messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 624 + 109x = -988"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 624 + 109x = -988 $\n\nMove all terms to the left (standard form):\n$ 109x + 1612 = 0 $\n\nIsolate the $x$ term:\n$ 109x = -1612 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 4600
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Differentiate with respect to $x$: $f(x) = (1x + -9)e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + -9)e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{1e^{3x... | {
"type": "calculus",
"seed": 1337,
"index": 4601
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^... | {
"type": "optimization",
"seed": 1337,
"index": 4602
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Evaluate: ((152 + 720/16) * 17) + 7^5 - log_6(36) + (70 mod 30) + round(138/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((152 + 720/16) * 17) + 7^5 - log_6(36) + (70 mod 30) + round(138/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 4603
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Prove that $f(x)=5x^2+9x+-4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+9x+-4$.\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": 4604
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Prove that $f(x)=4x^2+-3x+8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+-3x+8$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$... | {
"type": "optimization",
"seed": 1337,
"index": 4605
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute the indefinite integral: $\\int \\ln(6x + 5)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(6x + 5)\\,dx $\n\nUse standard antiderivatives (and integration by parts if ne... | {
"type": "calculus",
"seed": 1337,
"index": 4606
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? -4x + 42 + 24 = 156x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4x + 42 + 24 = 156x^2 $\n\nMove all terms to the left (standard form):\n$ -156x^2 + -4x + 66 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4607
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -970 - 743x = 964"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -970 - 743x = 964 $\n\nMove all terms to the left (standard form):\n$ -743x + -1934 = 0 $\n\nIsolate the $x$ term:\n$ -743x = 1934 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4608
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Differentiate with respect to $x$: $f(x) = 3e^{-2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3e^{-2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-6e^{-2x}} $"
}... | {
"type": "calculus",
"seed": 1337,
"index": 4609
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}6&-1\\\\8&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 6 & -1 \\\\ 8 & -9 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4610
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Prove that $f(x)=7x^2+-5x+3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+-5x+3$.\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": 4611
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. -12x^2 + 45 - 108 = 187x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -12x^2 + 45 - 108 = 187x $\n\nMove all terms to the left (standard form):\n$ -12x^2 + -187x + -63 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4612
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 4613
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -15 + 38 + 196x = 36x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15 + 38 + 196x = 36x^2 $\n\nMove all terms to the left (standard form):\n$ -36x^2 + 196x + 23 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4614
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 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\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 4615
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Compute the indefinite integral: $\\int 7e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 7e^{2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \... | {
"type": "calculus",
"seed": 1337,
"index": 4616
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute $(-37+-175) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-37+-175) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction modulo $n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4617
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Find the modular inverse of 10 modulo 21, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $10\\cdot a^{-1} \\equiv 1 \\pmod{21}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identi... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4618
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute the indefinite integral: $\\int 3e^{-3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3e^{-3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 4619
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -38x^2 + 60 - 153x = -2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -38x^2 + 60 - 153x = -2 $\n\nMove all terms to the left (standard form):\n$ -38x^2 + -153x + 62 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4620
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 657 - 194x = -392"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 657 - 194x = -392 $\n\nMove all terms to the left (standard form):\n$ -194x + 1049 = 0 $\n\nIsolate the $x$ term:\n$ -194x = -1049 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4621
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Prove that $(\\mathbb{Z}_16, +)$ is a group under addition modulo 16."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_16=\\{0,1,\\dots,15\\}$ with operation $+$ modulo $16$.\n\n**Closure:** If $a,b\\in... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4622
} |
[
{
"role": "user",
"content": "Please calculate this equation. 689 + 760 = -827x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 689 + 760 = -827x $\n\nMove all terms to the left (standard form):\n$ 827x + 1449 = 0 $\n\nIsolate the $x$ term:\n$ 827x = -1449 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 4623
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&3\\\\\\5&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}-27\\\\\\9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&3\\\\\\5&-6\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4624
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 24x + 182 = 192"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 24x + 182 = 192 $\n\nMove all terms to the left (standard form):\n$ 24x + -10 = 0 $\n\nIsolate the $x$ term:\n$ 24x = 10 $\n\nDivide both sides by the coeff... | {
"type": "linear_equation",
"seed": 1337,
"index": 4625
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the determinant: $A=\\begin{pmatrix}2&-1\\\\-3&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&-1\\\\\\-3&1\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4626
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 4627
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&1\\\\\\4&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}7\\\\\\-49\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&1\\\\\\4&-7\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4628
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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(-\\frac{1}... | {
"type": "trigonometry",
"seed": 1337,
"index": 4629
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((194 + 24/2) * 16) + 6^3 - log_10(100000) + (-137 mod 21) + floor(-154/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((194 + 24/2) * 16) + 6^3 - log_10(100000) + (-137 mod 21) + floor(-154/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4630
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Compute $(138+69) \\bmod 5$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (138+69) \\bmod 5 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4631
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 41x^2 - 163 - 143x = 29"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 41x^2 - 163 - 143x = 29 $\n\nMove all terms to the left (standard form):\n$ 41x^2 + -143x + -192 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4632
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((-111 + 125/25) * 17) + 2^5 - log_4(64) + (-171 mod 28) + ceil(-54/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-111 + 125/25) * 17) + 2^5 - log_4(64) + (-171 mod 28) + ceil(-54/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4633
} |
[
{
"role": "user",
"content": "Compute the solution for 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": 4634
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 4635
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe general solutions... | {
"type": "trigonometry",
"seed": 1337,
"index": 4636
} |
[
{
"role": "user",
"content": "solve: \n\n Compute the indefinite integral: $\\int (4x + -9)e^{6x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (4x + -9)e^{6x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int (4x + -9... | {
"type": "calculus",
"seed": 1337,
"index": 4637
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Evaluate: ((114 + -345/23) * 6) + 3^4 - log_7(343) + (42 mod 12) + floor(50/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((114 + -345/23) * 6) + 3^4 - log_7(343) + (42 mod 12) + floor(50/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4638
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Compute the indefinite integral: $\\int -7e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -7e^{2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 4639
} |
[
{
"role": "user",
"content": "solve: \n\n Compute the indefinite integral: $\\int 8e^{-3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 8e^{-3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int 8e^{-3x}\\,dx = \\boxe... | {
"type": "calculus",
"seed": 1337,
"index": 4640
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. 21 + 58 - 148x^2 = 169x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 21 + 58 - 148x^2 = 169x $\n\nMove all terms to the left (standard form):\n$ -148x^2 + -169x + 79 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4641
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Prove that $f(x,y)=\\frac12(7x^2+6y^2)+-1x+1y+-1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+6y^2)+-1x+1y+-1 $\n\n$ \\frac{\\partial^2 f}{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 4642
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Prove that $f(x)=6x^2+9x+7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+9x+7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 12x... | {
"type": "optimization",
"seed": 1337,
"index": 4643
} |
[
{
"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 = \\arct... | {
"type": "trigonometry",
"seed": 1337,
"index": 4644
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Evaluate: ((179 + 126/9) * 12) + 4^2 - log_5(125) + (95 mod 24) + ceil(178/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((179 + 126/9) * 12) + 4^2 - log_5(125) + (95 mod 24) + ceil(178/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4645
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Compute $(-186+-119) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-186+-119) \\bmod 15 $\n\nUse the rule that addition is compatible with red... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4646
} |
[
{
"role": "user",
"content": "solve: \n\n Find the modular inverse of 5 modulo 28, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{28}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $x,y$ with:\n$ 5x + ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4647
} |
[
{
"role": "user",
"content": "solve: Compute the indefinite integral: $\\int (2x + 1)e^{6x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (2x + 1)e^{6x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int (2x + 1)e^{6x}... | {
"type": "calculus",
"seed": 1337,
"index": 4648
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((193 + -8/8) * 19) + 11^3 - log_7(7) + (-175 mod 2) + round(-76/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((193 + -8/8) * 19) + 11^3 - log_7(7) + (-175 mod 2) + round(-76/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4649
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 13x + 110 + 89x^2 = -70"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13x + 110 + 89x^2 = -70 $\n\nMove all terms to the left (standard form):\n$ 89x^2 + 13x + 180 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4650
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Prove that $f(x,y)=\\frac12(8x^2+4y^2)+1x+4y+9$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(8x^2+4y^2)+1x+4y+9 $\n\n$ \\frac{\\partial^2 f}{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 4651
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arc... | {
"type": "trigonometry",
"seed": 1337,
"index": 4652
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve for $x$ (in radians): sin(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(1) = 1.5708 $\n\nThe... | {
"type": "trigonometry",
"seed": 1337,
"index": 4653
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-51 + 80/4) * 19) + 7^5 - log_5(125) + (-56 mod 8) + round(-137/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-51 + 80/4) * 19) + 7^5 - log_5(125) + (-56 mod 8) + round(-137/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 4654
} |
[
{
"role": "user",
"content": "Please solve this math problem. 19 + 24 + 18x^2 = -51x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19 + 24 + 18x^2 = -51x $\n\nMove all terms to the left (standard form):\n$ 18x^2 + 51x + 43 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4655
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Prove that $f(x)=6x^2+8x+3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+8x+3$.\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": 4656
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Compute the determinant: $A=\\begin{pmatrix}-4&9\\\\-9&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&9\\\\\\-9&-3\\end{pmatrix} $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4657
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((51 + 833/17) * 20) + 8^4 - log_7(16807) + (-49 mod 2) + round(-19/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((51 + 833/17) * 20) + 8^4 - log_7(16807) + (-49 mod 2) + round(-19/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4658
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((-85 + 459/17) * 19) + 5^4 - log_9(729) + (436 mod 19) + floor(61/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-85 + 459/17) * 19) + 5^4 - log_9(729) + (436 mod 19) + floor(61/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 4659
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&-2\\\\\\5&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}38\\\\\\29\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&-2\\\\\\5&-1... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4660
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((152 + 125/5) * 10) + 4^2 - log_3(243) + (-406 mod 25) + ceil(168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((152 + 125/5) * 10) + 4^2 - log_3(243) + (-406 mod 25) + ceil(168/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 4661
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Evaluate: ((175 + 1176/24) * 20) + 11^2 - log_7(2401) + (136 mod 2) + floor(-153/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((175 + 1176/24) * 20) + 11^2 - log_7(2401) + (136 mod 2) + floor(-153... | {
"type": "arithmetic",
"seed": 1337,
"index": 4662
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Compute the indefinite integral: $\\int -4x^3 + -8x^2 + 16x + 11\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4x^3 + -8x^2 + 16x + 11\\,dx $\n\nUse standard antiderivativ... | {
"type": "calculus",
"seed": 1337,
"index": 4663
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Compute $(145+151) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (145+151) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction mo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4664
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 4665
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Prove that $f(x,y)=\\frac12(7x^2+5y^2)+4x+-6y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+5y^2)+4x+-6y+-5 $\n\n$ \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 4666
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. -49 + 113 + 101x^2 = 174x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -49 + 113 + 101x^2 = 174x $\n\nMove all terms to the left (standard form):\n$ 101x^2 + -174x + 64 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4667
} |
[
{
"role": "user",
"content": "Please work out 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 $\n\nThe general s... | {
"type": "trigonometry",
"seed": 1337,
"index": 4668
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Evaluate: ((-65 + -70/7) * 19) + 3^5 - log_2(8) + (87 mod 12) + ceil(194/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-65 + -70/7) * 19) + 3^5 - log_2(8) + (87 mod 12) + ceil(194/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 4669
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((-200 + 989/23) * 11) + 4^4 - log_8(512) + (397 mod 3) + ceil(-164/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-200 + 989/23) * 11) + 4^4 - log_8(512) + (397 mod 3) + ceil(-164... | {
"type": "arithmetic",
"seed": 1337,
"index": 4670
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 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{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 4671
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -36x - 62 - 150x^2 = 75"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x - 62 - 150x^2 = 75 $\n\nMove all terms to the left (standard form):\n$ -150x^2 + -36x + -137 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4672
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. -3x + 97x^2 - 199 = -78"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -3x + 97x^2 - 199 = -78 $\n\nMove all terms to the left (standard form):\n$ 97x^2 + -3x + -121 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4673
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Find the modular inverse of 11 modulo 38, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{38}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4674
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-2&3\\\\\\3&-4&2\\\\\\-3&-3&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-3\\\\\\-2\\\\\\-3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4675
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = (4x + 5)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (4x + 5)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{4\\s... | {
"type": "calculus",
"seed": 1337,
"index": 4676
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Differentiate with respect to $x$: $f(x) = -3e^{-2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3e^{-2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{6e^{-2x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 4677
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 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 ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 4678
} |
[
{
"role": "user",
"content": "Solve the following math equation. 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": 4679
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = 3x^3 + -5x^2 + -8x + -4$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3x^3 + -5x^2 + -8x + -4 $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 4680
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((-120 + -100/4) * 7) + 2^5 - log_3(3) + (-379 mod 25) + round(84/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-120 + -100/4) * 7) + 2^5 - log_3(3) + (-379 mod 25) + round(84... | {
"type": "arithmetic",
"seed": 1337,
"index": 4681
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 25 - 16 - 174x = -39x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 25 - 16 - 174x = -39x^2 $\n\nMove all terms to the left (standard form):\n$ 39x^2 + -174x + 9 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4682
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 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": 4683
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Find the modular inverse of 23 modulo 31, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $23\\cdot a^{-1} \\equiv 1 \\pmod{31}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4684
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((-182 + -14/14) * 15) + 10^3 - log_3(3) + (-42 mod 6) + floor(99/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-182 + -14/14) * 15) + 10^3 - log_3(3) + (-42 mod 6) + floor(99/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 4685
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 616 - 157 = 550x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 616 - 157 = 550x $\n\nMove all terms to the left (standard form):\n$ -550x + 459 = 0 $\n\nIsolate the $x$ term:\n$ -550x = -459 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4686
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Solve for $x$ (in radians): sin(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 4687
} |
[
{
"role": "user",
"content": "Resolve 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{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 4688
} |
[
{
"role": "user",
"content": "Please compute and solve this 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 int... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4689
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute the indefinite integral: $\\int 6e^{-3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6e^{-3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed)... | {
"type": "calculus",
"seed": 1337,
"index": 4690
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute $(-102+91) \\bmod 16$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-102+91) \\bmod 16 $\n\nUse the rule that addition is compatible with... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4691
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Differentiate with respect to $x$: $f(x) = -3e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-12e^{4x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 4692
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute the indefinite integral: $\\int \\ln(8x + -4)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + -4)\\,dx $\n\nUse standard antiderivatives (and integration b... | {
"type": "calculus",
"seed": 1337,
"index": 4693
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((-27 + -36/18) * 9) + 4^2 - log_9(9) + (266 mod 14) + ceil(-65/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-27 + -36/18) * 9) + 4^2 - log_9(9) + (266 mod 14) + ceil(-65/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 4694
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((130 + 77/7) * 11) + 8^2 - log_2(4) + (364 mod 20) + floor(116/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((130 + 77/7) * 11) + 8^2 - log_2(4) + (364 mod 20) + floor(116/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4695
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 866 + 302 = -746x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 866 + 302 = -746x $\n\nMove all terms to the left (standard form):\n$ 746x + 1168 = 0 $\n\nIsolate the $x$ term:\n$ 746x = -1168 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 4696
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((130 + 128/4) * 15) + 2^3 - log_2(8) + (14 mod 29) + ceil(-134/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((130 + 128/4) * 15) + 2^3 - log_2(8) + (14 mod 29) + ceil(-134/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4697
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((26 + 924/22) * 5) + 11^5 - log_3(9) + (273 mod 26) + floor(134/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((26 + 924/22) * 5) + 11^5 - log_3(9) + (273 mod 26) + floor(134/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4698
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 36 + 125x - 149 = 112x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36 + 125x - 149 = 112x^2 $\n\nMove all terms to the left (standard form):\n$ -112x^2 + 125x + -113 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4699
} |
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