X equals 13 and that is the answer
Answer:
Hence - 7 is the answer
Pls mark me brainliest plss
neverminding the jumbled lingo, is simply asking for the equation of the tangent line at that point, it says all tangents, well, there's only one passing there.
we can simply get the derivative of f(x) and take it from there.

since now we know the slope when x = 3/2, then we can just plug that into its point-slope intercept form, along with the coordinates.

Answer:
44.18 cubic unit
Step-by-step explanation:
The intersection of the curve
and
is




Since we are rotating the region where
we will use the intersection x = 2 and y = 4
Using the shell method with x ranges from 0.5 to 2. The volume of the shell would be

where h is the difference between the y-coordinates of the curves, in other words

Plug h into the V integral and we have
![V = \int\limits^2_{0.5} {2\pi x (8 - 2x^2)} \, dx\\V = 4\pi\int\limits^2_{0.5} {(4x - x^3)} \, dx\\V = 4\pi[2x^2 - x^4/4]^2_{0.5}\\V = 4\pi(2*2^2 - 2^4/4 - 2*0.5^2 + 0.5^4/4)\\V = 4\pi(8 - 4 - 0.5 + 0.015625) \approx 44.18](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%5Climits%5E2_%7B0.5%7D%20%7B2%5Cpi%20x%20%288%20-%202x%5E2%29%7D%20%5C%2C%20dx%5C%5CV%20%3D%204%5Cpi%5Cint%5Climits%5E2_%7B0.5%7D%20%7B%284x%20-%20x%5E3%29%7D%20%5C%2C%20dx%5C%5CV%20%3D%204%5Cpi%5B2x%5E2%20-%20x%5E4%2F4%5D%5E2_%7B0.5%7D%5C%5CV%20%3D%204%5Cpi%282%2A2%5E2%20-%202%5E4%2F4%20-%202%2A0.5%5E2%20%2B%200.5%5E4%2F4%29%5C%5CV%20%3D%204%5Cpi%288%20-%204%20-%200.5%20%2B%200.015625%29%20%5Capprox%2044.18)