Two Calculus problems I need help with!?

1)
V = x^3
dV/dt = dV/dx * dx/dt (chain rule)
= 3x^2 * (-4)
= -12x^2 cubic inch(es)/hour

When each edge is 5 inches long,
-12(5)^2
= -300 cubic inches/hour, meaning that the volume is decreasing by 300 cubic inches per hour.

2)
Let x, y and z, respectively, be the distance between the pad and the station, the rocket and the pad, and the rocket and the station.

x^2 + y^2 = z^2 (Pythagorean theorem)
9 + y^2 = z^2
d(y^2)/dt = d(z^2)/dt
2y * dy/dt = 2z * dz/dt (chain rule)
dz/dt = 2y/z mile(s)/second

When the rocket is 4 miles up, and the distance between the rocket and the station is 5 miles,
The distance between the rocket and the station is increasing by
2 * 4/5 = 8/5 = 1.6 miles/second.

a million. it would want to in straightforward words have a vertical asymtote if the denominator is 0. b + a sin x = 0 ultimately leads to what value for sin x? Why is this not plausible? 2. For it to be a rectangle the bottom vertices may properly be symmetrically both fringe of the initiating. consequently the bottom length is 2x. a. A = 2x*y = 2x*e^(-x^2) b. Differentiate A = 2x*e^(-x^2) to get dA/dx utilizing the product and chain guidelines. treatment the equation dA/dx = 0 to discover x values. From this come around the truly section. the position plausible I opt to provide tricks truly than purely do it inquisitive about you. i desire that no man or woman factors the entire concepts yet as well attempt to end them your self first.

1. If the edges have length x inches and the volume is v inches^3 then
v=x^3 so dv/dt = (dv/dx)(dx/dt)=3x^2dx/dt. Given that dx/dt=-4 and x=5
you can now find dv/dt.

2. When the rocket R has moved y miles its distance from the
launching pad L is y. The distance from The radar station S to R is z
when angle SRL=Θ. dy/dt = 2 mps .
When y=4 from triangle RSL SR=5 and cosΘ=4/5.
dz/dt = dy/dt(cosΘ)=2(4/5)=1.6 miles per second.
Your 5 miles is the distance from S to R.
You can get dz/dt using z=√(y^2+9) and dz/dt=(dz/dy)(dy/dt)
=[y/√(y^2+9)]dy/dt and sub y=4, dy/dt=2