conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "In a triangle $ABC$, the angle bisector $\\overline{AT}$ intersects the opposite side $\\overline{BC}$ at $T$. The points $D$ and $E$ are on $\\overline{AB}$ and $\\overline{AC}$, respectively, such that $\\angle EAD = \\angle BAC$. If $BT = 2$, $CT = 3$, and $DE = 4$, compute... |
[
{
"from": "human",
"value": "I am reading following research paper - Feynman propagator in curved spacetime: A momentum-space representation. In page 2, Eq.2.8 and later they solve following differential equation for propagator (the equation is in Riemann-normal coordinates) - \n$$\\eta^{\\mu \\nu}\\partial... |
[
{
"from": "human",
"value": "Given that $x+\\sin y=2008$ and $x+2008 \\cos y=2007$, where $0 \\leq y \\leq \\frac{\\pi}{2}$, find the value of $x+y$.\n\nLet's try to create a new problem that requires a different approach.\n\nGiven that $x+\\sin y=2008$ and $x+2008 \\cos y=2007$, where $0 \\leq y \\leq \\fr... |
[
{
"from": "human",
"value": "Given a convex hexagon $ABCDEF$ with angles $\\angle A = \\angle B = 120^\\circ$ and side lengths $AB = BC = CD = EF = FA = 3$, find the maximum area of the hexagon if points $D$ and $E$ lie on a circle centered at point $C$."
},
{
"from": "gpt",
"value": "<think> Ok... |
[{"from":"human","value":"Quadrilateral $EFGH$ is a rectangle with $EG = 3$ cm and $EF = 4$ cm. Two (...TRUNCATED) |
[{"from":"human","value":"Given $\\alpha(x) = 2x^2 + 5x - 3$ and $\\beta(x) = x^2 - 2x - 6$, find $x(...TRUNCATED) |
[{"from":"human","value":"\\( \\Delta H_f^\\circ \\) for \\(\\text{CO}_2(g)\\) and \\(\\text{H}_2\\t(...TRUNCATED) |
[{"from":"human","value":"When this question was posted, it was caird coinheringaahing's birthday! ((...TRUNCATED) |
[{"from":"human","value":"In triangle $PQR$, $PQ=PR$ and $S$ is a point on $\\overline{PR}$ so that (...TRUNCATED) |
[{"from":"human","value":"Let $P(x)$ be a polynomial of degree $4$ such that the remainder when $P(x(...TRUNCATED) |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 40