messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please calculate this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-4&0\\\\\\3&0&-5\\\\\\-5&2&4\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\10\\\\\\-10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by G... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7800
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Prove that $f(x)=2x^2+3x+7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+3x+7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 4x + 3 $\n... | {
"type": "optimization",
"seed": 1337,
"index": 7801
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((170 + 576/16) * 17) + 9^2 - log_4(4096) + (60 mod 4) + ceil(-89/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((170 + 576/16) * 17) + 9^2 - log_4(4096) + (60 mod 4) + ceil(-89/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 7802
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Find the modular inverse of 23 modulo 33, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $23\\cdot a^{-1} \\equiv 1 \\pmod{33}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7803
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Differentiate with respect to $x$: $f(x) = 7\\sin(2x) + -1\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7\\sin(2x) + -1\\cos(1x) $\n\nApply the standard differentiation... | {
"type": "calculus",
"seed": 1337,
"index": 7804
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:... | {
"type": "optimization",
"seed": 1337,
"index": 7805
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Prove that $f(x)=9x^2+-5x+7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-5x+7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x + ... | {
"type": "optimization",
"seed": 1337,
"index": 7806
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Prove that $f(x)=2x^2+0x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+0x+-2$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 4x + 0 ... | {
"type": "optimization",
"seed": 1337,
"index": 7807
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Find $A^{-1}$ for $A=\\begin{pmatrix}0&-7\\\\5&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 0 & -7 \\\\ 5 & -2 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7808
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Evaluate: ((-186 + -330/10) * 17) + 12^5 - log_3(243) + (-112 mod 15) + floor(-86/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-186 + -330/10) * 17) + 12^5 - log_3(243) + (-112 mod 15) + floo... | {
"type": "arithmetic",
"seed": 1337,
"index": 7809
} |
[
{
"role": "user",
"content": "Find the numerical 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) = 0 $\n\nThe gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 7810
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&-1&-4\\\\\\-3&3&2\\\\\\-4&-5&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-2\\\\\\2\\\\\\-14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7811
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Evaluate: ((160 + 5/5) * 14) + 9^4 - log_6(1296) + (430 mod 22) + floor(180/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((160 + 5/5) * 14) + 9^4 - log_6(1296) + (430 mod 22) + floor(180/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 7812
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 7813
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute the determinant: $A=\\begin{pmatrix}6&7\\\\-6&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&7\\\\\\-6&7\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7814
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-9\\\\0&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -9 \\\\ 0 & -2 \\end{pmatrix} $\n\nCompute ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7815
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. -607 - 360 = -236x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -607 - 360 = -236x $\n\nMove all terms to the left (standard form):\n$ 236x + -967 = 0 $\n\nIsolate the $x$ term:\n$ 236x = 967 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7816
} |
[
{
"role": "user",
"content": "solve 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$ \\alpha = \\arccos(-\\frac{\\sqrt{2}}... | {
"type": "trigonometry",
"seed": 1337,
"index": 7817
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 7 + 174x^2 - 111 = -110x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 7 + 174x^2 - 111 = -110x $\n\nMove all terms to the left (standard form):\n$ 174x^2 + 110x + -104 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7818
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((-59 + 88/11) * 15) + 5^3 - log_7(49) + (-99 mod 3) + floor(63/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-59 + 88/11) * 15) + 5^3 - log_7(49) + (-99 mod 3) + floor(63/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 7819
} |
[
{
"role": "user",
"content": "solve -43x^2 + 39 + 99x = -33"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -43x^2 + 39 + 99x = -33 $\n\nMove all terms to the left (standard form):\n$ -43x^2 + 99x + 72 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7820
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute the indefinite integral: $\\int 1e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1e^{2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \... | {
"type": "calculus",
"seed": 1337,
"index": 7821
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Evaluate: ((20 + -34/17) * 17) + 6^5 - log_8(4096) + (180 mod 21) + ceil(-144/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((20 + -34/17) * 17) + 6^5 - log_8(4096) + (180 mod 21) + ceil(-14... | {
"type": "arithmetic",
"seed": 1337,
"index": 7822
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Compute $(-42+-128) \\bmod 18$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-42+-128) \\bmod 18 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7823
} |
[
{
"role": "user",
"content": "Compute 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) = 3.14159 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 7824
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}4&3\\\\8&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 4 & 3 \\\\ 8 & -4 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7825
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute the indefinite integral: $\\int (-3x + 5)e^{6x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + 5)e^{6x}\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 7826
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute $(173+130) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (173+130) \\bmod 12 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7827
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\... | {
"type": "optimization",
"seed": 1337,
"index": 7828
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute the indefinite integral: $\\int \\ln(1x + 5)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + 5)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 7829
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 6x^2 + 149 - 62x = -173"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 6x^2 + 149 - 62x = -173 $\n\nMove all terms to the left (standard form):\n$ 6x^2 + -62x + 322 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7830
} |
[
{
"role": "user",
"content": "solve: -4 + 165x^2 - 14 = 31x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4 + 165x^2 - 14 = 31x $\n\nMove all terms to the left (standard form):\n$ 165x^2 + -31x + -18 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4a... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7831
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Evaluate: ((-3 + 0/19) * 3) + 7^2 - log_10(1000) + (-337 mod 11) + ceil(156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-3 + 0/19) * 3) + 7^2 - log_10(1000) + (-337 mod 11) + ceil(156/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 7832
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Find the modular inverse of 11 modulo 12, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{12}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7833
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -45x^2 + 24 - 104 = -65x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -45x^2 + 24 - 104 = -65x $\n\nMove all terms to the left (standard form):\n$ -45x^2 + 65x + -80 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7834
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Compute the indefinite integral: $\\int (4x + -6)\\sin(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (4x + -6)\\sin(3x)\\,dx $\n\nUse standard antiderivatives (and integra... | {
"type": "calculus",
"seed": 1337,
"index": 7835
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Prove that $f(x,y)=\\frac12(4x^2+10y^2)+6x+-4y+-4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+10y^2)+6x+-4y+-4 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 7836
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute the indefinite integral: $\\int \\ln(5x + 7)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + 7)\\,dx $\n\nUse standard antiderivatives (and integration by parts if nee... | {
"type": "calculus",
"seed": 1337,
"index": 7837
} |
[
{
"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": 7838
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-\\... | {
"type": "trigonometry",
"seed": 1337,
"index": 7839
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 47 - 38 + 35x^2 = 166x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 47 - 38 + 35x^2 = 166x $\n\nMove all terms to the left (standard form):\n$ 35x^2 + -166x + 9 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7840
} |
[
{
"role": "user",
"content": "solve Compute the determinant: $A=\\begin{pmatrix}7&-8\\\\2&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&-8\\\\\\2&6\\end{pmatrix} $\n\nUse $\\det(A)=ad-bc$: \n$ \\det(A) = (7)(6... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7841
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. -634 - 622x = 884"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -634 - 622x = 884 $\n\nMove all terms to the left (standard form):\n$ -622x + -1518 = 0 $\n\nIsolate the $x$ term:\n$ -622x = 1518 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 7842
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 27 + 79x^2 + 75 = 160x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27 + 79x^2 + 75 = 160x $\n\nMove all terms to the left (standard form):\n$ 79x^2 + -160x + 102 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7843
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Prove that $f(x,y)=\\frac12(1x^2+9y^2)+3x+3y+3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+9y^2)+3x+3y+3 $\n\n$ \\frac{\\partial^2 f}{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 7844
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -44 + 93x - 191 = -183x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44 + 93x - 191 = -183x^2 $\n\nMove all terms to the left (standard form):\n$ 183x^2 + 93x + -235 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7845
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 734 - 320 = -848x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 734 - 320 = -848x $\n\nMove all terms to the left (standard form):\n$ 848x + 414 = 0 $\n\nIsolate the $x$ term:\n$ 848x = -414 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 7846
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&2&-4\\\\\\0&-5&3\\\\\\-5&3&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-10\\\\\\8\\\\\\10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7847
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Evaluate: ((-98 + -147/7) * 13) + 4^2 - log_4(64) + (354 mod 20) + round(36/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-98 + -147/7) * 13) + 4^2 - log_4(64) + (354 mod 20) + round(36/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 7848
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 46 + 29x^2 + 8 = -98x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 46 + 29x^2 + 8 = -98x $\n\nMove all terms to the left (standard form):\n$ 29x^2 + 98x + 54 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7849
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. -150x + 979 = -544"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -150x + 979 = -544 $\n\nMove all terms to the left (standard form):\n$ -150x + 1523 = 0 $\n\nIsolate the $x$ term:\n$ -150x = -1523 $\n\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 7850
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Evaluate: ((-192 + -320/20) * 16) + 11^3 - log_8(512) + (75 mod 9) + ceil(81/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-192 + -320/20) * 16) + 11^3 - log_8(512) + (75 mod 9) + ceil(81/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 7851
} |
[
{
"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": 7852
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((-126 + -216/18) * 5) + 8^5 - log_5(125) + (79 mod 24) + floor(-123/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-126 + -216/18) * 5) + 8^5 - log_5(125) + (79 mod 24) + floor(-123/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 7853
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Prove that $(\\mathbb{Z}_12, +)$ is a group under addition modulo 12."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_12=\\{0,1,\\dots,11\\}$ with operation $+$ modulo $12$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7854
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 36x^2 + 4 - 51x = 135"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36x^2 + 4 - 51x = 135 $\n\nMove all terms to the left (standard form):\n$ 36x^2 + -51x + -131 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7855
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 33x^2 + 162 - 59 = 28x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33x^2 + 162 - 59 = 28x $\n\nMove all terms to the left (standard form):\n$ 33x^2 + -28x + 103 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7856
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 41 - 189 + 170x^2 = 132x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 41 - 189 + 170x^2 = 132x $\n\nMove all terms to the left (standard form):\n$ 170x^2 + -132x + -148 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7857
} |
[
{
"role": "user",
"content": "Can you solve the equation below? -23 + 2x + 186 = -65x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23 + 2x + 186 = -65x^2 $\n\nMove all terms to the left (standard form):\n$ 65x^2 + 2x + 163 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7858
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Differentiate with respect to $x$: $f(x) = \\ln(1x + 2)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(1x + 2) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{1}{1x + ... | {
"type": "calculus",
"seed": 1337,
"index": 7859
} |
[
{
"role": "user",
"content": "Can you determine the solution of 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).\... | {
"type": "trigonometry",
"seed": 1337,
"index": 7860
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. -17x + 117 + 40x^2 = -110"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17x + 117 + 40x^2 = -110 $\n\nMove all terms to the left (standard form):\n$ 40x^2 + -17x + 227 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7861
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. 30 - 11 + 116x = -127x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 30 - 11 + 116x = -127x^2 $\n\nMove all terms to the left (standard form):\n$ 127x^2 + 116x + 19 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7862
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n -9 + 183 - 197x^2 = 4x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -9 + 183 - 197x^2 = 4x $\n\nMove all terms to the left (standard form):\n$ -197x^2 + -4x + 174 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7863
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Differentiate with respect to $x$: $f(x) = (3x + 10)e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (3x + 10)e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{3e^{... | {
"type": "calculus",
"seed": 1337,
"index": 7864
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 121 + 214x = -357"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 121 + 214x = -357 $\n\nMove all terms to the left (standard form):\n$ 214x + 478 = 0 $\n\nIsolate the $x$ term:\n$ 214x = -478 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 7865
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((68 + 380/10) * 6) + 5^4 - log_8(64) + (-409 mod 15) + floor(30/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((68 + 380/10) * 6) + 5^4 - log_8(64) + (-409 mod 15) + floor(30/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 7866
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&2&3\\\\\\4&3&5\\\\\\3&3&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-23\\\\\\-6\\\\\\21\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7867
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 456 + 402 = -709x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 456 + 402 = -709x $\n\nMove all terms to the left (standard form):\n$ 709x + 858 = 0 $\n\nIsolate the $x$ term:\n$ 709x = -858 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 7868
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. -265 - 638x = -288"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -265 - 638x = -288 $\n\nMove all terms to the left (standard form):\n$ -638x + 23 = 0 $\n\nIsolate the $x$ term:\n$ -638x = -23 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 7869
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Differentiate with respect to $x$: $f(x) = 6e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{24e^{4x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 7870
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -42x^2 - 123 + 190x = 175"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -42x^2 - 123 + 190x = 175 $\n\nMove all terms to the left (standard form):\n$ -42x^2 + 190x + -298 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7871
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-47 + -768/24) * 10) + 11^5 - log_2(8) + (302 mod 22) + ceil(77/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-47 + -768/24) * 10) + 11^5 - log_2(8) + (302 mod 22) + ceil(77/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 7872
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 10 + 93 + 196x^2 = -25x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 + 93 + 196x^2 = -25x $\n\nMove all terms to the left (standard form):\n$ 196x^2 + 25x + 103 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7873
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Find the modular inverse of 15 modulo 22, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $15\\cdot a^{-1} \\equiv 1 \\pmod{22}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7874
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Prove that $(\\mathbb{Z}_13, +)$ is a group under addition modulo 13."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_13=\\{0,1,\\dots,12\\}$ with operation $+$ modulo $13$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 7875
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. -971x - 965 = -509"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -971x - 965 = -509 $\n\nMove all terms to the left (standard form):\n$ -971x + -456 = 0 $\n\nIsolate the $x$ term:\n$ -971x = 456 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 7876
} |
[
{
"role": "user",
"content": "Solve the following math equation. Differentiate with respect to $x$: $f(x) = 9e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 9e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{36e^{4x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 7877
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Compute the indefinite integral: $\\int -1e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\... | {
"type": "calculus",
"seed": 1337,
"index": 7878
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Compute the determinant: $A=\\begin{pmatrix}6&-9\\\\-6&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&-9\\\\\\-6&-1\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7879
} |
[
{
"role": "user",
"content": "solve: -146x - 222 = -290"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -146x - 222 = -290 $\n\nMove all terms to the left (standard form):\n$ -146x + 68 = 0 $\n\nIsolate the $x$ term:\n$ -146x = -68 $\n\nDivide both sides by the coefficient of $x$:... | {
"type": "linear_equation",
"seed": 1337,
"index": 7880
} |
[
{
"role": "user",
"content": "Please work out this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&-5&4\\\\\\2&-2&-4\\\\\\-2&2&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\16\\\\\\16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by G... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7881
} |
[
{
"role": "user",
"content": "Find the answer 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 $f'(x)=0$, hence:... | {
"type": "optimization",
"seed": 1337,
"index": 7882
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((-44 + -893/19) * 10) + 8^5 - log_8(4096) + (170 mod 19) + floor(-165/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-44 + -893/19) * 10) + 8^5 - log_8(4096) + (170 mod 19) + floo... | {
"type": "arithmetic",
"seed": 1337,
"index": 7883
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} &... | {
"type": "optimization",
"seed": 1337,
"index": 7884
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((-103 + -162/6) * 4) + 8^5 - log_8(262144) + (-439 mod 18) + floor(87/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-103 + -162/6) * 4) + 8^5 - log_8(262144) + (-439 mod 18) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 7885
} |
[
{
"role": "user",
"content": "solve: Evaluate: ((21 + 32/2) * 18) + 2^3 - log_5(5) + (-364 mod 10) + round(30/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((21 + 32/2) * 18) + 2^3 - log_5(5) + (-364 mod 10) + round(30/2) $\n\nCompute each component:\n$ 32/2 = 16 $\n$ (2... | {
"type": "arithmetic",
"seed": 1337,
"index": 7886
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -23x + 186 + 188 = 13x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23x + 186 + 188 = 13x^2 $\n\nMove all terms to the left (standard form):\n$ -13x^2 + -23x + 374 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7887
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 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": 7888
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Differentiate with respect to $x$: $f(x) = (2x + -7)e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (2x + -7)e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{2e^{5x} + (2x +... | {
"type": "calculus",
"seed": 1337,
"index": 7889
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Compute the indefinite integral: $\\int -5x^3 + 8x^2 + 4x + -20\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5x^3 + 8x^2 + 4x + -20\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 7890
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 17x^2 - 10 - 164x = 33"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 17x^2 - 10 - 164x = 33 $\n\nMove all terms to the left (standard form):\n$ 17x^2 + -164x + -43 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7891
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 130 - 35x = 584"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 130 - 35x = 584 $\n\nMove all terms to the left (standard form):\n$ -35x + -454 = 0 $\n\nIsolate the $x$ term:\n$ -35x = 454 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7892
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-77 + -102/3) * 17) + 10^3 - log_8(262144) + (-40 mod 5) + round(50/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-77 + -102/3) * 17) + 10^3 - log_8(262144) + (-40 mod 5) + round(50/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 7893
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 7894
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&-4&-5\\\\\\-3&-4&0\\\\\\0&3&1\\end{pmatrix},\\quad b=\\begin{pmatrix}12\\\\\\-2\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 7895
} |
[
{
"role": "user",
"content": "Solve the following math equation. 19 + 135 - 18x = 196x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19 + 135 - 18x = 196x^2 $\n\nMove all terms to the left (standard form):\n$ -196x^2 + -18x + 154 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 7896
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. -799 + 826 = -503x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -799 + 826 = -503x $\n\nMove all terms to the left (standard form):\n$ 503x + 27 = 0 $\n\nIsolate the $x$ term:\n$ 503x = -27 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 7897
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -332x - 510 = 682"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -332x - 510 = 682 $\n\nMove all terms to the left (standard form):\n$ -332x + -1192 = 0 $\n\nIsolate the $x$ term:\n$ -332x = 1192 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 7898
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((-39 + 528/16) * 20) + 8^3 - log_10(100) + (229 mod 11) + ceil(51/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-39 + 528/16) * 20) + 8^3 - log_10(100) + (229 mod 11) + ceil(51/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 7899
} |
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