anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
The formula is 1/b-a int(equation) from zero to four. Just integrate normally and multiply by the first part.
regan
  • regan
integrate with limits 0,4 then divide by 4
anonymous
  • anonymous
Ie, \[1\div4 \int\limits_{0}^{4} 2\sqrt{1+5t ^{3}} dt\]

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regan
  • regan
nailed it
anonymous
  • anonymous
I got 14.691 What do a & b represent in the average rate equation?
anonymous
  • anonymous
It is the average value theorem.
anonymous
  • 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?
anonymous
  • anonymous
Why does a=2
anonymous
  • anonymous
Therefore, the average value theorem states that the average value is simply the integration times 1/b-a
anonymous
  • anonymous
I'm sorry, that was a typo. A is 0.
anonymous
  • anonymous
Ok, thanks

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