<h2>Greetings!</h2>
Answer:
x + 20 = area
Step-by-step explanation:
You need to recall the equation for a rectangle:
Width x Length = Area
So simply plug the values into this:
(0.5x+10) * 6
(0.5x * 6) + (10 * 6)
= 3x + 60
Simplified down by dividing by three:
= area
<h3>x + 20 = area</h3>
<h2>Hope this helps!</h2>
The volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16 is 24.74 cubic units.
<h3>What is the volume of the solid?</h3>
Find the volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16
From the sphere and cylinder, the cylindrical coordinate will be
And the radius of the cylinder is |r| < 1 and the 0 ≤ θ ≤ 2π.
Then the volume will be given as
![\rm V = \int _0^{2\pi} \int _0^1 \int _{- \sqrt{16 - r^2}}^{\sqrt{16-r^2}} \left ( r \ dz \ dr \ d\theta \right ) \\\\\\V = 2\pi \int_0^1 \left ( 2r\sqrt{16-r^2} \right ) \ dr\\\\\\V = 4\pi \left [ -\dfrac{1}{3} (16 - r^2)^{3/2} \right ]\\\\\\V = \dfrac{4\pi}{3} \left ( 16^{3/2} - 15^{3/2} \right )\\\\\\V = 24.74](https://tex.z-dn.net/?f=%5Crm%20V%20%3D%20%5Cint%20_0%5E%7B2%5Cpi%7D%20%5Cint%20_0%5E1%20%5Cint%20_%7B-%20%5Csqrt%7B16%20-%20r%5E2%7D%7D%5E%7B%5Csqrt%7B16-r%5E2%7D%7D%20%5Cleft%20%28%20r%20%5C%20dz%20%5C%20dr%20%5C%20d%5Ctheta%20%20%5Cright%20%29%20%5C%5C%5C%5C%5C%5CV%20%3D%202%5Cpi%20%5Cint_0%5E1%20%5Cleft%20%28%202r%5Csqrt%7B16-r%5E2%7D%20%5Cright%20%29%20%5C%20dr%5C%5C%5C%5C%5C%5CV%20%3D%204%5Cpi%20%5Cleft%20%5B%20-%5Cdfrac%7B1%7D%7B3%7D%20%2816%20-%20r%5E2%29%5E%7B3%2F2%7D%20%5Cright%20%5D%5C%5C%5C%5C%5C%5CV%20%3D%20%5Cdfrac%7B4%5Cpi%7D%7B3%7D%20%5Cleft%20%28%2016%5E%7B3%2F2%7D%20-%2015%5E%7B3%2F2%7D%20%5Cright%20%29%5C%5C%5C%5C%5C%5CV%20%3D%2024.74)
More about the volume of the solid link is given below.
brainly.com/question/23705404
#SPJ4
(2) So we know Ethan uses 1/4 cup of milk for his cake. And if he needs to make 3 times the amount of 1 cake, he'll make 3 cakes today. So we multiply the amount of cakes (3) by the amount of milk needed (1/4)
3 * 1/4 = 3/4
Ethan will need 3/4 cups of milk.
(3) We know Isabella need's 2/5 of a gallon of the food to make 1 gallon.
She want's to make 5 gallons, so like the other problem, we multiply the amount of gallons (5) by the amount of food needed (2/5):
5 * 2/5 = 10/5 = 2/1.
Isabella will need 2 gallons of food.
Answer:
expand (a + 7) * 2: 2a + 14
Step-by-step explanation:
(a + 7) * 2
= 2 ( a + 7)
apply the distributive law: a(b + c) = ab + ac
a = 2, b = a, c = 7
= 2a + 2 * 7
multiply the numbers: 2 * 7 = 14
= 2a + 14
