<h2>
Hello!</h2>
The answer is: There is a total of 5.797 gallons pumped during the given period.
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Why?</h2>
To solve this equation, we need to integrate the function at the given period (from t=0 to t=4)
The given function is:

So, the integral will be:

So, integrating we have:

Performing a change of variable, we have:

Then, substituting, we have:



![\frac{5}{9} \int\limits^4_0 {(1 )\ du- \frac{5}{9} \int\limits^4_0 {(\frac{1}{u })\ du=\frac{5}{9} (u-lnu)/[0,4]](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D%20%5Cint%5Climits%5E4_0%20%7B%281%20%29%5C%20du-%20%5Cfrac%7B5%7D%7B9%7D%20%5Cint%5Climits%5E4_0%20%7B%28%5Cfrac%7B1%7D%7Bu%20%7D%29%5C%20du%3D%5Cfrac%7B5%7D%7B9%7D%20%28u-lnu%29%2F%5B0%2C4%5D)
Reverting the change of variable, we have:
![\frac{5}{9} (u-lnu)/[0,4]=\frac{5}{9}((1+3t)-ln(1+3t))/[0,4]](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D%20%28u-lnu%29%2F%5B0%2C4%5D%3D%5Cfrac%7B5%7D%7B9%7D%28%281%2B3t%29-ln%281%2B3t%29%29%2F%5B0%2C4%5D)
Then, evaluating we have:
![\frac{5}{9}((1+3t)-ln(1+3t))[0,4]=(\frac{5}{9}((1+3(4)-ln(1+3(4)))-(\frac{5}{9}((1+3(0)-ln(1+3(0)))=\frac{5}{9}(10.435)-\frac{5}{9}(1)=5.797](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D%28%281%2B3t%29-ln%281%2B3t%29%29%5B0%2C4%5D%3D%28%5Cfrac%7B5%7D%7B9%7D%28%281%2B3%284%29-ln%281%2B3%284%29%29%29-%28%5Cfrac%7B5%7D%7B9%7D%28%281%2B3%280%29-ln%281%2B3%280%29%29%29%3D%5Cfrac%7B5%7D%7B9%7D%2810.435%29-%5Cfrac%7B5%7D%7B9%7D%281%29%3D5.797)
So, there is a total of 5.797 gallons pumped during the given period.
Have a nice day!
Answer:

Step-by-step explanation:
Given

Required
Simplify
To do this, we apply laws of indices:

So:

Add the exponents

Answer:
y - 11 = 3 (x - 2)
Step-by-step explanation:
This is in point slope form, that is by far the best form to be in. Point slope form is best when there is a point and it gives it to you in slope intercept form. you take the slope from the original equation and stick it into y - (y point) = slope (x - (x point)) you know it is the right equation because it gives you the slope, which is the same, and the point, which is given.
The way to get it into slope intersept form you just solve for y
Answer:
70 inches
Step-by-step explanation:
10 in x 7 in =70 inches
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