data_source stringclasses 1
value | answer stringlengths 1 204 | source_dataset stringclasses 4
values | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|---|
numina_math | -\sin(3t)/5+C_{1}\sin(2t)+C_{2}\cos(2t) | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: The following subproblems refer to the differential equation. $\\ddot{x}+4 x=\\sin (3 t)$\n\nSubproblem 0: Find $A$ so that $A \\sin (3 t)$ is a solution of $\\ddot{x}+... | math | {
"ground_truth": "-\\sin(3t)/5+C_{1}\\sin(2t)+C_{2}\\cos(2t)",
"style": "rule"
} | {
"index": 600,
"split": "test"
} |
numina_math | \frac{\pi}{2} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest possible positive $k$ such that all functions $x(t)=A \\cos (\\omega t-\\phi)$---where $\\phi$ is an odd multiple of $k$---satisfy $x(0)=0$? \\\\ Let's think... | math | {
"ground_truth": "\\frac{\\pi}{2}",
"style": "rule"
} | {
"index": 601,
"split": "test"
} |
numina_math | s^{2}+bs+1 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: The following subproblems refer to the differential equation $\\ddot{x}+b \\dot{x}+x=0$.\\\\\n\nWhat is the characteristic polynomial $p(s)$ of $\\ddot{x}+b \\dot{x}+x=... | math | {
"ground_truth": "s^{2}+bs+1",
"style": "rule"
} | {
"index": 602,
"split": "test"
} |
numina_math | \frac{37}{4}m | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: The following subproblems refer to the exponential function $e^{-t / 2} \\cos (3 t)$, which we will assume is a solution of the differential equation $m \\ddot{x}+b \\d... | math | {
"ground_truth": "\\frac{37}{4}m",
"style": "rule"
} | {
"index": 603,
"split": "test"
} |
numina_math | -8-8\sqrt{3}i | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: In the following problems, take $a = \\ln 2$ and $b = \\pi / 3$. \n\nSubproblem 0: Given $a = \\ln 2$ and $b = \\pi / 3$, rewrite $e^{a+b i}$ in the form $x + yi$, wher... | math | {
"ground_truth": "-8-8\\sqrt{3}i",
"style": "rule"
} | {
"index": 604,
"split": "test"
} |
numina_math | \frac{\sqrt{2}}{4}\cos(t-\pi/4) | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rewrite the function $\\operatorname{Re} \\frac{e^{i t}}{2+2 i}$ in the form $A \\cos (\\omega t-\\phi)$. It may help to begin by drawing a right triangle with sides $a$ and $b$.... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{4}\\cos(t-\\pi/4)",
"style": "rule"
} | {
"index": 605,
"split": "test"
} |
numina_math | 2 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: The following subproblems refer to the differential equation $\\ddot{x}+b \\dot{x}+x=0$.\\\\\n\nSubproblem 0: What is the characteristic polynomial $p(s)$ of $\\ddot{x}... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 606,
"split": "test"
} |
numina_math | \frac{e^{2it}}{(2+2i)}+Ce^{-2t} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the general (complex-valued) solution of the differential equation $\\dot{z}+2 z=e^{2 i t}$, using $C$ to stand for any complex-valued integration constants which may arise.... | math | {
"ground_truth": "\\frac{e^{2it}}{(2+2i)}+Ce^{-2t}",
"style": "rule"
} | {
"index": 607,
"split": "test"
} |
numina_math | -\tau\ln\Delta | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Consider the first-order system\n\\[\n\\tau \\dot{y}+y=u\n\\]\ndriven with a unit step from zero initial conditions. The input to this system is \\(u\\) and the output ... | math | {
"ground_truth": "-\\tau\\ln\\Delta",
"style": "rule"
} | {
"index": 608,
"split": "test"
} |
numina_math | 2.2\tau | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Consider the first-order system\n\\[\n\\tau \\dot{y}+y=u\n\\]\ndriven with a unit step from zero initial conditions. The input to this system is \\(u\\) and the output ... | math | {
"ground_truth": "2.2\\tau",
"style": "rule"
} | {
"index": 609,
"split": "test"
} |
numina_math | \frac{1}{s+a} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For each of the functions $y(t)$, find the Laplace Transform $Y(s)$ :\n\n$y(t)=e^{-a t}$ Let's think step by step and output the final answer within \\boxed{}.",
"r... | math | {
"ground_truth": "\\frac{1}{s+a}",
"style": "rule"
} | {
"index": 610,
"split": "test"
} |
numina_math | \omega_{n}^{2}e^{-\zeta\omega_{n}t}\cos(\omega_{n}\sqrt{1-\zeta^{2}}t)-\frac{\zeta\omega_{n}^{2}}{\sqrt{1-\zeta^{2}}}e^{-\zeta\omega_{n}t}\sin(\omega_{n}\sqrt{1-\zeta^{2}}t) | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For each Laplace Transform \\(Y(s)\\), find the function \\(y(t)\\) :\n\nSubproblem 0: \\[\nY(s)=\\boxed{\\frac{1}{(s+a)(s+b)}}\n\\]\n\n\nSolution: We can simplify with... | math | {
"ground_truth": "\\omega_{n}^{2}e^{-\\zeta\\omega_{n}t}\\cos(\\omega_{n}\\sqrt{1-\\zeta^{2}}t)-\\frac{\\zeta\\omega_{n}^{2}}{\\sqrt{1-\\zeta^{2}}}e^{-\\zeta\\omega_{n}t}\\sin(\\omega_{n}\\sqrt{1-\\zeta^{2}}t)",
"style": "rule"
} | {
"index": 611,
"split": "test"
} |
numina_math | \frac{1}{s+1}-\frac{e^{-1}}{s}-\frac{e^{-1}e^{-s}}{s+1}+\frac{e^{-1}e^{-s}}{s} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A signal \\(x(t)\\) is given by\n\\[\nx(t)=\\left(e^{-t}-e^{-1}\\right)\\left(u_{s}(t)-u_{s}(t-1)\\right)\n\\]\nCalculate its Laplace transform \\(X(s)\\). Make sure to clearly s... | math | {
"ground_truth": "\\frac{1}{s+1}-\\frac{e^{-1}}{s}-\\frac{e^{-1}e^{-s}}{s+1}+\\frac{e^{-1}e^{-s}}{s}",
"style": "rule"
} | {
"index": 612,
"split": "test"
} |
numina_math | 20 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: You are given an equation of motion of the form:\n\\[\n\\dot{y}+5 y=10 u\n\\]\n\nSubproblem 0: What is the time constant for this system?\n\n\nSolution: We find the hom... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 613,
"split": "test"
} |
numina_math | \frac{1}{s}-\frac{1}{s}e^{-sT} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A signal \\(w(t)\\) is defined as\n\\[\nw(t)=u_{s}(t)-u_{s}(t-T)\n\\]\nwhere \\(T\\) is a fixed time in seconds and \\(u_{s}(t)\\) is the unit step. Compute the Laplace transform... | math | {
"ground_truth": "\\frac{1}{s}-\\frac{1}{s}e^{-sT}",
"style": "rule"
} | {
"index": 614,
"split": "test"
} |
numina_math | \frac{1}{m}t | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Assume that we apply a unit step in force separately to a mass \\(m\\), a dashpot \\(c\\), and a spring \\(k\\). The mass moves in inertial space. The spring and dashpo... | math | {
"ground_truth": "\\frac{1}{m}t",
"style": "rule"
} | {
"index": 615,
"split": "test"
} |
numina_math | \frac{s+\sigma}{(s+\sigma)^{2}+\omega_{d}^{2}} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For each of the functions $y(t)$, find the Laplace Transform $Y(s)$ :\n\nSubproblem 0: $y(t)=e^{-a t}$\n\n\nSolution: This function is one of the most widely used in dy... | math | {
"ground_truth": "\\frac{s+\\sigma}{(s+\\sigma)^{2}+\\omega_{d}^{2}}",
"style": "rule"
} | {
"index": 616,
"split": "test"
} |
numina_math | \frac{\omega_{d}}{(s+\sigma)^{2}+\omega_{d}^{2}} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For each of the functions $y(t)$, find the Laplace Transform $Y(s)$ :\n\nSubproblem 0: $y(t)=e^{-a t}$\n\n\nSolution: This function is one of the most widely used in dy... | math | {
"ground_truth": "\\frac{\\omega_{d}}{(s+\\sigma)^{2}+\\omega_{d}^{2}}",
"style": "rule"
} | {
"index": 617,
"split": "test"
} |
numina_math | m\frac{dv}{dt}+bv=f | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Consider the mass \\(m\\) sliding horizontally under the influence of the applied force \\(f\\) and a friction force which can be approximated by a linear friction elem... | math | {
"ground_truth": "m\\frac{dv}{dt}+bv=f",
"style": "rule"
} | {
"index": 618,
"split": "test"
} |
numina_math | 1000 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Consider the rotor with moment of inertia \\(I\\) rotating under the influence of an applied torque \\(T\\) and the frictional torques from two bearings, each of which ... | math | {
"ground_truth": "1000",
"style": "rule"
} | {
"index": 619,
"split": "test"
} |
numina_math | 0.10 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Consider the mass \\(m\\) sliding horizontally under the influence of the applied force \\(f\\) and a friction force which can be approximated by a linear friction elem... | math | {
"ground_truth": "0.10",
"style": "rule"
} | {
"index": 620,
"split": "test"
} |
numina_math | (1-3e^{-2t}+2e^{-5t})u(t) | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Obtain the inverse Laplace transform of the following frequency-domain expression: $F(s) = -\\frac{(4 s-10)}{s(s+2)(s+5)}$.\nUse $u(t)$ to denote the unit step function. Let's th... | math | {
"ground_truth": "(1-3e^{-2t}+2e^{-5t})u(t)",
"style": "rule"
} | {
"index": 621,
"split": "test"
} |
numina_math | b\delta(t)+1-e^{-at} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A signal has a Laplace transform\n\\[\nX(s)=b+\\frac{a}{s(s+a)}\n\\]\nwhere \\(a, b>0\\), and with a region of convergence of \\(|s|>0\\). Find \\(x(t), t>0\\). Let's think step ... | math | {
"ground_truth": "b\\delta(t)+1-e^{-at}",
"style": "rule"
} | {
"index": 622,
"split": "test"
} |
numina_math | \frac{1}{b-a}(e^{-at}-e^{-bt}) | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For each Laplace Transform \\(Y(s)\\), find the function \\(y(t)\\) :\n\n\\[\nY(s)=\\boxed{\\frac{1}{(s+a)(s+b)}}\n\\] Let's think step by step and output the final ans... | math | {
"ground_truth": "\\frac{1}{b-a}(e^{-at}-e^{-bt})",
"style": "rule"
} | {
"index": 623,
"split": "test"
} |
numina_math | I\frac{d\omega}{dt}+2B\omega=T | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Consider the rotor with moment of inertia \\(I\\) rotating under the influence of an applied torque \\(T\\) and the frictional torques from two bearings, each of which ... | math | {
"ground_truth": "I\\frac{d\\omega}{dt}+2B\\omega=T",
"style": "rule"
} | {
"index": 624,
"split": "test"
} |
numina_math | (t+\frac{1}{2}\sin{2t})u(t) | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Obtain the inverse Laplace transform of the following frequency-domain expression: $F(s) = \\frac{4}{s^2(s^2+4)}$.\nUse $u(t)$ to denote the unit step function. Let's think step ... | math | {
"ground_truth": "(t+\\frac{1}{2}\\sin{2t})u(t)",
"style": "rule"
} | {
"index": 625,
"split": "test"
} |
numina_math | \frac{1}{LCs^{2}+RCs+1} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: This problem considers the simple RLC circuit, in which a voltage source $v_{i}$ is in series with a resistor $R$, inductor $L$, and capacitor $C$. We measure the volt... | math | {
"ground_truth": "\\frac{1}{LCs^{2}+RCs+1}",
"style": "rule"
} | {
"index": 626,
"split": "test"
} |
numina_math | 0.2 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: You are given an equation of motion of the form:\n\\[\n\\dot{y}+5 y=10 u\n\\]\n\nWhat is the time constant for this system? Let's think step by step and output the fina... | math | {
"ground_truth": "0.2",
"style": "rule"
} | {
"index": 627,
"split": "test"
} |
numina_math | 1e-8 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: This problem considers the simple RLC circuit, in which a voltage source $v_{i}$ is in series with a resistor $R$, inductor $L$, and capacitor $C$. We measure the volt... | math | {
"ground_truth": "1e-8",
"style": "rule"
} | {
"index": 628,
"split": "test"
} |
numina_math | 100 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Here we consider a system described by the differential equation\n\\[\n\\ddot{y}+10 \\dot{y}+10000 y=0 .\n\\]\n\nWhat is the value of the natural frequency \\(\\omega_{... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"index": 629,
"split": "test"
} |
numina_math | \frac{d^{2}v_{o}}{dt^{2}}+\frac{v_{o}}{LC}=\frac{v_{i}}{LC} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Consider a circuit in which a voltage source of voltage in $v_{i}(t)$ is connected in series with an inductor $L$ and capacitor $C$. We consider the voltage across the... | math | {
"ground_truth": "\\frac{d^{2}v_{o}}{dt^{2}}+\\frac{v_{o}}{LC}=\\frac{v_{i}}{LC}",
"style": "rule"
} | {
"index": 630,
"split": "test"
} |
numina_math | ml\ddot{\theta}(t)-mg\sin\theta(t)=f(t)\cos\theta(t) | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Write (but don't solve) the equation of motion for a pendulum consisting of a mass $m$ attached to a rigid massless rod, suspended from the ceiling and free to rotate in a single... | math | {
"ground_truth": "ml\\ddot{\\theta}(t)-mg\\sin\\theta(t)=f(t)\\cos\\theta(t)",
"style": "rule"
} | {
"index": 631,
"split": "test"
} |
numina_math | 99.9 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Here we consider a system described by the differential equation\n\\[\n\\ddot{y}+10 \\dot{y}+10000 y=0 .\n\\]\n\nSubproblem 0: What is the value of the natural frequenc... | math | {
"ground_truth": "99.9",
"style": "rule"
} | {
"index": 632,
"split": "test"
} |
numina_math | 0.05 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Here we consider a system described by the differential equation\n\\[\n\\ddot{y}+10 \\dot{y}+10000 y=0 .\n\\]\n\nSubproblem 0: What is the value of the natural frequenc... | math | {
"ground_truth": "0.05",
"style": "rule"
} | {
"index": 633,
"split": "test"
} |
numina_math | 3e8 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the speed of light in meters/second to 1 significant figure? Use the format $a \\times 10^{b}$ where a and b are numbers. Let's think step by step and output the final an... | math | {
"ground_truth": "3e8",
"style": "rule"
} | {
"index": 634,
"split": "test"
} |
numina_math | 1e11 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Give each of the following quantities to the nearest power of 10 and in the units requested. \n\nSubproblem 0: Age of our universe when most He nuclei were formed in mi... | math | {
"ground_truth": "1e11",
"style": "rule"
} | {
"index": 635,
"split": "test"
} |
numina_math | \frac{1}{\sqrt{2}}c | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: In a parallel universe, the Boston baseball team made the playoffs.\n\nManny Relativirez hits the ball and starts running towards first base at speed $\\beta$. How fast... | math | {
"ground_truth": "\\frac{1}{\\sqrt{2}}c",
"style": "rule"
} | {
"index": 636,
"split": "test"
} |
numina_math | m_{p}c^{2}(\gamma^{2}-1)\sin^{2}\theta | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: In the Sun, one of the processes in the He fusion chain is $p+p+e^{-} \\rightarrow d+\\nu$, where $d$ is a deuteron. Make the approximations that the deuteron rest mass... | math | {
"ground_truth": "m_{p}c^{2}(\\gamma^{2}-1)\\sin^{2}\\theta",
"style": "rule"
} | {
"index": 637,
"split": "test"
} |
numina_math | \lambda_{{red}}/\sqrt{2} | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: In a parallel universe, the Boston baseball team made the playoffs.\n\nSubproblem 0: Manny Relativirez hits the ball and starts running towards first base at speed $\\b... | math | {
"ground_truth": "\\lambda_{{red}}/\\sqrt{2}",
"style": "rule"
} | {
"index": 638,
"split": "test"
} |
numina_math | 10 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Give each of the following quantities to the nearest power of 10 and in the units requested. \n\nSubproblem 0: Age of our universe when most He nuclei were formed in mi... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 639,
"split": "test"
} |
numina_math | 5 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many down quarks does a tritium ($H^3$) nucleus contain? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 640,
"split": "test"
} |
numina_math | 4 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many up quarks does a tritium ($H^3$) nucleus contain? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 641,
"split": "test"
} |
numina_math | 1 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Give each of the following quantities to the nearest power of 10 and in the units requested. \n\nAge of our universe when most He nuclei were formed in minutes: Let's t... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 642,
"split": "test"
} |
numina_math | 8 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Give each of the following quantities to the nearest power of 10 and in the units requested. \n\nSubproblem 0: Age of our universe when most He nuclei were formed in mi... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 643,
"split": "test"
} |
numina_math | 400000 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Give each of the following quantities to the nearest power of 10 and in the units requested. \n\nSubproblem 0: Age of our universe when most He nuclei were formed in mi... | math | {
"ground_truth": "400000",
"style": "rule"
} | {
"index": 644,
"split": "test"
} |
numina_math | 560 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Potassium metal can be used as the active surface in a photodiode because electrons are relatively easily removed from a potassium surface. The energy needed is $2.15 \\times 10^... | math | {
"ground_truth": "560",
"style": "rule"
} | {
"index": 645,
"split": "test"
} |
numina_math | 671.02 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For red light of wavelength $(\\lambda) 6.7102 \\times 10^{-5} cm$, emitted by excited lithium atoms, calculate:\n\nSubproblem 0: the frequency $(v)$ in Hz, to 4 decima... | math | {
"ground_truth": "671.02",
"style": "rule"
} | {
"index": 646,
"split": "test"
} |
numina_math | +2 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the net charge of arginine in a solution of $\\mathrm{pH} \\mathrm{} 1.0$ ? Please format your answer as +n or -n. Let's think step by step and output the final answer wi... | math | {
"ground_truth": "+2",
"style": "rule"
} | {
"index": 647,
"split": "test"
} |
numina_math | 1.4903e4 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For red light of wavelength $(\\lambda) 6.7102 \\times 10^{-5} cm$, emitted by excited lithium atoms, calculate:\n\nSubproblem 0: the frequency $(v)$ in Hz, to 4 decima... | math | {
"ground_truth": "1.4903e4",
"style": "rule"
} | {
"index": 648,
"split": "test"
} |
numina_math | 4.03188 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the atomic weight of ${He}^{++}$ in amu to 5 decimal places from the values of its constituents. Let's think step by step and output the final answer within \\boxed{}."... | math | {
"ground_truth": "4.03188",
"style": "rule"
} | {
"index": 649,
"split": "test"
} |
numina_math | 566 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Determine the following values from a standard radio dial. \n\nSubproblem 0: What is the minimum wavelength in m for broadcasts on the AM band? Format your answer as an... | math | {
"ground_truth": "566",
"style": "rule"
} | {
"index": 650,
"split": "test"
} |
numina_math | 4100 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the wavelength of radiation emitted by hydrogen atoms in angstroms upon electron transitions from $n=6$ to $n=2$. Let's think step by step and output the final answer w... | math | {
"ground_truth": "4100",
"style": "rule"
} | {
"index": 651,
"split": "test"
} |
numina_math | 2.78 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Determine the following values from a standard radio dial. \n\nSubproblem 0: What is the minimum wavelength in m for broadcasts on the AM band? Format your answer as an... | math | {
"ground_truth": "2.78",
"style": "rule"
} | {
"index": 652,
"split": "test"
} |
numina_math | 0.264 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the \"Bohr radius\" in angstroms to 3 decimal places for ${He}^{+}$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "0.264",
"style": "rule"
} | {
"index": 653,
"split": "test"
} |
numina_math | 4.4677 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For red light of wavelength $(\\lambda) 6.7102 \\times 10^{-5} cm$, emitted by excited lithium atoms, calculate:\n\nthe frequency $(v)$ in Hz, to 4 decimal places. Let'... | math | {
"ground_truth": "4.4677",
"style": "rule"
} | {
"index": 654,
"split": "test"
} |
numina_math | 1.77e-6 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Electromagnetic radiation of frequency $3.091 \\times 10^{14} \\mathrm{~Hz}$ illuminates a crystal of germanium (Ge). Calculate the wavelength of photoemission in meters generate... | math | {
"ground_truth": "1.77e-6",
"style": "rule"
} | {
"index": 655,
"split": "test"
} |
numina_math | 1.3 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the energy gap (in eV, to 1 decimal place) between the electronic states $n=3$ and $n=8$ in a hydrogen atom? Let's think step by step and output the final answer within \... | math | {
"ground_truth": "1.3",
"style": "rule"
} | {
"index": 656,
"split": "test"
} |
numina_math | 5.47e5 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine for hydrogen the velocity in m/s of an electron in an ${n}=4$ state. Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places. Let's think step by... | math | {
"ground_truth": "5.47e5",
"style": "rule"
} | {
"index": 657,
"split": "test"
} |
numina_math | 1.9 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: A pure crystalline material (no impurities or dopants are present) appears red in transmitted light.\n\nSubproblem 0: Is this material a conductor, semiconductor or ins... | math | {
"ground_truth": "1.9",
"style": "rule"
} | {
"index": 658,
"split": "test"
} |
numina_math | 13.1 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the minimum potential $(V)$ in volts (to 1 decimal place) which must be applied to a free electron so that it has enough energy to excite, upon impact, the electron in ... | math | {
"ground_truth": "13.1",
"style": "rule"
} | {
"index": 659,
"split": "test"
} |
numina_math | 4080 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For light with a wavelength $(\\lambda)$ of $408 \\mathrm{~nm}$ determine:\n\nSubproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \\times 10^x$, wh... | math | {
"ground_truth": "4080",
"style": "rule"
} | {
"index": 660,
"split": "test"
} |
numina_math | 1.22 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Reference the information below to solve the following problems. \n$\\begin{array}{llll}\\text { Element } & \\text { Ionization Potential } & \\text { Element } & \\t... | math | {
"ground_truth": "1.22",
"style": "rule"
} | {
"index": 661,
"split": "test"
} |
numina_math | 2.19e6 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Light of wavelength $\\lambda=4.28 \\times 10^{-7} {~m}$ interacts with a \"motionless\" hydrogen atom. During this interaction it transfers all its energy to the orbiting electr... | math | {
"ground_truth": "2.19e6",
"style": "rule"
} | {
"index": 662,
"split": "test"
} |
numina_math | 6.62 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the minimum potential in V (to 2 decimal places) that must be applied to an $\\alpha$-particle so that on interaction with a hydrogen atom, a ground state electron will... | math | {
"ground_truth": "6.62",
"style": "rule"
} | {
"index": 663,
"split": "test"
} |
numina_math | 0.822 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Reference the information below to solve the following problems. \n$\\begin{array}{llll}\\text { Element } & \\text { Ionization Potential } & \\text { Element } & \\t... | math | {
"ground_truth": "0.822",
"style": "rule"
} | {
"index": 664,
"split": "test"
} |
numina_math | 1.70e4 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For \"yellow radiation\" (frequency, $v,=5.09 \\times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:\n\nSubproblem 0: the wavelength $(\\lambda)$ in m. Pleas... | math | {
"ground_truth": "1.70e4",
"style": "rule"
} | {
"index": 665,
"split": "test"
} |
numina_math | 0.5 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Subproblem 0: In the balanced equation for the reaction between $\\mathrm{CO}$ and $\\mathrm{O}_{2}$ to form $\\mathrm{CO}_{2}$, what is the coefficient of $\\mathrm{CO}$?\n\n\nS... | math | {
"ground_truth": "0.5",
"style": "rule"
} | {
"index": 666,
"split": "test"
} |
numina_math | 35.06 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.\n\n$\\mathrm{NH}_{4} \\mathrm{OH}$ Let's think step by step and o... | math | {
"ground_truth": "35.06",
"style": "rule"
} | {
"index": 667,
"split": "test"
} |
numina_math | 1 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Subproblem 0: In the balanced equation for the reaction between $\\mathrm{CO}$ and $\\mathrm{O}_{2}$ to form $\\mathrm{CO}_{2}$, what is the coefficient of $\\mathrm{CO}$?\n\n\nS... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 668,
"split": "test"
} |
numina_math | 24.310 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Magnesium (Mg) has the following isotopic distribution:\n\\[\n\\begin{array}{ll}\n24_{\\mathrm{Mg}} & 23.985 \\mathrm{amu} \\text { at } 0.7870 \\text { fractional abundance } \\... | math | {
"ground_truth": "24.310",
"style": "rule"
} | {
"index": 669,
"split": "test"
} |
numina_math | 1.87e6 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Electrons are accelerated by a potential of 10 Volts.\n\nDetermine their velocity in m/s. Please format your answer as $n \\times 10^x$, where $n$ is to 2 decimal place... | math | {
"ground_truth": "1.87e6",
"style": "rule"
} | {
"index": 670,
"split": "test"
} |
numina_math | 4.45e15 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the frequency (in $s^{-1}$ of radiation capable of generating, in atomic hydrogen, free electrons which have a velocity of $1.3 \\times 10^{6} {~ms}^{-1}$. Please forma... | math | {
"ground_truth": "4.45e15",
"style": "rule"
} | {
"index": 671,
"split": "test"
} |
numina_math | 1 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the balanced equation for the reaction between $\\mathrm{CO}$ and $\\mathrm{O}_{2}$ to form $\\mathrm{CO}_{2}$, what is the coefficient of $\\mathrm{CO}$? Let's think step by ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 672,
"split": "test"
} |
numina_math | 3.89e-10 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Electrons are accelerated by a potential of 10 Volts.\n\nSubproblem 0: Determine their velocity in m/s. Please format your answer as $n \\times 10^x$, where $n$ is to 2... | math | {
"ground_truth": "3.89e-10",
"style": "rule"
} | {
"index": 673,
"split": "test"
} |
numina_math | 9e11 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: In all likelihood, the Soviet Union and the United States together in the past exploded about ten hydrogen devices underground per year.\n\nIf each explosion converted ... | math | {
"ground_truth": "9e11",
"style": "rule"
} | {
"index": 674,
"split": "test"
} |
numina_math | 46.08 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.\n\nSubproblem 0: $\\mathrm{NH}_{4} \\mathrm{OH}$\n\n\nSolution: $... | math | {
"ground_truth": "46.08",
"style": "rule"
} | {
"index": 675,
"split": "test"
} |
numina_math | 56 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Subproblem 0: In the balanced equation for the reaction between $\\mathrm{CO}$ and $\\mathrm{O}_{2}$ to form $\\mathrm{CO}_{2}$, what is the coefficient of $\\mathrm{CO}$?\n\n\nS... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"index": 676,
"split": "test"
} |
numina_math | 5.89e-7 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For \"yellow radiation\" (frequency, $v,=5.09 \\times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:\n\nthe wavelength $(\\lambda)$ in m. Please format your ... | math | {
"ground_truth": "5.89e-7",
"style": "rule"
} | {
"index": 677,
"split": "test"
} |
numina_math | 7.4e-12 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a proton which has been subjected to an accelerating potential (V) of 15 Volts, determine its deBroglie wavelength in m. Please format your answer as $n \\times 10^x$, where ... | math | {
"ground_truth": "7.4e-12",
"style": "rule"
} | {
"index": 678,
"split": "test"
} |
numina_math | 7.353e14 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For light with a wavelength $(\\lambda)$ of $408 \\mathrm{~nm}$ determine:\n\nthe frequency in $s^{-1}$. Please format your answer as $n \\times 10^x$, where $n$ is to ... | math | {
"ground_truth": "7.353e14",
"style": "rule"
} | {
"index": 679,
"split": "test"
} |
numina_math | 1.55 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine in units of eV (to 2 decimal places) the energy of a photon ( $h v)$ with the wavelength of $800$ nm. Let's think step by step and output the final answer within \\boxe... | math | {
"ground_truth": "1.55",
"style": "rule"
} | {
"index": 680,
"split": "test"
} |
numina_math | 1.39e9 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine for barium (Ba) the linear density of atoms along the $<110>$ directions, in atoms/m. Let's think step by step and output the final answer within \\boxed{}.",
"role... | math | {
"ground_truth": "1.39e9",
"style": "rule"
} | {
"index": 681,
"split": "test"
} |
numina_math | 9.35e5 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A photon with a wavelength $(\\lambda)$ of $3.091 \\times 10^{-7} {~m}$ strikes an atom of hydrogen. Determine the velocity in m/s of an electron ejected from the excited state, ... | math | {
"ground_truth": "9.35e5",
"style": "rule"
} | {
"index": 682,
"split": "test"
} |
numina_math | 3.61e-10 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For the element copper (Cu) determine:\n\nthe distance of second nearest neighbors (in meters). Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal ... | math | {
"ground_truth": "3.61e-10",
"style": "rule"
} | {
"index": 683,
"split": "test"
} |
numina_math | 5 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A line of the Lyman series of the spectrum of hydrogen has a wavelength of $9.50 \\times 10^{-8} {~m}$. What was the \"upper\" quantum state $\\left({n}_{{i}}\\right)$ involved i... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 684,
"split": "test"
} |
numina_math | 1.45e-5 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the diffusivity $\\mathrm{D}$ of lithium ( $\\mathrm{Li}$ ) in silicon (Si) at $1200^{\\circ} \\mathrm{C}$, knowing that $D_{1100^{\\circ} \\mathrm{C}}=10^{-5} \\mathrm... | math | {
"ground_truth": "1.45e-5",
"style": "rule"
} | {
"index": 685,
"split": "test"
} |
numina_math | 2.88e16 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "By planar diffusion of antimony (Sb) into p-type germanium (Ge), a p-n junction is obtained at a depth of $3 \\times 10^{-3} \\mathrm{~cm}$ below the surface. What is the donor c... | math | {
"ground_truth": "2.88e16",
"style": "rule"
} | {
"index": 686,
"split": "test"
} |
numina_math | 700 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: One mole of electromagnetic radiation (light, consisting of energy packages called photons) has an energy of $171 \\mathrm{~kJ} /$ mole photons.\n\nDetermine the wavele... | math | {
"ground_truth": "700",
"style": "rule"
} | {
"index": 687,
"split": "test"
} |
numina_math | 0.13 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Two lasers generate radiation of (1) $9.5 \\mu {m}$ and (2) $0.1 \\mu {m}$ respectively.\n\nDetermine the photon energy (in eV, to two decimal places) of the laser gene... | math | {
"ground_truth": "0.13",
"style": "rule"
} | {
"index": 688,
"split": "test"
} |
numina_math | 8.64 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At $100^{\\circ} \\mathrm{C}$ copper $(\\mathrm{Cu})$ has a lattice constant of $3.655 \\AA$. What is its density in $g/cm^3$ at this temperature? Please round your answer to 2 d... | math | {
"ground_truth": "8.64",
"style": "rule"
} | {
"index": 689,
"split": "test"
} |
numina_math | 1.39e-10 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the atomic (metallic) radius of Mo in meters. Do not give the value listed in the periodic table; calculate it from the fact that Mo's atomic weight is $=95.94 \\mathrm... | math | {
"ground_truth": "1.39e-10",
"style": "rule"
} | {
"index": 690,
"split": "test"
} |
numina_math | 188 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Determine the following values from a standard radio dial. \n\nWhat is the minimum wavelength in m for broadcasts on the AM band? Format your answer as an integer. Let'... | math | {
"ground_truth": "188",
"style": "rule"
} | {
"index": 691,
"split": "test"
} |
numina_math | 6 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a (111) plane in an FCC structure. How many different [110]-type directions lie in this (111) plane? Let's think step by step and output the final answer within \\boxed{... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 692,
"split": "test"
} |
numina_math | 7.26e6 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the velocity of an electron (in $\\mathrm{m} / \\mathrm{s}$ ) that has been subjected to an accelerating potential $V$ of 150 Volt. Please format your answer as $n \\ti... | math | {
"ground_truth": "7.26e6",
"style": "rule"
} | {
"index": 693,
"split": "test"
} |
numina_math | 28.71 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a diffractometer experiment a specimen of thorium (Th) is irradiated with tungsten (W) $L_{\\alpha}$ radiation. Calculate the angle, $\\theta$, of the $4^{\\text {th }}$ refle... | math | {
"ground_truth": "28.71",
"style": "rule"
} | {
"index": 694,
"split": "test"
} |
numina_math | 181.3 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A metal is found to have BCC structure, a lattice constant of $3.31 \\AA$, and a density of $16.6 \\mathrm{~g} / \\mathrm{cm}^{3}$. Determine the atomic weight of this element in... | math | {
"ground_truth": "181.3",
"style": "rule"
} | {
"index": 695,
"split": "test"
} |
numina_math | 1.24e-8 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: Iron $\\left(\\rho=7.86 \\mathrm{~g} / \\mathrm{cm}^{3}\\right.$ ) crystallizes in a BCC unit cell at room temperature.\n\nCalculate the radius in cm of an iron atom in... | math | {
"ground_truth": "1.24e-8",
"style": "rule"
} | {
"index": 696,
"split": "test"
} |
numina_math | 2.55e-10 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Preamble: For the element copper (Cu) determine:\n\nSubproblem 0: the distance of second nearest neighbors (in meters). Please format your answer as $n \\times 10^x$ where $n$ is... | math | {
"ground_truth": "2.55e-10",
"style": "rule"
} | {
"index": 697,
"split": "test"
} |
numina_math | 900 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubpr... | math | {
"ground_truth": "900",
"style": "rule"
} | {
"index": 698,
"split": "test"
} |
numina_math | 7.25e-11 | weqweasdas/minerva_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the wavelength of $\\lambda_{K_{\\alpha}}$ for molybdenum (Mo). Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places, in meters. Let's think s... | math | {
"ground_truth": "7.25e-11",
"style": "rule"
} | {
"index": 699,
"split": "test"
} |
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