I have 4 problems. I have literally spent 5-6 hours on this, asked a Calculus III student for help, etc. I cannot get these answers or even get close to them.
Obviously, I'm in a need of a lot of help, which any is appreciated. I legitimately tried this, I'm not looking for an easy way out, but I do need to get solutions to them in order to understand them by tomorrow morning
1) Water is flowing at a rate of 6 m^3/min from a reservoir shaped like a hemispherical bowl of radius 13 m, shown here in profile. Answer the following questions, given that the volume of water in a hemispherical bowl of radius are is V=(Pi/3)y^2(3R-y) when the water is Y meters deep
a) At what rate is the water level changing when the water is 8 meters deep?
b) What is the radius r of the water's surface when the water is y meters deep?
c) At what rate is the radius r changing when the water is 8 meters deep?
**Answers from Book**
b)Square Root of 26y - y^2
2) A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec. Just when the balloon is 65 feet about the ground, a bicycle moving at a constant rate of 17 ft/sec passes under it. How fast is the distance s(t) between the bicycle and the balloon increasing 3 sec later?
**Answer from Book**
3) Coffee is draining from a conical filter nto a cylindrical coffee pot at the rate of 10 in^3/min.
a) How fast is the level in the pot rising when the coffee in the cone is 5 inches deep?
b) How hast is the level in the cone falling then?
[A diagram on the page shows the height and diameter of the cone is 6 inches; diameter of pot is also 6 inches]
4) You are videotaping a race from a stand 123 feet away from the track, following a car that is moviing at 180 mi/h (264 ft/sec). How fast will your camera angle theta be changing when the car is right in fron of you? A half second later?
Like I said, I really did try and try to get help, but my Calculus III buddy and I could not figure this out. I really am in some need of help.
Huge thanks to anyone in advance for any help