Calculate the second derivative $\frac{d^{2}y}{d{x}^2}$ for the plane curve defined by the equations $x(t)=t^2-4t$ and $y(t)=2t^3-6t$ with $-2t3.$

A plane is to fly directly from an airport at the origin in the direction of the point $(1,1,1)$ at a speed of $115f\frac{t}{sec}.$ What is the position of the plane after $15$ secs$?$

Evaluate the triple integral ${\displaystyle \underset{0}{\overset{1}{}}}{\displaystyle \underset{x}{\overset{2x}{}}}{\displaystyle \underset{0}{\overset{xy}{}}}2xydzdydx.$