Water flowing out of a pipe

1. Dec 26, 2007

ricekrispie

The problem statement, all variables and given/known data

t (hours) | R(t) (gallons per hour)
0 9,6
3 10,4
6 10,8
9 11,2
12 11,4
15 11,3
18 10,7
21 10,2
24 9,6​
The rate at which water flows out of a pipe, in gallons per hour, is given by a differentiable function R of time t. The table above shows the rate as measured every 3 hrs for a 24-hour period.

(a) Use a midpoint Riemann sum with 4 subdivisions of equal length to approximate $$\int_0^{24} R(t) dt$$. Using correct units, explain the meaning of your answer in terms of water flow.

(b) Is there some time t, 0 < t < 24, such that R´(t) = 0? Justify your answer.

(c) The rate of water flow R(t) can be approximated by Q(t) = (1/79)(768 + 23t - t^2).
Use Q(t) to approximate the average rate of water flow during the 24-hour time period. Indicate units of measure.

P.S.: THIS IS AN AP PROBLEM :(
P.S.2: SORRY, I DON´T HAVE A CLUE OF WHERE TO START

Last edited: Dec 26, 2007
2. Dec 26, 2007

NateTG

For multi-character limits of integration, you need to use {}'s:
$$\int_0^{24}$$

The question is basically asking how much water has flowed out of the pipe.

Do you know what a Riemann sum is?

3. Dec 26, 2007

ricekrispie

no.. i have no idea

4. Dec 26, 2007

NateTG

5. Dec 26, 2007