messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Differentiate with respect to $x$: $f(x) = -3x^3 + -9x^2 + 16x + -4$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + -9x^2 + 16x + -4 $\n\nApply the standard differentiation rules:\n$... | {
"type": "calculus",
"seed": 1337,
"index": 2900
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -61 + 488 = -762x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -61 + 488 = -762x $\n\nMove all terms to the left (standard form):\n$ 762x + 427 = 0 $\n\nIsolate the $x$ term:\n$ 762x = -427 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2901
} |
[
{
"role": "user",
"content": "Work out the result of 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 ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 2902
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&3&5\\\\\\3&-5&5\\\\\\3&-1&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}1\\\\\\27\\\\\\-6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solv... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2903
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Find the modular inverse of 24 modulo 35, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $24\\cdot a^{-1} \\equiv 1 \\pmod{35}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2904
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -29x^2 + 146 - 27x = -67"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29x^2 + 146 - 27x = -67 $\n\nMove all terms to the left (standard form):\n$ -29x^2 + -27x + 213 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2905
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 234x - 624 = 316"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 234x - 624 = 316 $\n\nMove all terms to the left (standard form):\n$ 234x + -940 = 0 $\n\nIsolate the $x$ term:\n$ 234x = 940 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 2906
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Prove that $(\\mathbb{Z}_22, +)$ is a group under addition modulo 22."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_22=\\{0,1,\\dots,21\\}$ with operation $+$ modulo $22$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2907
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 578 + 680x = -708"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 578 + 680x = -708 $\n\nMove all terms to the left (standard form):\n$ 680x + 1286 = 0 $\n\nIsolate the $x$ term:\n$ 680x = -1286 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2908
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -42 - 25x + 86 = 37x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -42 - 25x + 86 = 37x^2 $\n\nMove all terms to the left (standard form):\n$ -37x^2 + -25x + 44 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2909
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}7&4\\\\3&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 7 & 4 \\\\ 3 & 9 \\end{pmatrix} $\n\nCompute the d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2910
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. x + 198 + 93 = -115x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ x + 198 + 93 = -115x^2 $\n\nMove all terms to the left (standard form):\n$ 115x^2 + 1x + 291 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2911
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute the indefinite integral: $\\int -2\\sin(5x) + 0\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2\\sin(5x) + 0\\cos(6x)\\,dx $\n\nUse standard antiderivatives (and int... | {
"type": "calculus",
"seed": 1337,
"index": 2912
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Compute the indefinite integral: $\\int 1\\sin(7x) + 1\\cos(8x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1\\sin(7x) + 1\\cos(8x)\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 2913
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -18 - 86 + 48x^2 = -124x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -18 - 86 + 48x^2 = -124x $\n\nMove all terms to the left (standard form):\n$ 48x^2 + 124x + -104 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2914
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. 39 + 71x^2 + 64 = 200x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 39 + 71x^2 + 64 = 200x $\n\nMove all terms to the left (standard form):\n$ 71x^2 + -200x + 103 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2915
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Prove that $f(x)=4x^2+10x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+10x+-2$.\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": 2916
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Evaluate: ((-71 + -46/2) * 16) + 6^4 - log_4(64) + (197 mod 10) + floor(111/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-71 + -46/2) * 16) + 6^4 - log_4(64) + (197 mod 10) + floor(111/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 2917
} |
[
{
"role": "user",
"content": "solve: 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 = \\arcsin(-\\frac{\\sqrt{3}... | {
"type": "trigonometry",
"seed": 1337,
"index": 2918
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the determinant: $A=\\begin{pmatrix}-7&1\\\\-3&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&1\\\\\\-3&-9\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2919
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&3&-4\\\\\\-2&5&-5\\\\\\4&-4&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-14\\\\\\-20\\\\\\10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2920
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Differentiate with respect to $x$: $f(x) = \\ln(3x + -8)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(3x + -8) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{... | {
"type": "calculus",
"seed": 1337,
"index": 2921
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Compute the determinant: $A=\\begin{pmatrix}-5&-8\\\\2&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&-8\\\\\\2&9\\end{pmatrix} $\n\nUse $\\de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2922
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Differentiate with respect to $x$: $f(x) = -3\\sin(4x) + 5\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3\\sin(4x) + 5\\cos(6x) $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 2923
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((-128 + -176/4) * 1) + 5^5 - log_9(81) + (-454 mod 4) + floor(154/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-128 + -176/4) * 1) + 5^5 - log_9(81) + (-454 mod 4) + floor(154/2) $\n\nCompute each component:\n$ -176/... | {
"type": "arithmetic",
"seed": 1337,
"index": 2924
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Compute the indefinite integral: $\\int -3x^3 + 3x^2 + 1x + -11\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3x^3 + 3x^2 + 1x + -11\\,dx $\n\nUse standard antiderivatives (and int... | {
"type": "calculus",
"seed": 1337,
"index": 2925
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Differentiate with respect to $x$: $f(x) = 3x^3 + 8x^2 + -7x + -17$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3x^3 + 8x^2 + -7x + -17 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 2926
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&5\\\\\\5&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}-17\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&5\\\\\\5&-8\\end... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2927
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Compute $(147+117) \\bmod 6$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (147+117) \\bmod 6 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2928
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-1&-7\\\\\\9&6\\end{pmatrix},\\quad b=\\begin{pmatrix}33\\\\\\-69\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-1&-7\\\\\\9&6\\en... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2929
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Find the modular inverse of 7 modulo 34, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{34}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2930
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((3 + -90/6) * 7) + 9^5 - log_9(6561) + (-246 mod 15) + ceil(-167/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((3 + -90/6) * 7) + 9^5 - log_9(6561) + (-246 mod 15) + ceil(-167/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2931
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((-144 + -77/7) * 18) + 8^4 - log_4(64) + (485 mod 15) + round(-163/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-144 + -77/7) * 18) + 8^4 - log_4(64) + (485 mod 15) + round(-163/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 2932
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. -24 + 21x^2 + 51 = -166x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -24 + 21x^2 + 51 = -166x $\n\nMove all terms to the left (standard form):\n$ 21x^2 + 166x + 27 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2933
} |
[
{
"role": "user",
"content": "solve: \n\n 409x - 580 = 606"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 409x - 580 = 606 $\n\nMove all terms to the left (standard form):\n$ 409x + -1186 = 0 $\n\nIsolate the $x$ term:\n$ 409x = 1186 $\n\nDivide both sides by the coefficient of $x... | {
"type": "linear_equation",
"seed": 1337,
"index": 2934
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((-57 + -171/19) * 7) + 6^3 - log_5(5) + (-244 mod 20) + round(192/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-57 + -171/19) * 7) + 6^3 - log_5(5) + (-244 mod 20) + round(192/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2935
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Differentiate with respect to $x$: $f(x) = 2e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{8e^{4x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 2936
} |
[
{
"role": "user",
"content": "Please work out this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&1\\\\\\8&8\\end{pmatrix},\\quad b=\\begin{pmatrix}-2\\\\\\-16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&1\\\\\\8&8\\end{pmatrix} ,\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2937
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Find the modular inverse of 11 modulo 15, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{15}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2938
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Differentiate with respect to $x$: $f(x) = 2e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{2e^{1x}} ... | {
"type": "calculus",
"seed": 1337,
"index": 2939
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Differentiate with respect to $x$: $f(x) = 1\\sin(8x) + 9\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1\\sin(8x) + 9\\cos(6x) $\n\nApply the standard differentiation rules:\n$ f'(x)... | {
"type": "calculus",
"seed": 1337,
"index": 2940
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. -46x - 197x^2 - 109 = 183"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -46x - 197x^2 - 109 = 183 $\n\nMove all terms to the left (standard form):\n$ -197x^2 + -46x + -292 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2941
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Evaluate: ((-132 + 7/7) * 14) + 5^2 - log_2(4) + (94 mod 22) + round(-153/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-132 + 7/7) * 14) + 5^2 - log_2(4) + (94 mod 22) + round(-153/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 2942
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&3&-1\\\\\\0&1&3\\\\\\-4&1&0\\end{pmatrix},\\quad b=\\begin{pmatrix}-10\\\\\\-8\\\\\\10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2943
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute the determinant: $A=\\begin{pmatrix}-9&5\\\\-5&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-9&5\\\\\\-5&-4\\end{pmatrix... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2944
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Compute the indefinite integral: $\\int \\ln(3x + 9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(3x + 9)\\,dx $\n\nUse standard antiderivatives (and integration by part... | {
"type": "calculus",
"seed": 1337,
"index": 2945
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&-4&4\\\\\\4&5&4\\\\\\5&-2&3\\end{pmatrix},\\quad b=\\begin{pmatrix}10\\\\\\-8\\\\\\23\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2946
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Differentiate with respect to $x$: $f(x) = -7e^{-3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -7e^{-3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{21e^{-3x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 2947
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 2948
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. 23x^2 - 55 + 175 = -80x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23x^2 - 55 + 175 = -80x $\n\nMove all terms to the left (standard form):\n$ 23x^2 + 80x + 120 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2949
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. 192 - 866x = 861"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 192 - 866x = 861 $\n\nMove all terms to the left (standard form):\n$ -866x + -669 = 0 $\n\nIsolate the $x$ term:\n$ -866x = 669 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 2950
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Prove that $f(x)=10x^2+-6x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-6x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x... | {
"type": "optimization",
"seed": 1337,
"index": 2951
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-121 + 369/9) * 14) + 8^2 - log_4(16) + (-493 mod 19) + floor(114/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-121 + 369/9) * 14) + 8^2 - log_4(16) + (-493 mod 19) + floor(114/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 2952
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 32x - 42 + 129x^2 = 141"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 32x - 42 + 129x^2 = 141 $\n\nMove all terms to the left (standard form):\n$ 129x^2 + 32x + -183 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2953
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Differentiate with respect to $x$: $f(x) = -1\\sin(1x) + -5\\cos(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1\\sin(1x) + -5\\cos(5x) $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 2954
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Prove that $f(x)=6x^2+10x+-3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+10x+-3$.\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": 2955
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -19x^2 + 112 - 130 = 169x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -19x^2 + 112 - 130 = 169x $\n\nMove all terms to the left (standard form):\n$ -19x^2 + -169x + -18 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2956
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 306x + 197 = 284"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 306x + 197 = 284 $\n\nMove all terms to the left (standard form):\n$ 306x + -87 = 0 $\n\nIsolate the $x$ term:\n$ 306x = 87 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2957
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 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": 2958
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Differentiate with respect to $x$: $f(x) = 1\\sin(8x) + -1\\cos(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1\\sin(8x) + -1\\cos(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 2959
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Compute $(-92+100) \\bmod 20$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-92+100) \\bmod 20 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2960
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Differentiate with respect to $x$: $f(x) = 2x^3 + 6x^2 + -20x + 13$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + 6x^2 + -20x + 13 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 2961
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Differentiate with respect to $x$: $f(x) = -5e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-5e^{1x}} $"... | {
"type": "calculus",
"seed": 1337,
"index": 2962
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 16 + 153x + 98 = -99x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 16 + 153x + 98 = -99x^2 $\n\nMove all terms to the left (standard form):\n$ 99x^2 + 153x + 114 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2963
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -4 + 60 - 178x = -95x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4 + 60 - 178x = -95x^2 $\n\nMove all terms to the left (standard form):\n$ 95x^2 + -178x + 56 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2964
} |
[
{
"role": "user",
"content": "Find the value that satisfies 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 $\n\... | {
"type": "trigonometry",
"seed": 1337,
"index": 2965
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((-170 + 297/9) * 12) + 10^3 - log_3(729) + (271 mod 17) + round(-144/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-170 + 297/9) * 12) + 10^3 - log_3(729) + (271 mod 17) + round(-14... | {
"type": "arithmetic",
"seed": 1337,
"index": 2966
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 218 + 500x = 195"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 218 + 500x = 195 $\n\nMove all terms to the left (standard form):\n$ 500x + 23 = 0 $\n\nIsolate the $x$ term:\n$ 500x = -23 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 2967
} |
[
{
"role": "user",
"content": "Please find the value of this math 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$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 2968
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find the modular inverse of 5 modulo 11, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{11}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2969
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute $(-76+-25) \\bmod 11$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-76+-25) \\bmod 11 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2970
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 139 + 105 = -598x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 139 + 105 = -598x $\n\nMove all terms to the left (standard form):\n$ 598x + 244 = 0 $\n\nIsolate the $x$ term:\n$ 598x = -244 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 2971
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Evaluate: ((135 + -370/10) * 18) + 11^2 - log_10(1000) + (-190 mod 24) + ceil(-30/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((135 + -370/10) * 18) + 11^2 - log_10(1000) + (-190 mod 24) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2972
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-4\\\\-4&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -4 \\\\ -4 & -8 \\end{pmatrix} $\n\nComput... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2973
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((-125 + -539/11) * 9) + 8^3 - log_10(100) + (302 mod 3) + round(-121/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-125 + -539/11) * 9) + 8^3 - log_10(100) + (302 mod 3) + round(-121/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2974
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((141 + -1152/24) * 20) + 11^4 - log_2(4) + (253 mod 25) + floor(-46/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((141 + -1152/24) * 20) + 11^4 - log_2(4) + (253 mod 25) + flo... | {
"type": "arithmetic",
"seed": 1337,
"index": 2975
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&0&1\\\\\\-4&3&0\\\\\\1&-4&0\\end{pmatrix},\\quad b=\\begin{pmatrix}-22\\\\\\13\\\\\\0\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2976
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 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": 2977
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((-70 + -495/11) * 16) + 11^4 - log_5(3125) + (196 mod 6) + round(-189/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-70 + -495/11) * 16) + 11^4 - log_5(3125) + (196 mod 6) + round(-189/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 2978
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((-135 + -598/13) * 10) + 3^5 - log_8(262144) + (-321 mod 29) + round(31/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-135 + -598/13) * 10) + 3^5 - log_8(262144) + (-321 mod 29) + round(3... | {
"type": "arithmetic",
"seed": 1337,
"index": 2979
} |
[
{
"role": "user",
"content": "Solve the following math equation. 521x + 231 = -904"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 521x + 231 = -904 $\n\nMove all terms to the left (standard form):\n$ 521x + 1135 = 0 $\n\nIsolate the $x$ term:\n$ 521x = -1135 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 2980
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Differentiate with respect to $x$: $f(x) = \\ln(2x + 3)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(2x + 3) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac... | {
"type": "calculus",
"seed": 1337,
"index": 2981
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 558 + 199 = 769x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 558 + 199 = 769x $\n\nMove all terms to the left (standard form):\n$ -769x + 757 = 0 $\n\nIsolate the $x$ term:\n$ -769x = -757 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2982
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -15x^2 + 2 + 70x = 19"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15x^2 + 2 + 70x = 19 $\n\nMove all terms to the left (standard form):\n$ -15x^2 + 70x + -17 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2983
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((-48 + 6/2) * 16) + 3^5 - log_5(5) + (-354 mod 4) + floor(186/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-48 + 6/2) * 16) + 3^5 - log_5(5) + (-354 mod 4) + floor(186/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 2984
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. 393 + 102x = -772"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 393 + 102x = -772 $\n\nMove all terms to the left (standard form):\n$ 102x + 1165 = 0 $\n\nIsolate the $x$ term:\n$ 102x = -1165 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2985
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. 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{... | {
"type": "trigonometry",
"seed": 1337,
"index": 2986
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&3&-2\\\\\\-3&-1&5\\\\\\0&3&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}1\\\\\\-11\\\\\\11\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "So... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2987
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Prove that $f(x)=9x^2+9x+-8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+9x+-8$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.... | {
"type": "optimization",
"seed": 1337,
"index": 2988
} |
[
{
"role": "user",
"content": "Can you compute this equation? Differentiate with respect to $x$: $f(x) = \\ln(5x + 1)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(5x + 1) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{5}{5x + 1}} $"... | {
"type": "calculus",
"seed": 1337,
"index": 2989
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((108 + -65/5) * 5) + 8^2 - log_9(6561) + (94 mod 6) + floor(-188/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((108 + -65/5) * 5) + 8^2 - log_9(6561) + (94 mod 6) + floor(-188/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 2990
} |
[
{
"role": "user",
"content": "Please work out this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-1... | {
"type": "optimization",
"seed": 1337,
"index": 2991
} |
[
{
"role": "user",
"content": "Please work out this equation. Compute the determinant: $A=\\begin{pmatrix}6&2\\\\9&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&2\\\\\\9&8\\end{pmatrix} $\n\nUse $\\det(A)=ad-bc$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2992
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&-2&4\\\\\\-1&-3&-2\\\\\\-3&2&2\\end{pmatrix},\\quad b=\\begin{pmatrix}16\\\\\\-13\\\\\\4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "So... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2993
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 131 + 596 = -744x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 131 + 596 = -744x $\n\nMove all terms to the left (standard form):\n$ 744x + 727 = 0 $\n\nIsolate the $x$ term:\n$ 744x = -727 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 2994
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 2995
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 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 = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 2996
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -161 + 896 = -171x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -161 + 896 = -171x $\n\nMove all terms to the left (standard form):\n$ 171x + 735 = 0 $\n\nIsolate the $x$ term:\n$ 171x = -735 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2997
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 8 + 136x^2 + 195 = 40x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 8 + 136x^2 + 195 = 40x $\n\nMove all terms to the left (standard form):\n$ 136x^2 + -40x + 203 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2998
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. 22 + 713x = -383"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 22 + 713x = -383 $\n\nMove all terms to the left (standard form):\n$ 713x + 405 = 0 $\n\nIsolate the $x$ term:\n$ 713x = -405 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 2999
} |
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