Answer:
![4\pi\ln4](https://tex.z-dn.net/?f=4%5Cpi%5Cln4)
Step-by-step explanation:
We are given: ![f(x)=\frac{2}{\sqrt{x+2}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B2%7D%7B%5Csqrt%7Bx%2B2%7D%7D)
The volume will be calculated with integral.
![V = \pi\int\limits^2_{-1}(f(x))^2dx=\pi\int\limits^2_{-1}\frac{4}{x+2}dx=4\pi\ln(x+2)|^2_{-1}=4\pi\ln4](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%5Cint%5Climits%5E2_%7B-1%7D%28f%28x%29%29%5E2dx%3D%5Cpi%5Cint%5Climits%5E2_%7B-1%7D%5Cfrac%7B4%7D%7Bx%2B2%7Ddx%3D4%5Cpi%5Cln%28x%2B2%29%7C%5E2_%7B-1%7D%3D4%5Cpi%5Cln4)
Given that,
Length of the ladder = 20 ft
It casts a 12 ft shadow
To find,
If the statue casts a shadow that is 9 ft long then how tall is it?
Solution,
Let the ladder be x ft tall.
20 ft tall ladder = 12 ft shadow
9 ft tall ladder =
![\dfrac{20}{12}\times 9\\\\=15\ ft](https://tex.z-dn.net/?f=%5Cdfrac%7B20%7D%7B12%7D%5Ctimes%209%5C%5C%5C%5C%3D15%5C%20ft)
Hence, the required length is 15 ft.
Answer:
38.81cm³
Step-by-step explanation:
Volume of a sphere = 4/3πr³
Diameter is 4.2
radius= 4.2/2 = 2.1 or 21/10
4/3 × 22/7 × 21/10 × 21/10 × 21/10
= 4851/125
= 38.808
≈38.81cm³
Answer is down below
Step-by-step explanation: Have a brilliant day mate- Lily ^_^
Multiply 65 by .2 and then take that number and subtract it from the original 65. So it would be 65 - 13 = 52