messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Determine the solution for this math problem. Differentiate with respect to $x$: $f(x) = (6x + -7)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (6x + -7)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\... | {
"type": "calculus",
"seed": 1337,
"index": 7400
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((-184 + -60/3) * 9) + 2^3 - log_8(8) + (255 mod 11) + round(-91/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-184 + -60/3) * 9) + 2^3 - log_8(8) + (255 mod 11) + round(-91/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 7401
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Prove that $f(x,y)=\\frac12(9x^2+6y^2)+-3x+3y+6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+6y^2)+-3x+3y+6 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 7402
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 47 + 807 = -109x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 47 + 807 = -109x $\n\nMove all terms to the left (standard form):\n$ 109x + 854 = 0 $\n\nIsolate the $x$ term:\n$ 109x = -854 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 7403
} |
[
{
"role": "user",
"content": "Can you compute this equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&1\\\\\\5&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-14\\\\\\-10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&1\\\\\\5&3\\end{pmatrix}... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7404
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Compute the indefinite integral: $\\int 6e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if ... | {
"type": "calculus",
"seed": 1337,
"index": 7405
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. -580 + 787x = -537"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -580 + 787x = -537 $\n\nMove all terms to the left (standard form):\n$ 787x + -43 = 0 $\n\nIsolate the $x$ term:\n$ 787x = 43 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 7406
} |
[
{
"role": "user",
"content": "Can you solve the equation below? -214 - 162x = 746"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -214 - 162x = 746 $\n\nMove all terms to the left (standard form):\n$ -162x + -960 = 0 $\n\nIsolate the $x$ term:\n$ -162x = 960 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7407
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Compute the indefinite integral: $\\int -1\\sin(6x) + -4\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1\\sin(6x) + -4\\cos(6x)\\,dx $\n\nUse standard antiderivatives (and in... | {
"type": "calculus",
"seed": 1337,
"index": 7408
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((79 + -12/3) * 5) + 4^4 - log_7(7) + (-244 mod 8) + ceil(-129/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((79 + -12/3) * 5) + 4^4 - log_7(7) + (-244 mod 8) + ceil(-129/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 7409
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Prove that $f(x)=9x^2+-9x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-9x+-1$.\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": 7410
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 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^{-... | {
"type": "calculus",
"seed": 1337,
"index": 7411
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 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 $\n\nThe genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 7412
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((-53 + 570/19) * 14) + 4^2 - log_7(49) + (-272 mod 24) + floor(-5/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-53 + 570/19) * 14) + 4^2 - log_7(49) + (-272 mod 24) + floor(-5/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 7413
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. -518x + 740 = -662"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -518x + 740 = -662 $\n\nMove all terms to the left (standard form):\n$ -518x + 1402 = 0 $\n\nIsolate the $x$ term:\n$ -518x = -1402 $\n\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 7414
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((190 + -630/18) * 17) + 12^3 - log_8(8) + (181 mod 7) + round(-64/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((190 + -630/18) * 17) + 12^3 - log_8(8) + (181 mod 7) + round(-64/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 7415
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Differentiate with respect to $x$: $f(x) = 1\\sin(9x) + 4\\cos(9x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1\\sin(9x) + 4\\cos(9x) $\n\nApply the standard differentiation rules:\n$ f'... | {
"type": "calculus",
"seed": 1337,
"index": 7416
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute $(-16+-87) \\bmod 21$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-16+-87) \\bmod 21 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7417
} |
[
{
"role": "user",
"content": "Can you evaluate this math 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{\\partial^... | {
"type": "optimization",
"seed": 1337,
"index": 7418
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}1&-7\\\\1&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 1 & -7 \\\\ 1 & -1 \\end{pmatrix} $\n\nCompute the deter... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7419
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Compute the indefinite integral: $\\int \\ln(9x + 0)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(9x + 0)\\,dx $\n\nUse standard antiderivatives (and integration by parts if n... | {
"type": "calculus",
"seed": 1337,
"index": 7420
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&-4&2\\\\\\3&-4&0\\\\\\2&-2&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}25\\\\\\25\\\\\\14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7421
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((192 + -48/16) * 3) + 7^4 - log_3(243) + (488 mod 25) + round(106/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((192 + -48/16) * 3) + 7^4 - log_3(243) + (488 mod 25) + round(106/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 7422
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Compute $(84+-109) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (84+-109) \\bmod 12 $\n\nUse the rule that addition is compatible with redu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7423
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Find the modular inverse of 30 modulo 37, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $30\\cdot a^{-1} \\equiv 1 \\pmod{37}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7424
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Compute the indefinite integral: $\\int \\ln(7x + 6)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(7x + 6)\\,dx $\n\nUse standard antiderivatives (and integration by parts if n... | {
"type": "calculus",
"seed": 1337,
"index": 7425
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 7426
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Prove that $(\\mathbb{Z}_10, +)$ is a group under addition modulo 10."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_10=\\{0,1,\\dots,9\\}$ with operation $+$ modulo $10$.\n\n**Closure:** If $a,b\\in\\mathbb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7427
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Differentiate with respect to $x$: $f(x) = \\ln(5x + -7)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(5x + -7) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 7428
} |
[
{
"role": "user",
"content": "solve: \n\n -45x^2 - 166x - 51 = -163"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -45x^2 - 166x - 51 = -163 $\n\nMove all terms to the left (standard form):\n$ -45x^2 + -166x + 112 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sq... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7429
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((91 + 120/24) * 11) + 11^2 - log_2(16) + (125 mod 10) + ceil(-134/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((91 + 120/24) * 11) + 11^2 - log_2(16) + (125 mod 10) + ceil(-134... | {
"type": "arithmetic",
"seed": 1337,
"index": 7430
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Evaluate: ((192 + -270/15) * 5) + 7^3 - log_2(2) + (260 mod 14) + floor(-170/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((192 + -270/15) * 5) + 7^3 - log_2(2) + (260 mod 14) + floor(-170/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 7431
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Prove that $(\\mathbb{Z}_2, +)$ is a group under addition modulo 2."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_2=\\{0,1,\\dots,1\\}$ with operation $+$ modulo $2$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, th... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7432
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Evaluate: ((-82 + -258/6) * 5) + 5^4 - log_9(6561) + (91 mod 25) + round(-115/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-82 + -258/6) * 5) + 5^4 - log_9(6561) + (91 mod 25) + round(-11... | {
"type": "arithmetic",
"seed": 1337,
"index": 7433
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Evaluate: ((-128 + 405/15) * 2) + 11^4 - log_7(2401) + (-241 mod 30) + round(132/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-128 + 405/15) * 2) + 11^4 - log_7(2401) + (-241 mod 30) + round(... | {
"type": "arithmetic",
"seed": 1337,
"index": 7434
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute $(195+-128) \\bmod 3$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (195+-128) \\bmod 3 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7435
} |
[
{
"role": "user",
"content": "solve: \n\n 10 - 118 - 98x^2 = -108x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 - 118 - 98x^2 = -108x $\n\nMove all terms to the left (standard form):\n$ -98x^2 + 108x + -108 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7436
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -721x + 915 = 36"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -721x + 915 = 36 $\n\nMove all terms to the left (standard form):\n$ -721x + 879 = 0 $\n\nIsolate the $x$ term:\n$ -721x = -879 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 7437
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((140 + -588/21) * 15) + 8^5 - log_5(125) + (-91 mod 4) + round(144/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((140 + -588/21) * 15) + 8^5 - log_5(125) + (-91 mod 4) + round(144/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 7438
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Find the modular inverse of 9 modulo 32, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{32}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7439
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 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": 7440
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -23 - 160x + 62x^2 = -25"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23 - 160x + 62x^2 = -25 $\n\nMove all terms to the left (standard form):\n$ 62x^2 + -160x + 2 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7441
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Prove that $(\\mathbb{Z}_5, +)$ is a group under addition modulo 5."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_5=\\{0,1,\\dots,4\\}$ with operation $+$ modulo $5$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7442
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Prove that $f(x,y)=\\frac12(9x^2+3y^2)+4x+6y+2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+3y^2)+4x+6y+2 $\n\n$ \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 7443
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Evaluate: ((-162 + 287/7) * 12) + 11^2 - log_2(2) + (93 mod 14) + round(-68/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-162 + 287/7) * 12) + 11^2 - log_2(2) + (93 mod 14) + round(-68/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 7444
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((-146 + -210/6) * 16) + 5^3 - log_6(1296) + (-412 mod 23) + floor(60/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-146 + -210/6) * 16) + 5^3 - log_6(1296) + (-412 mod 23) + floor(60/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 7445
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&2&-2\\\\\\-4&-1&2\\\\\\-5&3&2\\end{pmatrix},\\quad b=\\begin{pmatrix}-9\\\\\\17\\\\\\16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7446
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&1&-4\\\\\\5&-4&2\\\\\\5&3&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-13\\\\\\17\\\\\\6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7447
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 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:\... | {
"type": "optimization",
"seed": 1337,
"index": 7448
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. -47 + 26x^2 + 52x = 0"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47 + 26x^2 + 52x = 0 $\n\nMove all terms to the left (standard form):\n$ 26x^2 + 52x + -47 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7449
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -25x - 403 = -174"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -25x - 403 = -174 $\n\nMove all terms to the left (standard form):\n$ -25x + -229 = 0 $\n\nIsolate the $x$ term:\n$ -25x = 229 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 7450
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Differentiate with respect to $x$: $f(x) = 3x^3 + 6x^2 + -17x + 8$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3x^3 + 6x^2 + -17x + 8 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 7451
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Differentiate with respect to $x$: $f(x) = -3\\sin(2x) + -2\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3\\sin(2x) + -2\\cos(7x) $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 7452
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -559 + 708 = -727x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -559 + 708 = -727x $\n\nMove all terms to the left (standard form):\n$ 727x + 149 = 0 $\n\nIsolate the $x$ term:\n$ 727x = -149 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 7453
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute $(109+-156) \\bmod 5$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (109+-156) \\bmod 5 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7454
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Evaluate: ((-6 + 84/4) * 6) + 6^4 - log_7(16807) + (203 mod 24) + floor(-107/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-6 + 84/4) * 6) + 6^4 - log_7(16807) + (203 mod 24) + floor(-107/... | {
"type": "arithmetic",
"seed": 1337,
"index": 7455
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((-31 + 399/19) * 20) + 11^2 - log_6(1296) + (453 mod 18) + ceil(-91/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-31 + 399/19) * 20) + 11^2 - log_6(1296) + (453 mod 18) + ceil(-91/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 7456
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Prove that $(\\mathbb{Z}_3, +)$ is a group under addition modulo 3."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_3=\\{0,1,\\dots,2\\}$ with operation $+$ modulo $3$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, t... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7457
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Find the modular inverse of 15 modulo 16, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $15\\cdot a^{-1} \\equiv 1 \\pmod{16}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees in... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7458
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-181 + -24/24) * 17) + 10^2 - log_5(25) + (-136 mod 8) + ceil(9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-181 + -24/24) * 17) + 10^2 - log_5(25) + (-136 mod 8) + ceil(9/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 7459
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alph... | {
"type": "trigonometry",
"seed": 1337,
"index": 7460
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute $(135+-181) \\bmod 9$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (135+-181) \\bmod 9 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7461
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Prove that $f(x)=2x^2+3x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+3x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 4x... | {
"type": "optimization",
"seed": 1337,
"index": 7462
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 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 $\n\nThe... | {
"type": "trigonometry",
"seed": 1337,
"index": 7463
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 31x^2 + 12 + 20x = 166"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31x^2 + 12 + 20x = 166 $\n\nMove all terms to the left (standard form):\n$ 31x^2 + 20x + -154 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7464
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((-157 + 36/4) * 11) + 4^4 - log_6(1296) + (-191 mod 6) + floor(-24/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-157 + 36/4) * 11) + 4^4 - log_6(1296) + (-191 mod 6) + floor(-24/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 7465
} |
[
{
"role": "user",
"content": "Please solve this math problem. 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 = \\arcsin(-\\frac{1... | {
"type": "trigonometry",
"seed": 1337,
"index": 7466
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. -10x + 62 - 88x^2 = 60"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -10x + 62 - 88x^2 = 60 $\n\nMove all terms to the left (standard form):\n$ -88x^2 + -10x + 2 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7467
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute $(-166+-160) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-166+-160) \\bmod 12 $\n\nUse the rule that addition is compatible wi... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7468
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 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": 7469
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Compute $(-65+-111) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-65+-111) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7470
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}0&3\\\\\\-8&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}12\\\\\\-16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}0&3\\\\\\-8&-8\\en... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7471
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. + 188x^2 + 135 = -44x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ + 188x^2 + 135 = -44x $\n\nMove all terms to the left (standard form):\n$ 188x^2 + 44x + 135 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7472
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Compute the determinant: $A=\\begin{pmatrix}3&0\\\\-6&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&0\\\\\\-6&0\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7473
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 677 - 568 = 324x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 677 - 568 = 324x $\n\nMove all terms to the left (standard form):\n$ -324x + 109 = 0 $\n\nIsolate the $x$ term:\n$ -324x = -109 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 7474
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided 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 $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 7475
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Prove that $f(x,y)=\\frac12(3x^2+10y^2)+-6x+2y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+10y^2)+-6x+2y+4 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 7476
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&3\\\\\\7&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}15\\\\\\48\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&3\\\\\\7&-6\\end{... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7477
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 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) = 3.1... | {
"type": "trigonometry",
"seed": 1337,
"index": 7478
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((-96 + -88/2) * 20) + 10^4 - log_2(8) + (471 mod 26) + round(-194/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-96 + -88/2) * 20) + 10^4 - log_2(8) + (471 mod 26) + round(-194/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 7479
} |
[
{
"role": "user",
"content": "Please find the value of this math 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": 7480
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -17 - 187x^2 - 93 = 199x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17 - 187x^2 - 93 = 199x $\n\nMove all terms to the left (standard form):\n$ -187x^2 + -199x + -110 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7481
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&-1&-4\\\\\\3&3&5\\\\\\0&3&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-20\\\\\\41\\\\\\24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by G... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7482
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 455 - 792 = -601x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 455 - 792 = -601x $\n\nMove all terms to the left (standard form):\n$ 601x + -337 = 0 $\n\nIsolate the $x$ term:\n$ 601x = 337 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 7483
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute the indefinite integral: $\\int 5e^{-4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5e^{-4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 7484
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -939 + 49x = -616"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -939 + 49x = -616 $\n\nMove all terms to the left (standard form):\n$ 49x + -323 = 0 $\n\nIsolate the $x$ term:\n$ 49x = 323 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 7485
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. 35x^2 + 17x + 192 = 71"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 35x^2 + 17x + 192 = 71 $\n\nMove all terms to the left (standard form):\n$ 35x^2 + 17x + 121 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7486
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 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 = \... | {
"type": "trigonometry",
"seed": 1337,
"index": 7487
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Evaluate: ((-141 + 1000/25) * 14) + 12^2 - log_4(1024) + (-450 mod 30) + round(138/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-141 + 1000/25) * 14) + 12^2 - log_4(1024) + (-450 mod 30) + round(138... | {
"type": "arithmetic",
"seed": 1337,
"index": 7488
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. -35x^2 + 143x - 58 = 43"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35x^2 + 143x - 58 = 43 $\n\nMove all terms to the left (standard form):\n$ -35x^2 + 143x + -101 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7489
} |
[
{
"role": "user",
"content": "solve: \n\n Compute the indefinite integral: $\\int -7\\sin(3x) + 4\\cos(7x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -7\\sin(3x) + 4\\cos(7x)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 7490
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((-1 + -64/16) * 20) + 6^4 - log_2(16) + (450 mod 24) + round(-116/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-1 + -64/16) * 20) + 6^4 - log_2(16) + (450 mod 24) + round(-116/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 7491
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. 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 = \\arcsin... | {
"type": "trigonometry",
"seed": 1337,
"index": 7492
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. 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 = \\arcsin(-\\... | {
"type": "trigonometry",
"seed": 1337,
"index": 7493
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Differentiate with respect to $x$: $f(x) = \\ln(1x + 8)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(1x + 8) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{... | {
"type": "calculus",
"seed": 1337,
"index": 7494
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&3&-4\\\\\\-1&1&-2\\\\\\1&-5&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}8\\\\\\2\\\\\\-25\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7495
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((-52 + 286/13) * 14) + 4^4 - log_3(243) + (-196 mod 9) + ceil(66/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-52 + 286/13) * 14) + 4^4 - log_3(243) + (-196 mod 9) + ceil(66/2) $\n\nCompute each co... | {
"type": "arithmetic",
"seed": 1337,
"index": 7496
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Evaluate: ((146 + -57/19) * 2) + 3^4 - log_10(1000) + (490 mod 25) + ceil(102/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((146 + -57/19) * 2) + 3^4 - log_10(1000) + (490 mod 25) + ceil(102/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 7497
} |
[
{
"role": "user",
"content": "Find the correct 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{\\... | {
"type": "optimization",
"seed": 1337,
"index": 7498
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-188 + 975/25) * 11) + 11^2 - log_10(1000000) + (-323 mod 4) + ceil(-127/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-188 + 975/25) * 11) + 11^2 - log_10(1000000) + (-323 mod 4) + ceil(-127/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 7499
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.