Answer:
it's C
Step-by-step explanation:
Answer:
The volume of the solid is 243
Step-by-step explanation:
From the information given:
BY applying sphere coordinates:
0 ≤ x² + y² + z² ≤ 81
0 ≤ ρ² ≤ 81
0 ≤ ρ ≤ 9
The intersection that takes place in the sphere and the cone is:
Thus; the region bounded is: 0 ≤ θ ≤ 2π
This implies that:
ρcosФ = ρsinФ
tanФ = 1
Ф = π/4
Similarly; in the X-Y plane;
z = 0
ρcosФ = 0
cosФ = 0
Ф = π/2
So here; 
Thus, volume: 
![V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}](https://tex.z-dn.net/?f=V%20%3D%20%5Cbigg%20%5B-cos%20%5Cphi%20%20%5Cbigg%5D%5E%7B%5Cpi%2F2%7D_%7B%5Cpi%2F4%7D%20%20%5Cbigg%20%5B%5Ctheta%20%20%5Cbigg%5D%5E%7B2%20%5Cpi%7D_%7B0%7D%20%5Cbigg%20%5B%5Cdfrac%7B%5Crho%5E3%7D%7B3%7D%20%20%5Cbigg%20%5D%5E%7B9%7D_%7B0%7D)
![V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]](https://tex.z-dn.net/?f=V%20%3D%20%5B%20-0%2B%20%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5D%5B2%20%5Cpi%20-0%5D%20%5B%5Cdfrac%7B9%5E3%7D%7B3%7D-%200%20%5D)
V = 243
Answer:
It takes 50 minutes to paint the whole box
Step-by-step explanation:
1. Write an equation using equal fractions to represent this situation. Use a box to represent the total time it takes to paint the bookcase.
Wilson paints 40% of a bookcase in 20 minutes.
For the total box
40% = 20 minutes
100% = x
40 × x = 100 × 20
x = 100 × 20/40
x = 50 minutes
Answer:
The number you would add to both sides of the equation to use the "Completing the Square" method would be 16.
Step-by-step explanation:
To find the number to add to both sides of an equation to complete the square, divide the first-degree term's coefficient by 2 and square your remainder. In this case, the coefficient of the first-degree term is -8. After dividing by 2 and squaring it, you'll get 16, so that is the number you must add to both sides of the equation in order to complete the square.
