Question

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?

Answer 1

The formula is 1/b-a int(equation) from zero to four. Just integrate normally and multiply by the first part.
integrate with limits 0,4 then divide by 4

1÷4 (limit o to 4)∫ 2√1+5t^3 dt
= 14.691

Answer 2

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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