = 0 $\n\nIsolate the $x$ term:\n$ 927x = 1243 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4436
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Prove that $f(x,y)=\\frac12(1x^2+5y^2)+-4x+-4y+1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+5y^2)+-4x+-4y+1 $\n\n$ \\frac{\\partial^2 f}{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 4437
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((129 + 230/5) * 12) + 10^3 - log_9(81) + (212 mod 12) + floor(86/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((129 + 230/5) * 12) + 10^3 - log_9(81) + (212 mod 12) + floor(86/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4438
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. -700 + 167x = -243"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -700 + 167x = -243 $\n\nMove all terms to the left (standard form):\n$ 167x + -457 = 0 $\n\nIsolate the $x$ term:\n$ 167x = 457 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4439
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&-3&-2\\\\\\-1&-1&2\\\\\\2&-1&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}16\\\\\\-3\\\\\\10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4440
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Find the modular inverse of 2 modulo 9, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $2\\cdot a^{-1} \\equiv 1 \\pmod{9}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4441
} |
[
{
"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": 4442
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve for $x$ (in radians): tan(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(-1) = -0.785398 $\n\nThe... | {
"type": "trigonometry",
"seed": 1337,
"index": 4443
} |
[
{
"role": "user",
"content": "Can you determine the solution of this 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": 4444
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Prove that $f(x,y)=\\frac12(7x^2+4y^2)+-3x+2y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+4y^2)+-3x+2y+4 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 4445
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find the modular inverse of 13 modulo 20, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{20}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees inte... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4446
} |
[
{
"role": "user",
"content": "Please determine the outcome of 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 = \\arc... | {
"type": "trigonometry",
"seed": 1337,
"index": 4447
} |
[
{
"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": 4448
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -202 - 992x = 918"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -202 - 992x = 918 $\n\nMove all terms to the left (standard form):\n$ -992x + -1120 = 0 $\n\nIsolate the $x$ term:\n$ -992x = 1120 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4449
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Prove that $f(x)=4x^2+8x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+8x+-2$.\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": 4450
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((89 + 744/24) * 20) + 2^5 - log_4(1024) + (-29 mod 11) + round(-13/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((89 + 744/24) * 20) + 2^5 - log_4(1024) + (-29 mod 11) + round(-13/... | {
"type": "arithmetic",
"seed": 1337,
"index": 4451
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Prove that $f(x,y)=\\frac12(5x^2+7y^2)+2x+0y+10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+7y^2)+2x+0y+10 $\n\n$ \\frac{\\partial^2 f}{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 4452
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((-105 + -228/19) * 19) + 7^4 - log_10(10000) + (-239 mod 6) + floor(-66/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-105 + -228/19) * 19) + 7^4 - log_10(10000) + (-239 mod 6) + floor(-66/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4453
} |
[
{
"role": "user",
"content": "solve: \n\n 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 $a,b\\in\\mathbb{Z}_n$, then $(a+b)\\bmod n\\in\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4454
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 31x^2 - 104x - 164 = 177"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31x^2 - 104x - 164 = 177 $\n\nMove all terms to the left (standard form):\n$ 31x^2 + -104x + -341 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4455
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 4456
} |
[
{
"role": "user",
"content": "Solve the equation shown below. -111x + 471 = -412"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -111x + 471 = -412 $\n\nMove all terms to the left (standard form):\n$ -111x + 883 = 0 $\n\nIsolate the $x$ term:\n$ -111x = -883 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4457
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 97 - 788x = -266"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 97 - 788x = -266 $\n\nMove all terms to the left (standard form):\n$ -788x + 363 = 0 $\n\nIsolate the $x$ term:\n$ -788x = -363 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 4458
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Evaluate: ((9 + 820/20) * 14) + 11^5 - log_10(10) + (-57 mod 30) + round(26/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((9 + 820/20) * 14) + 11^5 - log_10(10) + (-57 mod 30) + round(26/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4459
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Find $A^{-1}$ for $A=\\begin{pmatrix}2&-6\\\\-2&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 2 & -6 \\\\ -2 & 0 \\end{pmatrix} $\n\nCompu... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4460
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&5\\\\\\0&1\\end{pmatrix},\\quad b=\\begin{pmatrix}96\\\\\\3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&5\\\\\\0&1\\end{... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4461
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 4462
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. 41 + 191 + 109x = 115x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 41 + 191 + 109x = 115x^2 $\n\nMove all terms to the left (standard form):\n$ -115x^2 + 109x + 232 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4463
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Prove that $f(x,y)=\\frac12(8x^2+5y^2)+-4x+-6y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(8x^2+5y^2)+-4x+-6y+-2 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 4464
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $... | {
"type": "trigonometry",
"seed": 1337,
"index": 4465
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -41x + 136 - 66x^2 = -105"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -41x + 136 - 66x^2 = -105 $\n\nMove all terms to the left (standard form):\n$ -66x^2 + -41x + 241 = 0 $\n\nApply the quadrat... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4466
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. -36x^2 - 104x + 189 = -113"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x^2 - 104x + 189 = -113 $\n\nMove all terms to the left (standard form):\n$ -36x^2 + -104x + 302 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4467
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 36x^2 + 108 - 60 = -183x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36x^2 + 108 - 60 = -183x $\n\nMove all terms to the left (standard form):\n$ 36x^2 + 183x + 48 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4468
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 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 $... | {
"type": "trigonometry",
"seed": 1337,
"index": 4469
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Prove that $(\\mathbb{Z}_13, +)$ is a group under addition modulo 13."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_13=\\{0,1,\\dots,12\\}$ with operation $+$ modulo $13$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4470
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n -143 - 41x = 175"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -143 - 41x = 175 $\n\nMove all terms to the left (standard form):\n$ -41x + -318 = 0 $\n\nIsolate the $x$ term:\n$ -41x = 318 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 4471
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&0&3\\\\\\-5&2&1\\\\\\-1&1&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-3\\\\\\-23\\\\\\-17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "S... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4472
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 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": 4473
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 4x^2 - 12 + 158 = -186x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 4x^2 - 12 + 158 = -186x $\n\nMove all terms to the left (standard form):\n$ 4x^2 + 186x + 146 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4474
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Differentiate with respect to $x$: $f(x) = -2e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-2e^{1x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 4475
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Compute the indefinite integral: $\\int -4x^3 + 2x^2 + 20x + -17\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4x^3 + 2x^2 + 20x + -17\\,dx $\n\nUse standard antiderivatives (and integrat... | {
"type": "calculus",
"seed": 1337,
"index": 4476
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Find the modular inverse of 33 modulo 38, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $33\\cdot a^{-1} \\equiv 1 \\pmod{38}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4477
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((169 + 588/14) * 13) + 2^5 - log_4(1024) + (-6 mod 2) + ceil(170/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((169 + 588/14) * 13) + 2^5 - log_4(1024) + (-6 mod 2) + ceil(170/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4478
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Evaluate: ((-149 + 600/12) * 11) + 7^2 - log_4(256) + (317 mod 11) + ceil(-17/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-149 + 600/12) * 11) + 7^2 - log_4(256) + (317 mod 11) + ceil(-17/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4479
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Find the modular inverse of 5 modulo 18, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{18}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identit... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4480
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Compute the determinant: $A=\\begin{pmatrix}-3&6\\\\1&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&6\\\\\\1&-9\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4481
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -17x - 24x^2 - 182 = -108"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17x - 24x^2 - 182 = -108 $\n\nMove all terms to the left (standard form):\n$ -24x^2 + -17x + -74 = 0 $\n\nApply the quadr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4482
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute the indefinite integral: $\\int (1x + 3)\\sin(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + 3)\\sin(5x)\\,dx $\n\nUse standard antiderivatives (and integ... | {
"type": "calculus",
"seed": 1337,
"index": 4483
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Prove that $f(x,y)=\\frac12(6x^2+4y^2)+2x+1y+6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+4y^2)+2x+1y+6 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 6,\\quad \\frac... | {
"type": "optimization",
"seed": 1337,
"index": 4484
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((-23 + 513/19) * 7) + 6^3 - log_9(81) + (-86 mod 8) + round(-124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-23 + 513/19) * 7) + 6^3 - log_9(81) + (-86 mod 8) + round(-124/2) $\n\nCompute each c... | {
"type": "arithmetic",
"seed": 1337,
"index": 4485
} |
[
{
"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": 4486
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 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": 4487
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 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": 4488
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 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 $f'(x)=0$, he... | {
"type": "optimization",
"seed": 1337,
"index": 4489
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Compute the indefinite integral: $\\int 4e^{-2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4e^{-2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$... | {
"type": "calculus",
"seed": 1337,
"index": 4490
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. -46 - 42x + 69x^2 = -150"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -46 - 42x + 69x^2 = -150 $\n\nMove all terms to the left (standard form):\n$ 69x^2 + -42x + 104 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4491
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute the indefinite integral: $\\int 3\\sin(5x) + -8\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3\\sin(5x) + -8\\cos(2x)\\,dx $\n\nUse standard antiderivatives (... | {
"type": "calculus",
"seed": 1337,
"index": 4492
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Evaluate: ((-188 + -560/20) * 7) + 5^5 - log_2(64) + (394 mod 6) + ceil(107/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-188 + -560/20) * 7) + 5^5 - log_2(64) + (394 mod 6) + ceil(107/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4493
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Evaluate: ((39 + -880/20) * 15) + 5^3 - log_10(1000000) + (55 mod 27) + floor(168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((39 + -880/20) * 15) + 5^3 - log_10(1000000) + (55 mod 27) + floor(168... | {
"type": "arithmetic",
"seed": 1337,
"index": 4494
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}7&4\\\\3&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 7 & 4 \\\\ 3 & 8 \\end{pmatrix} $\n\nCompute the determi... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4495
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Prove that $(\\mathbb{Z}_6, +)$ is a group under addition modulo 6."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_6=\\{0,1,\\dots,5\\}$ with operation $+$ modulo $6$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4496
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 4497
} |
[
{
"role": "user",
"content": "Please solve this math problem. -434 + 225x = 347"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -434 + 225x = 347 $\n\nMove all terms to the left (standard form):\n$ 225x + -781 = 0 $\n\nIsolate the $x$ term:\n$ 225x = 781 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 4498
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -18 - 158 - 73x^2 = -186x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -18 - 158 - 73x^2 = -186x $\n\nMove all terms to the left (standard form):\n$ -73x^2 + 186x + -176 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4499
} |
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