Calc help

[math magic]

Hi I need help with the following questions. if you could help it would be greatly appreciated. Even if you could just get me started it would be great as that's where I'm stuck.

A TV camera is located on thr ground 15 kms from the point where a spacecraft is launched vertically. At what rate is the distance from the camera to the spacecraft increasing when the spacecraft is 12 kms high and rising at the rate of 3 kms per sec.

The region between the graph of y=e^x, the lines x=0 and x=2 and the x axis is rotated through one revolution about the x axis. Show that the exact volume of the solid formed is pi/2(e^4 -1) cubic units.

Find the antiderivative between e^2 and e of dx/(xsqrt(ln(x))) given x > 1. Us the substitution w=ln (x)

Find dy/dx if y^3 x^2 - 2x^3 = 4y

[MaximilianMayrhofer]

Q: A TV camera is located on thr ground 15 kms from the point where a spacecraft is launched vertically. At what rate is the distance from the camera to the spacecraft increasing when the spacecraft is 12 kms high and rising at the rate of 3 kms per sec.

A:

Q: The region between the graph of y=e^x, the lines x=0 and x=2 and the x axis is rotated through one revolution about the x axis. Show that the exact volume of the solid formed is pi/2(e^4 -1) cubic units.

A:

Q: Find dy/dx if y^3 x^2 - 2x^3 = 4y

A:

Q: Find the antiderivative between e^2 and e of dx/(xsqrt(ln(x))) given x > 1. Us the substitution w=ln (x)

A: