#1

Subject:

Comments:
: : I have been working through my pages of homework and I have come across a few related rate problems that seem to have confused me. So I wanted to see if someone could help me with these. Thank you in advance. : : 1. Find the rate of change of the distance between the origin and a moving point on the graph of y=sin(x) if dx/dt=2 centimeters per second. : : I figured you had to use the distance formula from here but I am not sure at how to. : I don't think you can get a numerical solution to this without also knowing x. Given only dx/dt you can get the answer in terms of x. : Call the distance you are looking for s. You can find s in terms of x, and then relate ds/dt to dx/dt using: : ds/dt = ds/dx * dx/dt : Pythagoras tells you that : s = (x^2 + sin^2(x))^(1/2) : so ds/dx = (x + sin(x)cos(x))/((x^2 + sin^2(x))^(1/2)) : and ds/dt is 2 times that. : : 2. The radius r of a sphere is increasing at a rate of 2 inches per minutes. Find the rate of change of the volume when r=6 inches and r=24 inches. : : I worked it out and I recieved a hilatious answer. For r=6 inches I got 288(pi) and for r=24 I got 4608(pi). Here is my work. I differentiated the volume for a sphere and got dv/dt=4(pi)r^2(dr/dt) and then pluged in the numbers 4(pi)6^2(2)=dv/dt=288(pi)and 4(pi)24^2(2)=dv/dt=4608(pi). right? wrong? : : 3.All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is 1 centimeter? : : My work. Took the volume for a cube and differentiated it dv/dt=dl/dt(dw/tw)(dh/dt) and just plugged in the 1 for each and recieved a answer of 1. I have no clue if I did that right. : : 4.The formula for a volume of a cone is v=(1/3)(pi)r^2(h). Find the rate of change of the volume if dr/dt is 2 inches per minute and h=3r when r=6 inches. : : My work. Replaced h for 3r in the formula and differentiated. Recieved dv/dt=3(pi)dr/dt(r^2+2r) plugged the numbers in again and recieved 288(pi) : : 5.A conical tank (with vertex down) is 10 feet acros the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rete of change of the depth of the water when the water is 8 feet deep. : : For some reason couldn't figure this one at in any shape or form. Again, thank you in advance : : C. Slayden

Optional Link URL:
Link Title:
Optional Image URL: