messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the equation and state the result. Prove that $(\\mathbb{Z}_14, +)$ is a group under addition modulo 14."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_14=\\{0,1,\\dots,13\\}$ with operation $+$ modulo $14$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4100
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&-1&-2\\\\\\-5&0&0\\\\\\1&0&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}8\\\\\\0\\\\\\12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.,... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4101
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -37x - 49 - 12x^2 = 133"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37x - 49 - 12x^2 = 133 $\n\nMove all terms to the left (standard form):\n$ -12x^2 + -37x + -182 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4102
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. 47x^2 + 190x + 133 = 8"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 47x^2 + 190x + 133 = 8 $\n\nMove all terms to the left (standard form):\n$ 47x^2 + 190x + 125 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4103
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Compute the determinant: $A=\\begin{pmatrix}-1&-2\\\\-8&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&-2\\\\\\-8&-1\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4104
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((-152 + 299/23) * 8) + 8^5 - log_7(343) + (-191 mod 28) + floor(141/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-152 + 299/23) * 8) + 8^5 - log_7(343) + (-191 mod 28) + floor(141/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4105
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 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": 4106
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((42 + -592/16) * 6) + 12^4 - log_2(8) + (89 mod 19) + floor(-48/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((42 + -592/16) * 6) + 12^4 - log_2(8) + (89 mod 19) + floor(-48/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4107
} |
[
{
"role": "user",
"content": "Please work out this equation. Compute the determinant: $A=\\begin{pmatrix}8&3\\\\8&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}8&3\\\\\\8&-4\\end{pmatrix} $\n\nUse $\\det(A)=ad-b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4108
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value... | {
"type": "trigonometry",
"seed": 1337,
"index": 4109
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-5&7\\\\\\4&9\\end{pmatrix},\\quad b=\\begin{pmatrix}-65\\\\\\-21\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-5&7\\\\\\4&9... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4110
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Compute $(-43+10) \\bmod 3$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-43+10) \\bmod 3 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4111
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&4\\\\\\-2&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}-34\\\\\\-6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&4\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4112
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&-1\\\\\\2&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}17\\\\\\-69\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&-1\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4113
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. 126 - 477x = 651"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 126 - 477x = 651 $\n\nMove all terms to the left (standard form):\n$ -477x + -525 = 0 $\n\nIsolate the $x$ term:\n$ -477x = 525 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 4114
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Differentiate with respect to $x$: $f(x) = -6e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-18e^{3x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 4115
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 808 + 713 = -775x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 808 + 713 = -775x $\n\nMove all terms to the left (standard form):\n$ 775x + 1521 = 0 $\n\nIsolate the $x$ term:\n$ 775x = -1521 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4116
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Evaluate: ((-103 + -658/14) * 7) + 3^5 - log_8(8) + (196 mod 27) + round(-109/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-103 + -658/14) * 7) + 3^5 - log_8(8) + (196 mod 27) + round(-109/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 4117
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 622 + 691x = -628"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 622 + 691x = -628 $\n\nMove all terms to the left (standard form):\n$ 691x + 1250 = 0 $\n\nIsolate the $x$ term:\n$ 691x = -1250 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4118
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Compute $(-193+-62) \\bmod 20$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-193+-62) \\bmod 20 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4119
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute the indefinite integral: $\\int \\ln(2x + 7)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + 7)\\,dx $\n\nUse standard antiderivatives (and integration by parts ... | {
"type": "calculus",
"seed": 1337,
"index": 4120
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. 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\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4121
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&-2&3\\\\\\-4&-3&-2\\\\\\3&2&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-10\\\\\\-6\\\\\\14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4122
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? -715 - 220x = 20"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -715 - 220x = 20 $\n\nMove all terms to the left (standard form):\n$ -220x + -735 = 0 $\n\nIsolate the $x$ term:\n$ -220x = 735 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 4123
} |
[
{
"role": "user",
"content": "Work through and solve 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 genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 4124
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Prove that $f(x)=5x^2+-6x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-6x+0$.\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": 4125
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 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 val... | {
"type": "trigonometry",
"seed": 1337,
"index": 4126
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute $(197+-87) \\bmod 10$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (197+-87) \\bmod 10 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4127
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. -12 + 161 - 78x = -197x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -12 + 161 - 78x = -197x^2 $\n\nMove all terms to the left (standard form):\n$ 197x^2 + -78x + 149 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4128
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Compute the indefinite integral: $\\int -1e^{-5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1e^{-5x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 4129
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute the determinant: $A=\\begin{pmatrix}9&-1\\\\0&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}9&-1\\\\\\0&0\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4130
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Prove that $f(x)=3x^2+-4x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+-4x+-9$.\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": 4131
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((70 + -57/19) * 3) + 7^3 - log_6(46656) + (337 mod 13) + round(-85/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((70 + -57/19) * 3) + 7^3 - log_6(46656) + (337 mod 13) + round(-85/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 4132
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Evaluate: ((66 + -638/22) * 16) + 4^2 - log_5(5) + (-496 mod 8) + ceil(-158/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((66 + -638/22) * 16) + 4^2 - log_5(5) + (-496 mod 8) + ceil(-158/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4133
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 8x^2 + 65 + 129 = -75x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 8x^2 + 65 + 129 = -75x $\n\nMove all terms to the left (standard form):\n$ 8x^2 + 75x + 194 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4134
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Evaluate: ((-180 + -120/4) * 18) + 8^2 - log_10(100000) + (-14 mod 30) + ceil(49/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-180 + -120/4) * 18) + 8^2 - log_10(100000) + (-14 mod 30) + cei... | {
"type": "arithmetic",
"seed": 1337,
"index": 4135
} |
[
{
"role": "user",
"content": "Solve the equation shown below. -513x + 625 = -792"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -513x + 625 = -792 $\n\nMove all terms to the left (standard form):\n$ -513x + 1417 = 0 $\n\nIsolate the $x$ term:\n$ -513x = -1417 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 4136
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute the indefinite integral: $\\int \\ln(5x + -4)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + -4)\\,dx $\n\nUse standard antiderivatives (and integration by parts ... | {
"type": "calculus",
"seed": 1337,
"index": 4137
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -90 + 387x = -208"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -90 + 387x = -208 $\n\nMove all terms to the left (standard form):\n$ 387x + 118 = 0 $\n\nIsolate the $x$ term:\n$ 387x = -118 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4138
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 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$ \\alpha = \\arctan(\\frac{\\sq... | {
"type": "trigonometry",
"seed": 1337,
"index": 4139
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute the indefinite integral: $\\int 4\\sin(9x) + 8\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4\\sin(9x) + 8\\cos(5x)\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 4140
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 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 $\n\nThe general so... | {
"type": "trigonometry",
"seed": 1337,
"index": 4141
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Evaluate: ((114 + 552/12) * 5) + 12^3 - log_5(625) + (481 mod 13) + ceil(85/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((114 + 552/12) * 5) + 12^3 - log_5(625) + (481 mod 13) + ceil(85/2) $\n\nCompute each co... | {
"type": "arithmetic",
"seed": 1337,
"index": 4142
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 13 - 78 - 62x^2 = -160x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13 - 78 - 62x^2 = -160x $\n\nMove all terms to the left (standard form):\n$ -62x^2 + 160x + -65 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4143
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&1&5\\\\\\-5&-5&-2\\\\\\4&-4&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}10\\\\\\-30\\\\\\-8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.,... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4144
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Evaluate: ((167 + -744/24) * 18) + 7^4 - log_6(7776) + (-189 mod 27) + round(4/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((167 + -744/24) * 18) + 7^4 - log_6(7776) + (-189 mod 27) + round(4/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 4145
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((-174 + -64/2) * 11) + 5^3 - log_5(15625) + (136 mod 16) + ceil(-34/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-174 + -64/2) * 11) + 5^3 - log_5(15625) + (136 mod 16) + ceil(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 4146
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 37 + 176 + 104x = 175x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 + 176 + 104x = 175x^2 $\n\nMove all terms to the left (standard form):\n$ -175x^2 + 104x + 213 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4147
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 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": 4148
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 485 - 942 = 916x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 485 - 942 = 916x $\n\nMove all terms to the left (standard form):\n$ -916x + -457 = 0 $\n\nIsolate the $x$ term:\n$ -916x = 457 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4149
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((41 + 400/10) * 17) + 10^2 - log_2(16) + (168 mod 14) + floor(141/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((41 + 400/10) * 17) + 10^2 - log_2(16) + (168 mod 14) + floor(141/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4150
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((147 + -440/22) * 14) + 8^4 - log_8(32768) + (99 mod 17) + round(121/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((147 + -440/22) * 14) + 8^4 - log_8(32768) + (99 mod 17) + round(121/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 4151
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 42 - 80x + 74 = 61x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 42 - 80x + 74 = 61x^2 $\n\nMove all terms to the left (standard form):\n$ -61x^2 + -80x + 116 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4152
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -33 - 142x^2 - 156x = 118"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -33 - 142x^2 - 156x = 118 $\n\nMove all terms to the left (standard form):\n$ -142x^2 + -156x + -151 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4153
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((-90 + 336/7) * 13) + 6^2 - log_3(729) + (381 mod 28) + floor(-94/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-90 + 336/7) * 13) + 6^2 - log_3(729) + (381 mod 28) + floor(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 4154
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 457x + 308 = -552"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 457x + 308 = -552 $\n\nMove all terms to the left (standard form):\n$ 457x + 860 = 0 $\n\nIsolate the $x$ term:\n$ 457x = -860 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 4155
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&8\\\\\\1&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}-71\\\\\\-1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&8\\\\\\1&-6\\end{p... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4156
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((-176 + -525/15) * 5) + 6^2 - log_7(49) + (399 mod 15) + floor(71/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-176 + -525/15) * 5) + 6^2 - log_7(49) + (399 mod 15) + floor(71/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4157
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((35 + -300/20) * 15) + 9^2 - log_4(16) + (-293 mod 27) + ceil(-54/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((35 + -300/20) * 15) + 9^2 - log_4(16) + (-293 mod 27) + ceil(-54/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 4158
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -837 - 200 = -314x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -837 - 200 = -314x $\n\nMove all terms to the left (standard form):\n$ 314x + -1037 = 0 $\n\nIsolate the $x$ term:\n$ 314x = 1037 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 4159
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Find the modular inverse of 17 modulo 30, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{30}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees int... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4160
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 4161
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. 195 - 530 = -75x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 195 - 530 = -75x $\n\nMove all terms to the left (standard form):\n$ 75x + -335 = 0 $\n\nIsolate the $x$ term:\n$ 75x = 335 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4162
} |
[
{
"role": "user",
"content": "Calculate the answer 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": 4163
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Prove that $(\\mathbb{Z}_25, +)$ is a group under addition modulo 25."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_25=\\{0,1,\\dots,24\\}$ with operation $+$ modulo $25$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4164
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. -732x - 472 = -430"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -732x - 472 = -430 $\n\nMove all terms to the left (standard form):\n$ -732x + -42 = 0 $\n\nIsolate the $x$ term:\n$ -732x = 42 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 4165
} |
[
{
"role": "user",
"content": "solve: 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}{2}) = 1.0472 $\n\nThe gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 4166
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&1\\\\\\-9&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}-80\\\\\\144\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&1\\\\\\-9... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4167
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&6\\\\\\8&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}62\\\\\\-55\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&6\\\\\\8&... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4168
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Differentiate with respect to $x$: $f(x) = (-1x + 6)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-1x + 6)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 4169
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute the determinant: $A=\\begin{pmatrix}9&-8\\\\1&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}9&-8\\\\\\1&8\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4170
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. -x + 83x^2 + 14 = -97"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -x + 83x^2 + 14 = -97 $\n\nMove all terms to the left (standard form):\n$ 83x^2 + -1x + 111 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4171
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Compute the indefinite integral: $\\int -7e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -7e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts ... | {
"type": "calculus",
"seed": 1337,
"index": 4172
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 4173
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Prove that $f(x,y)=\\frac12(9x^2+4y^2)+-4x+-6y+9$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+4y^2)+-4x+-6y+9 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 4174
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((18 + -299/13) * 3) + 6^2 - log_2(2) + (430 mod 11) + floor(167/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((18 + -299/13) * 3) + 6^2 - log_2(2) + (430 mod 11) + floor(167/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4175
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((-4 + 225/5) * 18) + 11^4 - log_10(100000) + (354 mod 11) + floor(52/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-4 + 225/5) * 18) + 11^4 - log_10(100000) + (354 mod 11) + floor... | {
"type": "arithmetic",
"seed": 1337,
"index": 4176
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Evaluate: ((-42 + -306/18) * 2) + 11^2 - log_3(9) + (-382 mod 7) + ceil(88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-42 + -306/18) * 2) + 11^2 - log_3(9) + (-382 mod 7) + ceil(88/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4177
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Find the modular inverse of 22 modulo 29, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $22\\cdot a^{-1} \\equiv 1 \\pmod{29}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identi... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4178
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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 $\n\nThe general so... | {
"type": "trigonometry",
"seed": 1337,
"index": 4179
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 37 + 134x - 39x^2 = 115"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 + 134x - 39x^2 = 115 $\n\nMove all terms to the left (standard form):\n$ -39x^2 + 134x + -78 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4180
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. 634x - 979 = -524"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 634x - 979 = -524 $\n\nMove all terms to the left (standard form):\n$ 634x + -455 = 0 $\n\nIsolate the $x$ term:\n$ 634x = 455 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 4181
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. -34x + 510 = -859"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -34x + 510 = -859 $\n\nMove all terms to the left (standard form):\n$ -34x + 1369 = 0 $\n\nIsolate the $x$ term:\n$ -34x = -1369 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4182
} |
[
{
"role": "user",
"content": "Compute the final answer to 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 4183
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&8\\\\\\3&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-16\\\\\\52\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&8\\\\\\3&4\\end{pmatri... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4184
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Prove that $f(x,y)=\\frac12(5x^2+10y^2)+1x+-4y+-8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+10y^2)+1x+-4y+-8 $\n\n$ \\frac{\\partial^2 f}{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 4185
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha =... | {
"type": "trigonometry",
"seed": 1337,
"index": 4186
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. -16 + 8x^2 - 196 = -9x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -16 + 8x^2 - 196 = -9x $\n\nMove all terms to the left (standard form):\n$ 8x^2 + 9x + -212 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4187
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. -4x^2 + 172x + 200 = 121"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4x^2 + 172x + 200 = 121 $\n\nMove all terms to the left (standard form):\n$ -4x^2 + 172x + 79 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4188
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((182 + -28/7) * 10) + 9^4 - log_6(1296) + (361 mod 3) + ceil(151/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((182 + -28/7) * 10) + 9^4 - log_6(1296) + (361 mod 3) + ceil(151/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 4189
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 748 + 949x = -629"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 748 + 949x = -629 $\n\nMove all terms to the left (standard form):\n$ 949x + 1377 = 0 $\n\nIsolate the $x$ term:\n$ 949x = -1377 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 4190
} |
[
{
"role": "user",
"content": "Can you compute this equation? Compute the indefinite integral: $\\int \\ln(8x + -8)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + -8)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$... | {
"type": "calculus",
"seed": 1337,
"index": 4191
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Differentiate with respect to $x$: $f(x) = -9e^{-1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9e^{-1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{9e^{-1x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 4192
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute $(-125+-23) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-125+-23) \\bmod 8 $\n\nUse the rule that addition is compatible with reduction mo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4193
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -294 - 234x = -891"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -294 - 234x = -891 $\n\nMove all terms to the left (standard form):\n$ -234x + 597 = 0 $\n\nIsolate the $x$ term:\n$ -234x = -597 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4194
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-4&-6\\\\1&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -4 & -6 \\\\ 1 & -3 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4195
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((42 + -968/22) * 13) + 5^3 - log_6(1296) + (279 mod 2) + ceil(142/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((42 + -968/22) * 13) + 5^3 - log_6(1296) + (279 mod 2) + ceil(142/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 4196
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-1&2\\\\1&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -1 & 2 \\\\ 1 & 7 \\end{pmatrix} $\n\nCompute the determ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4197
} |
[
{
"role": "user",
"content": "Please determine the outcome of this 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 $a,b\\in\\mat... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4198
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 578 + 709x = 269"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 578 + 709x = 269 $\n\nMove all terms to the left (standard form):\n$ 709x + 309 = 0 $\n\nIsolate the $x$ term:\n$ 709x = -309 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4199
} |
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