Any calculus nerds want to me on this ?

Water flows in with rate and out with rate . The net rate - call it - at which it flows through the pipe is .

a. This part is asking how much water flows into the pipe, regardless of how much flows out of it. To find this, we integrate :

(I assume you know how to find this value with a graphing calculator?)

b. The amount of water in the pipe increases when . For , we have , which means the amount of water is decreasing at this time.

c. You can use the first derivative test here. is a critical point if , and a minimum occurs at this if for , and for . Refer to a plot - you'll see that this is the case for between and . Use your calculator to get a reasonable approximation (by solving and picking the value between 2 and 4.)

d. The pipe starts with 30 ft^3 of water, so the amount of water in the pipe at any time is

The pipe will overflow for the first time when this is equal to 50.

i would be happy to . most people on would also love to i'm sure. if you just want someone who has done algebra before and want a little more personal relationship than just begging strangers for , i can certainly be of service. i do have college myself so i might not be 24/7.