Average is the geometrical mean of the set of numbers. The average rate of water flow, in gallons per minute, is 14.691 gallons/min.
What is average?
The average is the geometrical mean of the set of numbers. It is given by the formula,
\(\rm Average = \dfrac{\text{Sum of all the obsevations}}{\text{Number of observations}}\)
As it is given that the rate at which water is sprayed on a field of vegetables is R(t)=2sqrt(1+5t^3).
In order to find the average rate of water flow During the time interval 0 to 4, we need to add the rate at which water is sprayed on a field of vegetables during the interval and then divide the sum by 4, therefore, the mean can be written as,
\(\text{Average rate of water flow}= \dfrac{\int_0^4 2\sqrt{(1+5t^3)}}{4}\)
\(\text{Average rate of water flow}= \dfrac{58.76417}{4} = 14.691\rm\ gallons/min.\)
Hence, the average rate of water flow, in gallons per minute is 14.691 gallons/min.
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