conversations listlengths 2 2 |
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[
{
"from": "human",
"value": "The snow pile began to melt at 8 am and continued to melt at a constant rate. At 12 pm there were 28 inches left, at 2 pm there were 23 inches left, and at 4 pm there was nothing left.\n\nAt what time did the snow pile begin to melt?\n\nExpress your answer in the format of \"X:Y... |
[
{
"from": "human",
"value": "The area of the region bounded by the curve $y=f(x)$, the $x$-axis, and the vertical lines $x=4$ and $x=6$ is equal to 2 square units. If $f(x) = \\frac{x^2}{Ax^2 + Bx + C}$, where $A,B,$ and $C$ are integers, then find $A+B+C$."
},
{
"from": "gpt",
"value": "<think>... |
[
{
"from": "human",
"value": "Identify all isomers of CH\\(_3\\)CH\\(_2\\)CH\\(_2\\)OH."
},
{
"from": "gpt",
"value": "<think> Okay, so I need to identify all the isomers of CH3CH2CH2OH. Hmm, let me start by writing down the molecular formula for this compound. The given structure is CH3CH2CH2OH,... |
[
{
"from": "human",
"value": "There are two kinds of positions on a cyclohexane ring. Six axial hydrogens are perpendicular to the plane of the ring, while six equatorial hydrogens are roughly in the plane of the ring. Each carbon has one axial hydrogen and one equatorial hydrogen, and all hydrogens on the s... |
[
{
"from": "human",
"value": "Given on the moon (or other place with 1/6th the gravity of the earth, though let's use the moon to keep this anchored in a real scenario) a \"flying room\" within which to fly, such as a large enough dome or underground space, and filled with your choice of gas (O2 for breathin... |
[{"from":"human","value":"Find all $\\theta \\in [0, \\frac{\\pi}{2}]$ for which\n\\[\\cos(x+\\theta(...TRUNCATED) |
[{"from":"human","value":"Two of the altitudes of an acute triangle divide the sides into segments o(...TRUNCATED) |
[{"from":"human","value":"Determine the number of 6-digit positive integers whose digits contain exa(...TRUNCATED) |
[{"from":"human","value":"Let $f(z) = z^2 - 4z + 5$. Find the number of values of $z$ satisfying bot(...TRUNCATED) |
[{"from":"human","value":"Related: Ellipse circumference\nIntroduction\nAn ellipsoid (Wikipedia / Ma(...TRUNCATED) |
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