Answer:
90
Step-by-step explanation:
both sides are equal
both sides have to match
therefore y is 90 and x is 30
it is a symmetry thing
<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:
3:13
Step-by-step explanation:
hope this helps you and good luck
Answer: Approximately 13 ft
Step-by-step explanation: For this, you have to do the Pythagorean Theorem. First set up an equation. That equation is a squared+b squared=c squared. Next, plug in values. A=12 and b=4. The equation becomes 12 squared+4 squared=c squared. Do the math and you'll get 144+16=c squared. Add and get 160=c squared. Then do the square root of both sides and you'll get 12.649=c. Round to nearest whole number to get approximately 13 ft. You can also represent it as the square root symbol with 160 inside, like this(√160).
Since this is a right triangle, we could use the pythagorean theorem: a²+b²=c² where this problem already gave us a=10 and b=√60, and we want to solve for c.
10²+(√60)²=c² ← 10² is 100, and the square cancels out the square root on the 60
100 + 60 = c²
160 = c² ← To isolate c, we take the square root of both sides
√160 = c ← √160 is the same as 4√10
Answer: 4√10
