<h2>
Hello!</h2>
The answer is: There is a total of 5.797 gallons pumped during the given period.
<h2>
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:
D
Step-by-step explanation:
(if he gathers 4 coins each month you will need the variable by it. he was given 20 coins so it is added on to how many coins he has. plus it would be greater than because the question asked when he will have MORE than 50 coins.)
Answer:
33,600
Step-by-step explanation:
length=20m
wide=14m
area= 28m²
1m= 28
cost = 120*28= rs33600 per m²
AMOUNT DEPOSITED: $15k ($15,000)
INTEREST RATE PER YEAR: 0.07% (7%)
STEPS:
→Multiply the amount deposited ($15k) by the interest rate per year (7%).
15,000 * 0.07
= $1,050 (interest earned in 1 year)
→Multiply the interest earned from the first year ($1,050) by the amount of years that you want to calculate (3 years)
$1,050 * 3
=3,150 (interest earned in 3 years)
→ Add the interest earned (in 3 years, in this particular equation) to the amount that you deposited ($15k)
$15,000 + $3,150
=$18,150
FINAL ANSWER: $18,150
Answer is 1080 degrees
Formula for calculating angles in a polygon (Shape with 4 or more sides) is (n-2) x 180, where n is the number of sides on the shape. Octagon has eight sides, so you subtract it by 2, which is 6. Multiply that by 180 to get 1080, which is the sum of the angles.
