Answer:
The volume of the solid is π/40 cubic units.
Step-by-step explanation:
Please refer to the graph below.
Recall that the area of a semi-circle is given by:
The volume of the solid will be the integral from <em>x</em> = 0 to <em>x</em> = 1 of area A. Since the diameter is given by <em>y</em>, then the radius is <em>y/2</em>. Hence, the volume of the solid is:
Substitute:
Simplify:
Integrate:
![\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B1%7D%7B2%7D%5Cpi%20%5Cleft%5B%5Cfrac%7Bx%5E5%7D%7B20%7D%5CBig%7C_0%5E1%5Cright%5D)
Evaluate:
The volume of the solid is π/40 cubic units.
Step-by-step explanation:
1. 3 multiplied by x is the same value of 6
2. since 3x is on the left side we have to divide the equation by 3 on both sides which doesn't change the value of x, but it helps us get the value for x. so when you divide the equation by 3 the answer for x=6/2 which 2 divided by 6=3
Hope that helps :)
10v⁶y⁷ = <u>2</u> * 5 * <u>vvvvv</u>v * <u>yyy</u>yyyy
6w⁴v⁵y³ = <u>2</u> * 3 * wwww * <u>vvvvv</u> * <u>yyy</u>
GCF: 2v⁴y³
<em>The LCM is the GCF and everything leftover</em>
LCM: 2v⁴y³ * (5 * v * yyyy) * (3 * wwww)
= (2 * 5 * 3) * (v⁴ * v) * (w⁴) * (y³ * y⁴)
= 30 v⁵ w⁴ y⁷
Answer: LCM = 30v⁵w⁴y⁷
Answer:
b = - 14
Step-by-step explanation:
Given
- 
(8 + 5b) = 75 + 
b
Multiply through by 6 ( the LCM of 6 and 3 ) to clear the fractions
- 5(8 + 5b) = 450 + 10b ← distribute left side
- 40 - 25b = 450 + 10b ( subtract 10b from both sides )
- 40 - 35b = 450 ( add 40 to both sides )
- 35b = 490 ( divide both sides by - 35 )
b = - 14
We claim that the answer is 
Since the two graphs both open down, and all the answer choices, in addition to the equation of the blue graph, are quadratic polynomials, the leading coefficient must be negative. This immediately rules out answer choices A, B, and C, leaving D as the answer.
