Q29 (10 points)
Determine the value of the parameter $k$ for which the work done by the force
$\vec{F} = \begin{pmatrix} x^2 - xy \ y^2 - x^2 \end{pmatrix}$
along the parabolic arc $y^2 = 2kx$ connecting the origin with $(k/2, k)$ is 9/5.
Q30 (12 points)
Consider the astroid curve $x = cos^3(t)$, $y = sin^3(t)$ for $t \in [0, 2\pi]$.
1. Find the slope of tangent line to the asteroid curve in terms of the parameter $t$. Determine the points having
vertical tangents and those having horizontal tangents.
2. Compute the length of the curve.