messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the following mathematical problem. -918x - 429 = 892"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -918x - 429 = 892 $\n\nMove all terms to the left (standard form):\n$ -918x + -1321 = 0 $\n\nIsolate the $x$ term:\n$ -918x = 1321 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3900
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute $(77+-63) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (77+-63) \\bmod 17 $\n\nUse the rule that addition is compatible with reduction modu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3901
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((-98 + -304/8) * 6) + 4^5 - log_8(262144) + (-416 mod 22) + round(-49/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-98 + -304/8) * 6) + 4^5 - log_8(262144) + (-416 mod 22) + round(-49/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3902
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -25 - 121x^2 + 90 = 39x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -25 - 121x^2 + 90 = 39x $\n\nMove all terms to the left (standard form):\n$ -121x^2 + -39x + 65 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3903
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 40 + 26 - 124x = 31x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 40 + 26 - 124x = 31x^2 $\n\nMove all terms to the left (standard form):\n$ -31x^2 + -124x + 66 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3904
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -655x + 211 = -204"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -655x + 211 = -204 $\n\nMove all terms to the left (standard form):\n$ -655x + 415 = 0 $\n\nIsolate the $x$ term:\n$ -655x = -415 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 3905
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -402 - 810 = -58x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -402 - 810 = -58x $\n\nMove all terms to the left (standard form):\n$ 58x + -1212 = 0 $\n\nIsolate the $x$ term:\n$ 58x = 1212 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 3906
} |
[
{
"role": "user",
"content": "solve -7x - 72 - 86 = -69x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -7x - 72 - 86 = -69x^2 $\n\nMove all terms to the left (standard form):\n$ 69x^2 + -7x + -158 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3907
} |
[
{
"role": "user",
"content": "Can you determine the solution of 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)... | {
"type": "trigonometry",
"seed": 1337,
"index": 3908
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. -332 - 968 = 850x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -332 - 968 = 850x $\n\nMove all terms to the left (standard form):\n$ -850x + -1300 = 0 $\n\nIsolate the $x$ term:\n$ -850x = 1300 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3909
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. -473 - 76x = -315"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -473 - 76x = -315 $\n\nMove all terms to the left (standard form):\n$ -76x + -158 = 0 $\n\nIsolate the $x$ term:\n$ -76x = 158 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 3910
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((166 + -60/3) * 8) + 4^2 - log_5(15625) + (-77 mod 15) + ceil(-116/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((166 + -60/3) * 8) + 4^2 - log_5(15625) + (-77 mod 15) + ceil(-116/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 3911
} |
[
{
"role": "user",
"content": "Find the solution to the following 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\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3912
} |
[
{
"role": "user",
"content": "Can you compute this equation? Find $A^{-1}$ for $A=\\begin{pmatrix}-3&0\\\\-3&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -3 & 0 \\\\ -3 & 4 \\end{pmatrix} $\n\nCompute the determinant:... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3913
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 864 - 696 = 317x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 864 - 696 = 317x $\n\nMove all terms to the left (standard form):\n$ -317x + 168 = 0 $\n\nIsolate the $x$ term:\n$ -317x = -168 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 3914
} |
[
{
"role": "user",
"content": "Please solve this math problem. 2x - 77 = 36"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 2x - 77 = 36 $\n\nMove all terms to the left (standard form):\n$ 2x + -113 = 0 $\n\nIsolate the $x$ term:\n$ 2x = 113 $\n\nDivide both sides by the coefficient... | {
"type": "linear_equation",
"seed": 1337,
"index": 3915
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Differentiate with respect to $x$: $f(x) = (5x + -8)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (5x + -8)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\bo... | {
"type": "calculus",
"seed": 1337,
"index": 3916
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Differentiate with respect to $x$: $f(x) = -1\\sin(4x) + 2\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1\\sin(4x) + 2\\cos(7x) $\n\nApply the standard differentiation r... | {
"type": "calculus",
"seed": 1337,
"index": 3917
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Prove that $f(x,y)=\\frac12(10x^2+4y^2)+-2x+3y+-1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+4y^2)+-2x+3y+-1 $\n\n$ \\frac{\\partial^2 f}{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 3918
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Find the modular inverse of 11 modulo 17, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{17}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees int... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3919
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Prove that $(\\mathbb{Z}_18, +)$ is a group under addition modulo 18."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_18=\\{0,1,\\dots,17\\}$ with operation $+$ modulo $18$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, th... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3920
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((161 + -90/6) * 1) + 6^3 - log_9(729) + (312 mod 20) + round(191/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((161 + -90/6) * 1) + 6^3 - log_9(729) + (312 mod 20) + round(191/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 3921
} |
[
{
"role": "user",
"content": "solve: -6 + 66x - 27 = 52x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6 + 66x - 27 = 52x^2 $\n\nMove all terms to the left (standard form):\n$ -52x^2 + 66x + -33 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3922
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Differentiate with respect to $x$: $f(x) = 7\\sin(6x) + 4\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7\\sin(6x) + 4\\cos(1x) $\n\nApply the standard differentiation ru... | {
"type": "calculus",
"seed": 1337,
"index": 3923
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -290 + 945x = 151"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -290 + 945x = 151 $\n\nMove all terms to the left (standard form):\n$ 945x + -441 = 0 $\n\nIsolate the $x$ term:\n$ 945x = 441 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3924
} |
[
{
"role": "user",
"content": "Can you compute 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(-\\frac{1}... | {
"type": "trigonometry",
"seed": 1337,
"index": 3925
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Differentiate with respect to $x$: $f(x) = \\ln(8x + 9)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(8x + 9) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 3926
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 3927
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 605 + 135x = -355"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 605 + 135x = -355 $\n\nMove all terms to the left (standard form):\n$ 135x + 960 = 0 $\n\nIsolate the $x$ term:\n$ 135x = -960 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 3928
} |
[
{
"role": "user",
"content": "Please calculate 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$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3929
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Find the modular inverse of 17 modulo 26, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{26}$.\n\nSince $\\gcd(a,m)=1$, Bézout's iden... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3930
} |
[
{
"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": 3931
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((34 + -294/6) * 19) + 11^5 - log_2(32) + (-276 mod 10) + floor(-141/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((34 + -294/6) * 19) + 11^5 - log_2(32) + (-276 mod 10) + floor(-141/2) $\n\nCompute each component:\n$ -... | {
"type": "arithmetic",
"seed": 1337,
"index": 3932
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Prove that $f(x)=5x^2+8x+-10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+8x+-10$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(... | {
"type": "optimization",
"seed": 1337,
"index": 3933
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 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": 3934
} |
[
{
"role": "user",
"content": "solve: \n\n Prove that $f(x)=4x^2+4x+-4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+4x+-4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 8x + 4 $\n$ f''(x) = 8 $\n\nS... | {
"type": "optimization",
"seed": 1337,
"index": 3935
} |
[
{
"role": "user",
"content": "Please find the value of 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{\\... | {
"type": "optimization",
"seed": 1337,
"index": 3936
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 833 - 529x = 8"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 833 - 529x = 8 $\n\nMove all terms to the left (standard form):\n$ -529x + 825 = 0 $\n\nIsolate the $x$ term:\n$ -529x = -825 $\n\nDivide both sides by the... | {
"type": "linear_equation",
"seed": 1337,
"index": 3937
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((113 + -74/2) * 1) + 8^4 - log_10(10) + (86 mod 20) + floor(-176/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((113 + -74/2) * 1) + 8^4 - log_10(10) + (86 mod 20) + floor(-176/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 3938
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 3939
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alph... | {
"type": "trigonometry",
"seed": 1337,
"index": 3940
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute the indefinite integral: $\\int (-5x + -2)e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-5x + -2)e^{2x}\\,dx $\n\nUse standard antiderivatives (and integrat... | {
"type": "calculus",
"seed": 1337,
"index": 3941
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Prove that $(\\mathbb{Z}_29, +)$ is a group under addition modulo 29."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_29=\\{0,1,\\dots,28\\}$ with operation $+$ modulo $29$.\n\n**Closure:** If $a,b\\in\\mathbb{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3942
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Find the modular inverse of 23 modulo 36, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $23\\cdot a^{-1} \\equiv 1 \\pmod{36}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3943
} |
[
{
"role": "user",
"content": "Solve the following mathematical 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$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3944
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -64x - 696 = 219"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -64x - 696 = 219 $\n\nMove all terms to the left (standard form):\n$ -64x + -915 = 0 $\n\nIsolate the $x$ term:\n$ -64x = 915 $\n\nDivide both sides by the ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3945
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 900 + 917 = 597x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 900 + 917 = 597x $\n\nMove all terms to the left (standard form):\n$ -597x + 1817 = 0 $\n\nIsolate the $x$ term:\n$ -597x = -1817 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3946
} |
[
{
"role": "user",
"content": "Please solve this mathematical 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 3947
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Compute $(-71+-180) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-71+-180) \\bmod 12 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3948
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((-160 + 408/24) * 4) + 11^3 - log_5(15625) + (169 mod 12) + round(-9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-160 + 408/24) * 4) + 11^3 - log_5(15625) + (169 mod 12) + round(-9/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3949
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Compute $(-95+-13) \\bmod 25$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-95+-13) \\bmod 25 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3950
} |
[
{
"role": "user",
"content": "Can you solve the 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$ 4x(x^... | {
"type": "optimization",
"seed": 1337,
"index": 3951
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. -495x - 355 = -850"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -495x - 355 = -850 $\n\nMove all terms to the left (standard form):\n$ -495x + 495 = 0 $\n\nIsolate the $x$ term:\n$ -495x = -495 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3952
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 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": 3953
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. -559x + 138 = -213"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -559x + 138 = -213 $\n\nMove all terms to the left (standard form):\n$ -559x + 351 = 0 $\n\nIsolate the $x$ term:\n$ -559x = -351 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 3954
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&1&4\\\\\\-4&3&-4\\\\\\-4&-4&4\\end{pmatrix},\\quad b=\\begin{pmatrix}0\\\\\\8\\\\\\20\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3955
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-1&-2\\\\\\-3&5&-3\\\\\\2&-2&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}3\\\\\\11\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Sol... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3956
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. -20x - 461 = -224"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -20x - 461 = -224 $\n\nMove all terms to the left (standard form):\n$ -20x + -237 = 0 $\n\nIsolate the $x$ term:\n$ -20x = 237 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 3957
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Find the modular inverse of 19 modulo 32, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{32}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees in... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3958
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 40 - 75x + 52 = -186x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 40 - 75x + 52 = -186x^2 $\n\nMove all terms to the left (standard form):\n$ 186x^2 + -75x + 92 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3959
} |
[
{
"role": "user",
"content": "Compute 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": 3960
} |
[
{
"role": "user",
"content": "Please compute the solution to this 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 3961
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. -7 + 20x^2 + 37x = 162"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -7 + 20x^2 + 37x = 162 $\n\nMove all terms to the left (standard form):\n$ 20x^2 + 37x + -169 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3962
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. -35 - 174x + 2 = 122x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35 - 174x + 2 = 122x^2 $\n\nMove all terms to the left (standard form):\n$ -122x^2 + -174x + -33 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3963
} |
[
{
"role": "user",
"content": "solve: Evaluate: ((-152 + 56/7) * 6) + 6^5 - log_5(5) + (-480 mod 4) + floor(183/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-152 + 56/7) * 6) + 6^5 - log_5(5) + (-480 mod 4) + floor(183/2) $\n\nCompute each component:\n$ 56/7 = 8 $\n$ (... | {
"type": "arithmetic",
"seed": 1337,
"index": 3964
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Prove that $f(x,y)=\\frac12(1x^2+8y^2)+5x+-4y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+8y^2)+5x+-4y+-5 $\n\n$ \\frac{\\partial^2 f}{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 3965
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. -511 - x = 469"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -511 - x = 469 $\n\nMove all terms to the left (standard form):\n$ -1x + -980 = 0 $\n\nIsolate the $x$ term:\n$ -1x = 980 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3966
} |
[
{
"role": "user",
"content": "solve: \n\n 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 $\n\nThe general solutions for $\\cos... | {
"type": "trigonometry",
"seed": 1337,
"index": 3967
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Differentiate with respect to $x$: $f(x) = (-1x + -4)e^{6x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-1x + -4)e^{6x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-... | {
"type": "calculus",
"seed": 1337,
"index": 3968
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 3969
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 29x + 25 - 91 = -39x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 29x + 25 - 91 = -39x^2 $\n\nMove all terms to the left (standard form):\n$ 39x^2 + 29x + -66 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3970
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Evaluate: ((126 + -24/4) * 12) + 12^2 - log_2(8) + (-378 mod 19) + floor(-126/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((126 + -24/4) * 12) + 12^2 - log_2(8) + (-378 mod 19) + floor(-126/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 3971
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&-2&5\\\\\\-1&0&-2\\\\\\0&-2&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}3\\\\\\6\\\\\\5\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3972
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -36x - 135x^2 - 105 = -18"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x - 135x^2 - 105 = -18 $\n\nMove all terms to the left (standard form):\n$ -135x^2 + -36x + -87 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3973
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Compute the indefinite integral: $\\int (-3x + 10)e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + 10)e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 3974
} |
[
{
"role": "user",
"content": "Solve the following math equation. Differentiate with respect to $x$: $f(x) = (5x + -3)e^{6x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (5x + -3)e^{6x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{5e^{6x} + (... | {
"type": "calculus",
"seed": 1337,
"index": 3975
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\nThe gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 3976
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-1&-3\\\\\\-4&0&2\\\\\\5&2&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\-6\\\\\\17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3977
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&-6\\\\\\-4&8\\end{pmatrix},\\quad b=\\begin{pmatrix}-68\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&-6\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3978
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Differentiate with respect to $x$: $f(x) = 3\\sin(4x) + 9\\cos(9x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3\\sin(4x) + 9\\cos(9x) $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 3979
} |
[
{
"role": "user",
"content": "solve: \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} & \\frac{\\partial^2 f}{\\partial x\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 3980
} |
[
{
"role": "user",
"content": "solve Prove that $f(x,y)=\\frac12(2x^2+7y^2)+6x+-1y+1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+7y^2)+6x+-1y+1 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 2,\\quad \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 3981
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -570 + 542x = 751"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -570 + 542x = 751 $\n\nMove all terms to the left (standard form):\n$ 542x + -1321 = 0 $\n\nIsolate the $x$ term:\n$ 542x = 1321 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 3982
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -961 + 779x = 887"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -961 + 779x = 887 $\n\nMove all terms to the left (standard form):\n$ 779x + -1848 = 0 $\n\nIsolate the $x$ term:\n$ 779x = 1848 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3983
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Prove that $f(x)=4x^2+4x+-5$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+4x+-5$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 8x + ... | {
"type": "optimization",
"seed": 1337,
"index": 3984
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = \\ln(9x + -3)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(9x + -3) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\... | {
"type": "calculus",
"seed": 1337,
"index": 3985
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 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": 3986
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Evaluate: ((-130 + 69/23) * 2) + 12^2 - log_3(9) + (457 mod 11) + round(-7/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-130 + 69/23) * 2) + 12^2 - log_3(9) + (457 mod 11) + round(-7/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 3987
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find the modular inverse of 11 modulo 39, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{39}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3988
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Differentiate with respect to $x$: $f(x) = (-3x + 7)\\sin(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-3x + 7)\\sin(6x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed... | {
"type": "calculus",
"seed": 1337,
"index": 3989
} |
[
{
"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": 3990
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((194 + -648/24) * 13) + 3^4 - log_6(46656) + (99 mod 23) + ceil(-16/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((194 + -648/24) * 13) + 3^4 - log_6(46656) + (99 mod 23) + ceil(-16/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3991
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Prove that $f(x,y)=\\frac12(6x^2+9y^2)+2x+2y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+9y^2)+2x+2y+-2 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 3992
} |
[
{
"role": "user",
"content": "Please solve this math problem. -20 + 197x^2 + 144 = 2x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20 + 197x^2 + 144 = 2x $\n\nMove all terms to the left (standard form):\n$ 197x^2 + -2x + 124 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3993
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Prove that $f(x)=3x^2+8x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+8x+-9$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = ... | {
"type": "optimization",
"seed": 1337,
"index": 3994
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((-104 + -340/20) * 12) + 5^4 - log_4(4) + (-289 mod 30) + round(159/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-104 + -340/20) * 12) + 5^4 - log_4(4) + (-289 mod 30) + round(159/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 3995
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. 5 - 27 - 17x = -155x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 5 - 27 - 17x = -155x^2 $\n\nMove all terms to the left (standard form):\n$ 155x^2 + -17x + -22 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3996
} |
[
{
"role": "user",
"content": "Please work out 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^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 3997
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. 725 - 989 = 43x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 725 - 989 = 43x $\n\nMove all terms to the left (standard form):\n$ -43x + -264 = 0 $\n\nIsolate the $x$ term:\n$ -43x = 264 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 3998
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Differentiate with respect to $x$: $f(x) = 9\\sin(8x) + -5\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 9\\sin(8x) + -5\\cos(4x) $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 3999
} |
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