Answer: slope of segment KL = slope of segment MN
Step-by-step explanation:
we know that a parallelogram always have two pairs of opposite sides that are parallel and therefore the slopes of the opposite sides must be same to be parallel to each other.
Perimeter = 4 x sides
48 = 4 (x + 3)
48 = 4x + 12
36 = 4x
x = 9
Check:
x + 3 = 9 + 3 = 12
12 x 4 = 48
The volume of the solid of revolution is approximately 37439.394 cubic units.
<h3>
How to find the solid of revolution enclosed by two functions</h3>
Let be
and
, whose points of intersection are
,
, respectively. The formula for the solid of revolution generated about the y-axis is:
(1)
Now we proceed to solve the integral: 
(2)

![V = 6\pi \left[(y-1)\cdot \ln y\right]\right|_{1}^{e^{35/6}}](https://tex.z-dn.net/?f=V%20%3D%206%5Cpi%20%5Cleft%5B%28y-1%29%5Ccdot%20%5Cln%20y%5Cright%5D%5Cright%7C_%7B1%7D%5E%7Be%5E%7B35%2F6%7D%7D)
![V = 6\pi \cdot \left[(e^{35/6}-1)\cdot \left(\frac{35}{6} \right)-(1-1)\cdot 0\right]](https://tex.z-dn.net/?f=V%20%3D%206%5Cpi%20%5Ccdot%20%5Cleft%5B%28e%5E%7B35%2F6%7D-1%29%5Ccdot%20%5Cleft%28%5Cfrac%7B35%7D%7B6%7D%20%5Cright%29-%281-1%29%5Ccdot%200%5Cright%5D)


The volume of the solid of revolution is approximately 37439.394 cubic units. 
To learn more on solids of revolution, we kindly invite to check this verified question: brainly.com/question/338504
<u>End behavior: </u>
The parent function is: f(x) = x³, which starts (from the left side) at -∞ and ends (on the right side) at +∞.
<u>Zeroes:</u>
f(x) = x³ + 2x² - 8x
0 = x³ + 2x² - 8x
0 = x(x² + 2x - 8)
0 = x(x + 4)(x - 2)
0 = x 0 = x + 4 0 = x - 2
x = 0 x = -4 x = 2
<u>Intervals:</u>
Put the zeroes in order: -4, 0, 2
since f(x) is increasing from the left then the interval from -4 to 0 is positive and the interval from 0 to 2 is negative.
<u>Graph:</u>
see attachment