First, we have to convert our function (of x) into a function of y (we revolve the curve around the y-axis). So:

And the derivative of x:

Now, we can calculate the area of the surface:

We could calculate this integral (not very hard, but long), or use
(1),
(2) and
(3) to get:



Calculate indefinite integral:

And the area:
![A=2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx=2\pi\cdot\dfrac{1}{12}\bigg[\left(4x^2+1\right)^\frac{3}{2}\bigg]_0^{10}=\\\\\\= \dfrac{\pi}{6}\left[\big(4\cdot10^2+1\big)^\frac{3}{2}-\big(4\cdot0^2+1\big)^\frac{3}{2}\right]=\dfrac{\pi}{6}\Big(\big401^\frac{3}{2}-1^\frac{3}{2}\Big)=\boxed{\dfrac{401^\frac{3}{2}-1}{6}\pi}](https://tex.z-dn.net/?f=A%3D2%5Cpi%5Cint%5Climits_0%5E%7B10%7Dx%5Csqrt%7B4x%5E2%2B1%7D%5C%2Cdx%3D2%5Cpi%5Ccdot%5Cdfrac%7B1%7D%7B12%7D%5Cbigg%5B%5Cleft%284x%5E2%2B1%5Cright%29%5E%5Cfrac%7B3%7D%7B2%7D%5Cbigg%5D_0%5E%7B10%7D%3D%5C%5C%5C%5C%5C%5C%3D%20%5Cdfrac%7B%5Cpi%7D%7B6%7D%5Cleft%5B%5Cbig%284%5Ccdot10%5E2%2B1%5Cbig%29%5E%5Cfrac%7B3%7D%7B2%7D-%5Cbig%284%5Ccdot0%5E2%2B1%5Cbig%29%5E%5Cfrac%7B3%7D%7B2%7D%5Cright%5D%3D%5Cdfrac%7B%5Cpi%7D%7B6%7D%5CBig%28%5Cbig401%5E%5Cfrac%7B3%7D%7B2%7D-1%5E%5Cfrac%7B3%7D%7B2%7D%5CBig%29%3D%5Cboxed%7B%5Cdfrac%7B401%5E%5Cfrac%7B3%7D%7B2%7D-1%7D%7B6%7D%5Cpi%7D)
Answer D.
Answer: C A L C U L A T O R probably on calculator soup
Step-by-step explanation:
The amount of drugs that will be left after 12 hours is 17.42 mg provided Sarah takes 550 mg of an antibiotic every hour.
<h3>What is exponential decay?</h3>
Exponential decay can be described as a reduced amount of an original substance by a definite percentage over a period of time. It can be determined by using the formula:

where;
- y = total amount,
- a = initial amount = 550 mg
- r = the growth rate = 0.25
- t = number of growth periods = 12 hours

y = 17.42 mg
Therefore, we can conclude that the amount of drugs that will be left after 12 hours is 17.42 mg.
Learn more about the exponential decay model here:
brainly.com/question/12940982
<span>What is the metric unit for capacity?
</span>it would be liter