Ok i have 2 problems that i am stuck on. Please show me how to work this out as compared to simply posting the answer, thanks.
1. A light is affixed to the top of a 12 foot tall lamp-post. A 6 foot tall man walks away from the lamp post at a rate of 5 ft/sec. How fast i the length of his shadow increasing when he is 5 feet away?
Work so far: I set ds/dt as 5 ft/s because it is the rate of change. I am thinking that to solve this i should break it down into two triangles but i am lost as to how i can do that because i have no idea how to get the current distance of his shadow.
2. A water tank has the shape of an inverted right circular cone of altitude 12 feet and base radius 6 feet. If water is being pumped into the tank at a rate of 10 gal/min, at what rate is the water level rising when the water is 3 feet deep?
Work so far: Again i set dh/dt at 10 gal/min. I believe i should use (πr^2h)/3 but i have no idea what to sub in for R or H and how to solve it.
Update: For number 2 i believe dv/dt is 45π/2, i came to this conclusion by solving for V=(1/3)π(6h/12)^2(h), however i am not sure if this is correct
Any help anyone can provide is greatly appreciated, thanks