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An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis 50, and minor axis 40. The hyperbola has conjugate axis of length 20. Let $P$ be a point on both the hyperbola and ellipse. What is $PA \c...

A skier traveling at 26.2 m/s encounters a 23 degree slope. (a)If you could ignore friction, to the nearest meter, how far up the hill does he go? (b)If the coefficient of kinetic friction in the previous problem was actually 0.11 and the slope 30 degrees...

Let $x$, $y$, and $z$ be positive real numbers that satisfy \[2 \log_x (2y) = 2 \log_{2x} (4z) = \log_{2x^4} (8yz) \neq 0.\] The value of $xy^5 z$ can be expressed in the form $\frac{1}{2^{p/q}}$, where $p$ and $q$ are relatively prime positive integers....

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