messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Calculate the answer for this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&-1&2\\\\\\0&5&0\\\\\\2&1&2\\end{pmatrix},\\quad b=\\begin{pmatrix}12\\\\\\10\\\\\\6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.,... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2700
} |
[
{
"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": 2701
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Differentiate with respect to $x$: $f(x) = \\ln(4x + -1)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(4x + -1) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{... | {
"type": "calculus",
"seed": 1337,
"index": 2702
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Evaluate: ((-167 + -123/3) * 4) + 8^4 - log_9(531441) + (179 mod 18) + ceil(-124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-167 + -123/3) * 4) + 8^4 - log_9(531441) + (179 mod 18) + ceil(-124/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 2703
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((-71 + -63/21) * 14) + 4^4 - log_4(256) + (-301 mod 15) + round(62/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-71 + -63/21) * 14) + 4^4 - log_4(256) + (-301 mod 15) + roun... | {
"type": "arithmetic",
"seed": 1337,
"index": 2704
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((-20 + 207/23) * 10) + 2^4 - log_8(8) + (485 mod 24) + floor(-131/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-20 + 207/23) * 10) + 2^4 - log_8(8) + (485 mod 24) + floor(-131/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 2705
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Evaluate: ((103 + -144/18) * 5) + 2^2 - log_2(2) + (-468 mod 20) + round(198/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((103 + -144/18) * 5) + 2^2 - log_2(2) + (-468 mod 20) + round(198/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2706
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((111 + -60/5) * 6) + 4^2 - log_9(59049) + (-293 mod 29) + ceil(183/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((111 + -60/5) * 6) + 4^2 - log_9(59049) + (-293 mod 29) + ceil(... | {
"type": "arithmetic",
"seed": 1337,
"index": 2707
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Differentiate with respect to $x$: $f(x) = -7\\sin(5x) + -7\\cos(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -7\\sin(5x) + -7\\cos(5x) $\n\nApply the standard differentiatio... | {
"type": "calculus",
"seed": 1337,
"index": 2708
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((-115 + 264/12) * 9) + 7^2 - log_8(4096) + (-122 mod 20) + floor(-122/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-115 + 264/12) * 9) + 7^2 - log_8(4096) + (-122 mod 20) + floor(-122/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2709
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -417 - 677 = 169x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -417 - 677 = 169x $\n\nMove all terms to the left (standard form):\n$ -169x + -1094 = 0 $\n\nIsolate the $x$ term:\n$ -169x = 1094 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 2710
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. -8 + 60x^2 + 99 = -155x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -8 + 60x^2 + 99 = -155x $\n\nMove all terms to the left (standard form):\n$ 60x^2 + 155x + 91 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2711
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. -44x - 26 - 17x^2 = 99"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44x - 26 - 17x^2 = 99 $\n\nMove all terms to the left (standard form):\n$ -17x^2 + -44x + -125 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2712
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Compute the indefinite integral: $\\int \\ln(8x + 9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + 9)\\,dx $\n\nUse standard antiderivatives (and integration by parts if ... | {
"type": "calculus",
"seed": 1337,
"index": 2713
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 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 $\n\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 2714
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. -7 + 101x^2 - x = 101"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -7 + 101x^2 - x = 101 $\n\nMove all terms to the left (standard form):\n$ 101x^2 + -1x + -108 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2715
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute the indefinite integral: $\\int 9e^{-5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 9e^{-5x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$... | {
"type": "calculus",
"seed": 1337,
"index": 2716
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((108 + 20/20) * 17) + 4^3 - log_8(512) + (-470 mod 30) + ceil(183/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((108 + 20/20) * 17) + 4^3 - log_8(512) + (-470 mod 30) + ceil(183/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2717
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Differentiate with respect to $x$: $f(x) = -5e^{-3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5e^{-3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{15e^{-3x}}... | {
"type": "calculus",
"seed": 1337,
"index": 2718
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Compute the indefinite integral: $\\int 5e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5e^{5x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 2719
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 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{\\partia... | {
"type": "optimization",
"seed": 1337,
"index": 2720
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Compute the indefinite integral: $\\int -1\\sin(1x) + 6\\cos(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1\\sin(1x) + 6\\cos(3x)\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 2721
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Compute the determinant: $A=\\begin{pmatrix}-2&2\\\\-2&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-2&2\\\\\\-2&-7\\end{pmatrix} $\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2722
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 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$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 2723
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 66 - 637x = -104"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 66 - 637x = -104 $\n\nMove all terms to the left (standard form):\n$ -637x + 170 = 0 $\n\nIsolate the $x$ term:\n$ -637x = -170 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2724
} |
[
{
"role": "user",
"content": "Can you compute this equation? -14x - 39 + 20x^2 = 109"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -14x - 39 + 20x^2 = 109 $\n\nMove all terms to the left (standard form):\n$ 20x^2 + -14x + -148 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2725
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-7&-4\\\\-6&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -7 & -4 \\\\ -6 & 2 \\end{pmatrix} $\n\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2726
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Compute $(90+-133) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (90+-133) \\bmod 17 $\n\nUse the rule that addition is compatible with ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2727
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Find $A^{-1}$ for $A=\\begin{pmatrix}1&-8\\\\-2&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 1 & -8 \\\\ -2 & 7 \\end{pmatrix} $\n\nComput... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2728
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Evaluate: ((-175 + 215/5) * 7) + 2^3 - log_3(3) + (-313 mod 16) + round(-14/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-175 + 215/5) * 7) + 2^3 - log_3(3) + (-313 mod 16) + round(-14/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 2729
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Prove that $f(x,y)=\\frac12(3x^2+9y^2)+6x+4y+0$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+9y^2)+6x+4y+0 $\n\n$ \\frac{\\partial^2 f}{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 2730
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((-156 + -76/4) * 11) + 6^4 - log_3(9) + (-479 mod 9) + round(-57/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-156 + -76/4) * 11) + 6^4 - log_3(9) + (-479 mod 9) + round(-57/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2731
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Prove that $(\\mathbb{Z}_6, +)$ is a group under addition modulo 6."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_6=\\{0,1,\\dots,5\\}$ with operation $+$ modulo $6$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2732
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Differentiate with respect to $x$: $f(x) = 1e^{-4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1e^{-4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-4e^{-4... | {
"type": "calculus",
"seed": 1337,
"index": 2733
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 14 - 96x - 160 = 89x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 14 - 96x - 160 = 89x^2 $\n\nMove all terms to the left (standard form):\n$ -89x^2 + -96x + -146 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2734
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Find the modular inverse of 21 modulo 40, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $21\\cdot a^{-1} \\equiv 1 \\pmod{40}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2735
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((87 + -182/14) * 15) + 5^5 - log_4(256) + (-365 mod 30) + floor(133/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((87 + -182/14) * 15) + 5^5 - log_4(256) + (-365 mod 30) + flo... | {
"type": "arithmetic",
"seed": 1337,
"index": 2736
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 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 = \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 2737
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -5x + 73 + 187 = -104x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -5x + 73 + 187 = -104x^2 $\n\nMove all terms to the left (standard form):\n$ 104x^2 + -5x + 260 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2738
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((-31 + -357/17) * 7) + 2^5 - log_8(32768) + (-338 mod 25) + round(-39/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-31 + -357/17) * 7) + 2^5 - log_8(32768) + (-338 mod 25) + round(-39/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 2739
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 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 $\n\nThe... | {
"type": "trigonometry",
"seed": 1337,
"index": 2740
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((-102 + -600/20) * 11) + 2^3 - log_8(262144) + (247 mod 23) + round(162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-102 + -600/20) * 11) + 2^3 - log_8(262144) + (247 mod 23) + round(162... | {
"type": "arithmetic",
"seed": 1337,
"index": 2741
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 596 + 540 = 850x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 596 + 540 = 850x $\n\nMove all terms to the left (standard form):\n$ -850x + 1136 = 0 $\n\nIsolate the $x$ term:\n$ -850x = -1136 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 2742
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}3&-6\\\\8&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & -6 \\\\ 8 & 1 \\end{pmatrix} $\n\nCompute the deter... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2743
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. -36x^2 - 139 - 68 = -3x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x^2 - 139 - 68 = -3x $\n\nMove all terms to the left (standard form):\n$ -36x^2 + 3x + -207 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2744
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\nThe gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 2745
} |
[
{
"role": "user",
"content": "solve: Evaluate: ((-70 + -66/11) * 18) + 2^2 - log_9(729) + (-285 mod 18) + floor(-57/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-70 + -66/11) * 18) + 2^2 - log_9(729) + (-285 mod 18) + floor(-57/2) $\n\nCompute each component:\n$ -66/1... | {
"type": "arithmetic",
"seed": 1337,
"index": 2746
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Find the modular inverse of 16 modulo 35, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $16\\cdot a^{-1} \\equiv 1 \\pmod{35}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2747
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Prove that $(\\mathbb{Z}_15, +)$ is a group under addition modulo 15."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_15=\\{0,1,\\dots,14\\}$ with operation $+$ modulo $15$.\n\n**Closure:** If $a,b\\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2748
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 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{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 2749
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((125 + -18/2) * 15) + 2^3 - log_5(125) + (-460 mod 5) + floor(95/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((125 + -18/2) * 15) + 2^3 - log_5(125) + (-460 mod 5) + floor(95/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2750
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 108 + 452 = -317x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 108 + 452 = -317x $\n\nMove all terms to the left (standard form):\n$ 317x + 560 = 0 $\n\nIsolate the $x$ term:\n$ 317x = -560 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2751
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Evaluate: ((-91 + 1125/25) * 3) + 9^4 - log_4(64) + (-73 mod 30) + round(-43/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-91 + 1125/25) * 3) + 9^4 - log_4(64) + (-73 mod 30) + round(-43/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 2752
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n -19x^2 + 55 + 144x = 72"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -19x^2 + 55 + 144x = 72 $\n\nMove all terms to the left (standard form):\n$ -19x^2 + 144x + -17 = 0 $\n\nApply the quadrat... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2753
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Prove that $f(x)=9x^2+-1x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-1x+-9$.\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": 2754
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 982 - 527x = -581"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 982 - 527x = -581 $\n\nMove all terms to the left (standard form):\n$ -527x + 1563 = 0 $\n\nIsolate the $x$ term:\n$ -527x = -1563 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 2755
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. -15 + 173x + 158x^2 = 131"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15 + 173x + 158x^2 = 131 $\n\nMove all terms to the left (standard form):\n$ 158x^2 + 173x + -146 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2756
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 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{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 2757
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Compute the indefinite integral: $\\int 5\\sin(8x) + 8\\cos(9x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5\\sin(8x) + 8\\cos(9x)\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 2758
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Compute $(-161+137) \\bmod 22$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-161+137) \\bmod 22 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2759
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 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) = 3.14... | {
"type": "trigonometry",
"seed": 1337,
"index": 2760
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Evaluate: ((-140 + 3/3) * 18) + 11^4 - log_2(2) + (480 mod 27) + ceil(-59/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-140 + 3/3) * 18) + 11^4 - log_2(2) + (480 mod 27) + ceil(-59/2) $\n\nCompute each co... | {
"type": "arithmetic",
"seed": 1337,
"index": 2761
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((-31 + -215/5) * 6) + 10^4 - log_2(16) + (441 mod 3) + ceil(26/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-31 + -215/5) * 6) + 10^4 - log_2(16) + (441 mod 3) + ceil(26/2) $\n\nCompute each compon... | {
"type": "arithmetic",
"seed": 1337,
"index": 2762
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\... | {
"type": "optimization",
"seed": 1337,
"index": 2763
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical 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 $... | {
"type": "trigonometry",
"seed": 1337,
"index": 2764
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Evaluate: ((92 + 416/13) * 2) + 5^3 - log_2(4) + (353 mod 24) + round(178/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((92 + 416/13) * 2) + 5^3 - log_2(4) + (353 mod 24) + round(178/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2765
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Find the modular inverse of 3 modulo 5, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{5}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2766
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((45 + 975/25) * 8) + 8^4 - log_5(25) + (53 mod 9) + ceil(98/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((45 + 975/25) * 8) + 8^4 - log_5(25) + (53 mod 9) + ceil(98/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 2767
} |
[
{
"role": "user",
"content": "solve: \n\n Prove that $f(x,y)=\\frac12(9x^2+8y^2)+-5x+5y+5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+8y^2)+-5x+5y+5 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 9,\\quad \\frac{\... | {
"type": "optimization",
"seed": 1337,
"index": 2768
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((168 + 210/10) * 18) + 8^5 - log_2(32) + (349 mod 10) + round(58/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((168 + 210/10) * 18) + 8^5 - log_2(32) + (349 mod 10) + round(58/2) $\n\nCompute each c... | {
"type": "arithmetic",
"seed": 1337,
"index": 2769
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Find $A^{-1}$ for $A=\\begin{pmatrix}3&5\\\\-6&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & 5 \\\\ -6 & -6 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2770
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Differentiate with respect to $x$: $f(x) = 2x^3 + -3x^2 + -14x + 10$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + -3x^2 + -14x + 10 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 2771
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&5&2\\\\\\2&2&2\\\\\\4&2&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-10\\\\\\2\\\\\\25\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2772
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Evaluate: ((-175 + 144/18) * 4) + 12^5 - log_4(4096) + (-260 mod 23) + round(56/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-175 + 144/18) * 4) + 12^5 - log_4(4096) + (-260 mod 23) + round(56/... | {
"type": "arithmetic",
"seed": 1337,
"index": 2773
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-56 + 800/20) * 5) + 3^3 - log_4(256) + (-133 mod 2) + floor(-44/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-56 + 800/20) * 5) + 3^3 - log_4(256) + (-133 mod 2) + floor(-44/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 2774
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-8&-9\\\\8&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -8 & -9 \\\\ 8 & -8 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2775
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Differentiate with respect to $x$: $f(x) = \\ln(6x + 4)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(6x + 4) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{... | {
"type": "calculus",
"seed": 1337,
"index": 2776
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute the indefinite integral: $\\int -4x^3 + 0x^2 + -19x + -6\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4x^3 + 0x^2 + -19x + -6\\,dx $\n\nUse standard antideriva... | {
"type": "calculus",
"seed": 1337,
"index": 2777
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Compute the determinant: $A=\\begin{pmatrix}-5&-4\\\\-9&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&-4\\\\\\-9&-5\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2778
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Differentiate with respect to $x$: $f(x) = 5x^3 + 8x^2 + -7x + -9$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 5x^3 + 8x^2 + -7x + -9 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 2779
} |
[
{
"role": "user",
"content": "solve: Compute the determinant: $A=\\begin{pmatrix}7&-5\\\\5&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&-5\\\\\\5&9\\end{pmatrix} $\n\nUse $\\det(A)=ad-bc$: \n$ \\det(A) = (7)(... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2780
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2781
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Find the modular inverse of 5 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2782
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Find the modular inverse of 3 modulo 23, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{23}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees i... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2783
} |
[
{
"role": "user",
"content": "solve: \n\n -48x^2 - 80 + 48x = 66"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48x^2 - 80 + 48x = 66 $\n\nMove all terms to the left (standard form):\n$ -48x^2 + 48x + -146 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2784
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((-101 + -429/13) * 9) + 11^3 - log_8(64) + (-363 mod 8) + floor(-67/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-101 + -429/13) * 9) + 11^3 - log_8(64) + (-363 mod 8) + floor(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 2785
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Differentiate with respect to $x$: $f(x) = -6x^3 + 2x^2 + -20x + -6$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + 2x^2 + -20x + -6 $\n\nApply the standard differentiation rules:\n... | {
"type": "calculus",
"seed": 1337,
"index": 2786
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).... | {
"type": "trigonometry",
"seed": 1337,
"index": 2787
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 10 + 133 - 141x^2 = -113x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 + 133 - 141x^2 = -113x $\n\nMove all terms to the left (standard form):\n$ -141x^2 + 113x + 143 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2788
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 3 - 109x^2 + 182 = -165x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 3 - 109x^2 + 182 = -165x $\n\nMove all terms to the left (standard form):\n$ -109x^2 + 165x + 185 = 0 $\n\nApply the quadra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2789
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Prove that $(\\mathbb{Z}_4, +)$ is a group under addition modulo 4."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_4=\\{0,1,\\dots,3\\}$ with operation $+$ modulo $4$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2790
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 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 $\n\nThe gener... | {
"type": "trigonometry",
"seed": 1337,
"index": 2791
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. 834 + 245x = 662"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 834 + 245x = 662 $\n\nMove all terms to the left (standard form):\n$ 245x + 172 = 0 $\n\nIsolate the $x$ term:\n$ 245x = -172 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 2792
} |
[
{
"role": "user",
"content": "solve Find the modular inverse of 5 modulo 9, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{9}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $x,y$ with:\n$ 5x + 9y = 1.... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2793
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 8 - 52x^2 - 12x = -90"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 8 - 52x^2 - 12x = -90 $\n\nMove all terms to the left (standard form):\n$ -52x^2 + -12x + 98 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2794
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Find the modular inverse of 3 modulo 20, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{20}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2795
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Prove that $(\\mathbb{Z}_28, +)$ is a group under addition modulo 28."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_28=\\{0,1,\\dots,27\\}$ with operation $+$ modulo $28$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2796
} |
[
{
"role": "user",
"content": "solve 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 y} \... | {
"type": "optimization",
"seed": 1337,
"index": 2797
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. 359x + 139 = 205"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 359x + 139 = 205 $\n\nMove all terms to the left (standard form):\n$ 359x + -66 = 0 $\n\nIsolate the $x$ term:\n$ 359x = 66 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 2798
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 456 - 113x = -755"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 456 - 113x = -755 $\n\nMove all terms to the left (standard form):\n$ -113x + 1211 = 0 $\n\nIsolate the $x$ term:\n$ -113x = -1211 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 2799
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.