Slope = rise/run = (change in y)/(change in x)
Slope = (4-6)/(0-(-4)) = (-2)/(4)
Slope = -1/2 = -0.5
Answer:
C
Step-by-step explanation:
The wanted region(shaded part)..is greater or equal to 2 due to the bold line...so hence the first inequality is....y is greater than or equal to 2
And the second solution....is y is less than x because of the continuous broken line...hence it cant be less than or equal to
We need to get the limits first. When y = 0
0 = 64x - 8x^2
x = 0 and x = 8
The volume is
V = ∫ y dx from 0 to 8
V = ∫ (64x - 8x^2) dx from 0 to 8
V = 32x^2 - 8x^3/3 from 0 to 8
V = 682.67<span />
ANSWER
The required angle is
![60 \degree](https://tex.z-dn.net/?f=60%20%5Cdegree)
EXPLANATION
Let the angle whose sine is
![\frac{ \sqrt{3} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B2%7D%20)
be
![x \degree](https://tex.z-dn.net/?f=x%20%5Cdegree)
Then
![\sin(x \degree) = \frac{ \sqrt{3} }{2}](https://tex.z-dn.net/?f=%20%5Csin%28x%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B2%7D%20)
We take the inverse sign of both sides to obtain,
![x = \sin ^{ - 1} ( \frac{ \sqrt{3} }{2} )](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csin%20%5E%7B%20-%201%7D%20%28%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B2%7D%20%29%20)
We use our scientific calculator to evaluate and obtain,