messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((186 + -154/14) * 13) + 5^4 - log_9(9) + (-33 mod 14) + round(-173/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((186 + -154/14) * 13) + 5^4 - log_9(9) + (-33 mod 14) + round(-173/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 7300
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. -31 - 74x + 165 = -176x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -31 - 74x + 165 = -176x^2 $\n\nMove all terms to the left (standard form):\n$ 176x^2 + -74x + 134 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7301
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -45x^2 + 20 + 11 = 158x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -45x^2 + 20 + 11 = 158x $\n\nMove all terms to the left (standard form):\n$ -45x^2 + -158x + 31 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7302
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 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": 7303
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute $(15+135) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (15+135) \\bmod 12 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7304
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the determinant: $A=\\begin{pmatrix}2&1\\\\0&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&1\\\\\\0&-9\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7305
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 437 + 944x = -28"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 437 + 944x = -28 $\n\nMove all terms to the left (standard form):\n$ 944x + 465 = 0 $\n\nIsolate the $x$ term:\n$ 944x = -465 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 7306
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Evaluate: ((73 + 80/20) * 13) + 7^2 - log_5(25) + (385 mod 14) + floor(198/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((73 + 80/20) * 13) + 7^2 - log_5(25) + (385 mod 14) + floor(198/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 7307
} |
[
{
"role": "user",
"content": "Please evaluate and compute 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 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 7308
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. -22 - 142x + 194 = 75x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -22 - 142x + 194 = 75x^2 $\n\nMove all terms to the left (standard form):\n$ -75x^2 + -142x + 172 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7309
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -298 + 846x = 937"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -298 + 846x = 937 $\n\nMove all terms to the left (standard form):\n$ 846x + -1235 = 0 $\n\nIsolate the $x$ term:\n$ 846x = 1235 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 7310
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. 665 + 468x = -438"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 665 + 468x = -438 $\n\nMove all terms to the left (standard form):\n$ 468x + 1103 = 0 $\n\nIsolate the $x$ term:\n$ 468x = -1103 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 7311
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. -870 - 70 = 806x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -870 - 70 = 806x $\n\nMove all terms to the left (standard form):\n$ -806x + -940 = 0 $\n\nIsolate the $x$ term:\n$ -806x = 940 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 7312
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -35x - 68 + 63x^2 = 68"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35x - 68 + 63x^2 = 68 $\n\nMove all terms to the left (standard form):\n$ 63x^2 + -35x + -136 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7313
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Evaluate: ((65 + -32/2) * 5) + 4^5 - log_9(729) + (95 mod 2) + round(-124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((65 + -32/2) * 5) + 4^5 - log_9(729) + (95 mod 2) + round(-124/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 7314
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Find the modular inverse of 2 modulo 7, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $2\\cdot a^{-1} \\equiv 1 \\pmod{7}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7315
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Prove that $f(x,y)=\\frac12(10x^2+7y^2)+1x+2y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+7y^2)+1x+2y+-2 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 7316
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -25 + 111x^2 + 28 = -9x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -25 + 111x^2 + 28 = -9x $\n\nMove all terms to the left (standard form):\n$ 111x^2 + 9x + 3 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7317
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Prove that $f(x)=2x^2+-1x+2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+-1x+2$.\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": 7318
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 485x - 853 = 977"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 485x - 853 = 977 $\n\nMove all terms to the left (standard form):\n$ 485x + -1830 = 0 $\n\nIsolate the $x$ term:\n$ 485x = 1830 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7319
} |
[
{
"role": "user",
"content": "Work through and solve 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{\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 7320
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Evaluate: ((-145 + 216/12) * 9) + 6^5 - log_8(8) + (-270 mod 11) + round(31/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-145 + 216/12) * 9) + 6^5 - log_8(8) + (-270 mod 11) + round(31/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 7321
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Find the modular inverse of 17 modulo 19, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{19}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7322
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((141 + 196/14) * 12) + 3^3 - log_3(9) + (-313 mod 14) + ceil(-110/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((141 + 196/14) * 12) + 3^3 - log_3(9) + (-313 mod 14) + ceil(-110/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 7323
} |
[
{
"role": "user",
"content": "Determine the value produced by 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 = \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 7324
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Prove that $f(x,y)=\\frac12(2x^2+2y^2)+3x+4y+-4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+2y^2)+3x+4y+-4 $\n\n$ \\frac{\\partial^2 f}{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 7325
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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 $\n\nThe general solut... | {
"type": "trigonometry",
"seed": 1337,
"index": 7326
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((172 + 240/10) * 16) + 7^5 - log_9(81) + (-118 mod 28) + round(-92/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((172 + 240/10) * 16) + 7^5 - log_9(81) + (-118 mod 28) + round(-92/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 7327
} |
[
{
"role": "user",
"content": "Determine the solution of the given 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": 7328
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((197 + -1000/25) * 12) + 7^3 - log_5(3125) + (224 mod 26) + floor(109/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((197 + -1000/25) * 12) + 7^3 - log_5(3125) + (224 mod 26) + floor(10... | {
"type": "arithmetic",
"seed": 1337,
"index": 7329
} |
[
{
"role": "user",
"content": "Can you compute this equation? Prove that $(\\mathbb{Z}_27, +)$ is a group under addition modulo 27."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_27=\\{0,1,\\dots,26\\}$ with operation $+$ modulo $27$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7330
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}1&9\\\\\\-6&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}57\\\\\\-13\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}1&9\\\\\\-6&-7... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7331
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. -94x + 136 = 66"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -94x + 136 = 66 $\n\nMove all terms to the left (standard form):\n$ -94x + 70 = 0 $\n\nIsolate the $x$ term:\n$ -94x = -70 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 7332
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute $(133+7) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (133+7) \\bmod 13 $\n\nUse the rule that addition is compatible with reduction modulo ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7333
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute $(41+-192) \\bmod 11$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (41+-192) \\bmod 11 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7334
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Find the modular inverse of 9 modulo 11, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{11}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7335
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. - 119x^2 - 32 = -181x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ - 119x^2 - 32 = -181x $\n\nMove all terms to the left (standard form):\n$ -119x^2 + 181x + -32 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7336
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 997 + 553x = -773"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 997 + 553x = -773 $\n\nMove all terms to the left (standard form):\n$ 553x + 1770 = 0 $\n\nIsolate the $x$ term:\n$ 553x = -1770 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 7337
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute the indefinite integral: $\\int 6\\sin(1x) + 5\\cos(9x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6\\sin(1x) + 5\\cos(9x)\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 7338
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((-13 + 744/24) * 15) + 8^5 - log_3(27) + (-269 mod 27) + ceil(-74/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-13 + 744/24) * 15) + 8^5 - log_3(27) + (-269 mod 27) + ceil(-74/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 7339
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. -5 - 310 = -377x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -5 - 310 = -377x $\n\nMove all terms to the left (standard form):\n$ 377x + -315 = 0 $\n\nIsolate the $x$ term:\n$ 377x = 315 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 7340
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 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": 7341
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Differentiate with respect to $x$: $f(x) = 6x^3 + -3x^2 + -17x + 11$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6x^3 + -3x^2 + -17x + 11 $\n\nApply the standard differentiation rules:\n... | {
"type": "calculus",
"seed": 1337,
"index": 7342
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&-4\\\\\\-7&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-9\\\\\\-29\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&-4\\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7343
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((-38 + -120/5) * 7) + 8^4 - log_10(10) + (-123 mod 10) + floor(111/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-38 + -120/5) * 7) + 8^4 - log_10(10) + (-123 mod 10) + floor(111/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 7344
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 74 + 303x = -981"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 74 + 303x = -981 $\n\nMove all terms to the left (standard form):\n$ 303x + 1055 = 0 $\n\nIsolate the $x$ term:\n$ 303x = -1055 $\n\... | {
"type": "linear_equation",
"seed": 1337,
"index": 7345
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 13x + 112 + 195 = -46x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13x + 112 + 195 = -46x^2 $\n\nMove all terms to the left (standard form):\n$ 46x^2 + 13x + 307 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7346
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n -40x^2 + 192 + 155 = -71x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40x^2 + 192 + 155 = -71x $\n\nMove all terms to the left (standard form):\n$ -40x^2 + 71x + 347 = 0 $\n\nApply the quad... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7347
} |
[
{
"role": "user",
"content": "Please evaluate and compute 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 7348
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 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 = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 7349
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -30 + 147x^2 - 56x = 192"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -30 + 147x^2 - 56x = 192 $\n\nMove all terms to the left (standard form):\n$ 147x^2 + -56x + -222 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7350
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Differentiate with respect to $x$: $f(x) = \\ln(6x + -1)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(6x + -1) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\fra... | {
"type": "calculus",
"seed": 1337,
"index": 7351
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((132 + -72/3) * 2) + 2^2 - log_2(4) + (-314 mod 14) + round(144/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((132 + -72/3) * 2) + 2^2 - log_2(4) + (-314 mod 14) + round(144/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 7352
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Differentiate with respect to $x$: $f(x) = (-3x + -5)e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-3x + -5)e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 7353
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. -715x - 79 = 836"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -715x - 79 = 836 $\n\nMove all terms to the left (standard form):\n$ -715x + -915 = 0 $\n\nIsolate the $x$ term:\n$ -715x = 915 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 7354
} |
[
{
"role": "user",
"content": "Can you find 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 $f'(x)=0$, hence... | {
"type": "optimization",
"seed": 1337,
"index": 7355
} |
[
{
"role": "user",
"content": "Please solve this math problem. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 7356
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute the determinant: $A=\\begin{pmatrix}-1&3\\\\-1&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&3\\\\\\-1&2\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7357
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Compute the indefinite integral: $\\int \\ln(1x + 7)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + 7)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 7358
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((177 + -650/25) * 13) + 11^4 - log_4(16) + (457 mod 29) + ceil(38/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((177 + -650/25) * 13) + 11^4 - log_4(16) + (457 mod 29) + ceil(38/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 7359
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Evaluate: ((-74 + 50/2) * 6) + 12^5 - log_4(16) + (169 mod 24) + floor(-78/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-74 + 50/2) * 6) + 12^5 - log_4(16) + (169 mod 24) + floor(-78/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 7360
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. -30x - 172 - 148x^2 = -12"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -30x - 172 - 148x^2 = -12 $\n\nMove all terms to the left (standard form):\n$ -148x^2 + -30x + -160 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7361
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Prove that $f(x,y)=\\frac12(7x^2+10y^2)+2x+-3y+-6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+10y^2)+2x+-3y+-6 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 7362
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 41x - 5 + 67x^2 = 81"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 41x - 5 + 67x^2 = 81 $\n\nMove all terms to the left (standard form):\n$ 67x^2 + 41x + -86 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7363
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute the determinant: $A=\\begin{pmatrix}6&-9\\\\4&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&-9\\\\\\4&9\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7364
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. -31 + 45 + 141x^2 = 72x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -31 + 45 + 141x^2 = 72x $\n\nMove all terms to the left (standard form):\n$ 141x^2 + -72x + 14 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7365
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute the indefinite integral: $\\int (4x + 9)\\sin(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (4x + 9)\\sin(6x)\\,dx $\n\nUse standard antiderivatives (and integration ... | {
"type": "calculus",
"seed": 1337,
"index": 7366
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Compute $(16+-137) \\bmod 24$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (16+-137) \\bmod 24 $\n\nUse the rule that addition is compatible with reduction modulo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7367
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&9\\\\\\-7&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-48\\\\\\14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&9\\\\\\-7&-5\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7368
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&4&-3\\\\\\-4&4&0\\\\\\-3&2&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}26\\\\\\0\\\\\\6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7369
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 793x + 874 = 975"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 793x + 874 = 975 $\n\nMove all terms to the left (standard form):\n$ 793x + -101 = 0 $\n\nIsolate the $x$ term:\n$ 793x = 101 $\n\nDivide both sides by the coefficient of ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7370
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Prove that $f(x)=1x^2+-1x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+-1x+6$.\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": 7371
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute the determinant: $A=\\begin{pmatrix}1&-3\\\\-4&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}1&-3\\\\\\-4&-2\\end{pmatrix} $\n\nUse $\\det(A)... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7372
} |
[
{
"role": "user",
"content": "Find the final answer to the given 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": 7373
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 623 + 458 = -737x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 623 + 458 = -737x $\n\nMove all terms to the left (standard form):\n$ 737x + 1081 = 0 $\n\nIsolate the $x$ term:\n$ 737x = -1081 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 7374
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. 10 - 77x^2 - 188 = 79x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 - 77x^2 - 188 = 79x $\n\nMove all terms to the left (standard form):\n$ -77x^2 + -79x + -178 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7375
} |
[
{
"role": "user",
"content": "Please work out this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&-9\\\\\\-3&0\\end{pmatrix},\\quad b=\\begin{pmatrix}30\\\\\\-9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&-9\\\\\\-3&0\\end{pmatrix}... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7376
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -885x - 170 = -526"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -885x - 170 = -526 $\n\nMove all terms to the left (standard form):\n$ -885x + 356 = 0 $\n\nIsolate the $x$ term:\n$ -885x = -356 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7377
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -45 - 136 + 135x^2 = 67x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -45 - 136 + 135x^2 = 67x $\n\nMove all terms to the left (standard form):\n$ 135x^2 + -67x + -181 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7378
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Prove that $f(x,y)=\\frac12(2x^2+8y^2)+-4x+4y+-7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+8y^2)+-4x+4y+-7 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 7379
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute the indefinite integral: $\\int \\ln(6x + 1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(6x + 1)\\,dx $\n\nUse standard antiderivatives (and integration by parts if ne... | {
"type": "calculus",
"seed": 1337,
"index": 7380
} |
[
{
"role": "user",
"content": "Please calculate this equation. Differentiate with respect to $x$: $f(x) = (1x + 8)\\sin(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + 8)\\sin(1x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{1\\sin(1x)... | {
"type": "calculus",
"seed": 1337,
"index": 7381
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((-45 + -621/23) * 9) + 12^4 - log_7(117649) + (418 mod 2) + round(-11/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-45 + -621/23) * 9) + 12^4 - log_7(117649) + (418 mod 2) + round(-1... | {
"type": "arithmetic",
"seed": 1337,
"index": 7382
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 61x - 787 = -834"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 61x - 787 = -834 $\n\nMove all terms to the left (standard form):\n$ 61x + 47 = 0 $\n\nIsolate the $x$ term:\n$ 61x = -47 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 7383
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 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 $\n\nThe... | {
"type": "trigonometry",
"seed": 1337,
"index": 7384
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Evaluate: ((88 + -238/7) * 16) + 8^2 - log_3(729) + (326 mod 22) + floor(-39/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((88 + -238/7) * 16) + 8^2 - log_3(729) + (326 mod 22) + floor(-39/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 7385
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 6 - 151x^2 + 160 = -156x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 6 - 151x^2 + 160 = -156x $\n\nMove all terms to the left (standard form):\n$ -151x^2 + 156x + 166 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7386
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. -44x - 3x^2 + 70 = -63"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44x - 3x^2 + 70 = -63 $\n\nMove all terms to the left (standard form):\n$ -3x^2 + -44x + 133 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7387
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Prove that $f(x,y)=\\frac12(9x^2+9y^2)+6x+-1y+9$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+9y^2)+6x+-1y+9 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 7388
} |
[
{
"role": "user",
"content": "Solve the equation and calculate 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).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 7389
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. -39 - 124x^2 - 104x = 145"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -39 - 124x^2 - 104x = 145 $\n\nMove all terms to the left (standard form):\n$ -124x^2 + -104x + -184 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7390
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -133x - 809 = 880"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -133x - 809 = 880 $\n\nMove all terms to the left (standard form):\n$ -133x + -1689 = 0 $\n\nIsolate the $x$ term:\n$ -133x = 1689 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 7391
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}3&0\\\\9&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & 0 \\\\ 9 & -3 \\end{pmatrix} $\n\nCompute the determinant:... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7392
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Find the modular inverse of 7 modulo 10, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{10}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7393
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((128 + 224/8) * 11) + 12^3 - log_4(1024) + (246 mod 23) + round(27/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((128 + 224/8) * 11) + 12^3 - log_4(1024) + (246 mod 23) + round(27/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 7394
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-2&-6\\\\\\-1&6\\end{pmatrix},\\quad b=\\begin{pmatrix}52\\\\\\-46\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-2&-6\\\\\\-1&6\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7395
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 7396
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute the determinant: $A=\\begin{pmatrix}-2&-4\\\\2&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-2&-4\\\\\\2&-9\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7397
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Differentiate with respect to $x$: $f(x) = -4\\sin(6x) + -3\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4\\sin(6x) + -3\\cos(1x) $\n\nApply the standard differentiation rules:\n$ f'... | {
"type": "calculus",
"seed": 1337,
"index": 7398
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-131 + -989/23) * 20) + 4^2 - log_4(64) + (82 mod 13) + ceil(-184/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-131 + -989/23) * 20) + 4^2 - log_4(64) + (82 mod 13) + ceil(-184/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 7399
} |
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