## anonymous 5 years ago The rate at which water is sprayed on a field of vegetables is given by R(t)=2sqrt(1+5t^3), where t is in minutes and R(t) is in gallons per minute. During the time interval 0 to 4 inclusive, what is the average rate of water flow, in gallons per minute?

1. anonymous

The formula is 1/b-a int(equation) from zero to four. Just integrate normally and multiply by the first part.

2. anonymous

integrate with limits 0,4 then divide by 4

3. anonymous

Ie, $1\div4 \int\limits_{0}^{4} 2\sqrt{1+5t ^{3}} dt$

4. anonymous

nailed it

5. anonymous

I got 14.691 What do a & b represent in the average rate equation?

6. anonymous

It is the average value theorem.

7. anonymous

Essentially, to explain geometrically, it is the same as taking the average of any numbers. You take the sum and then divide by how many numbers you had originally, right? You had a certain amount between b, which is 4, and a, which is 2. That is represented by the integration. You divide by their difference because it is the space between in terms of x, or in this case, t. Does that answer your question?

8. anonymous

Why does a=2

9. anonymous

Therefore, the average value theorem states that the average value is simply the integration times 1/b-a

10. anonymous

I'm sorry, that was a typo. A is 0.

11. anonymous

Ok, thanks