Answer:

Step-by-step explanation:
It can be found by integral.
First let's find the intersection points.

Only intersection point is x = 2.
And it is asked to find the area in the interval (2, 4).

We will use integration by parts.


Answer:
11/12
Step-by-step explanation:
We need to get a common denominator of 12
2/3 *4/4 = 8/12
1/4 *3/3 = 3/12
2/3 +1/4
8/12+3/12
11/12
The volume generated by rotating the given region
about OC is
<h3>
Washer method</h3>
Because the given region (
) has a look like a washer, we will apply the washer method to find the volume generated by rotating the given region about the specific line.
solution
We first find the value of x and y









![v= \pi \int\limits^2_o= [\frac{y^{2} }{4} - \frac{y^{8} }{2^{8} }} ] dy](https://tex.z-dn.net/?f=v%3D%20%5Cpi%20%5Cint%5Climits%5E2_o%3D%20%5B%5Cfrac%7By%5E%7B2%7D%20%7D%7B4%7D%20-%20%5Cfrac%7By%5E%7B8%7D%20%7D%7B2%5E%7B8%7D%20%7D%7D%20%20%5D%20dy)
![v= \pi [\int\limits^2_o {\frac{y^{2} }{4} } \, dy - \int\limits^2_o {\frac{y}{2^{8} } ^{8} } \, dy ]](https://tex.z-dn.net/?f=v%3D%20%5Cpi%20%5B%5Cint%5Climits%5E2_o%20%7B%5Cfrac%7By%5E%7B2%7D%20%7D%7B4%7D%20%7D%20%5C%2C%20dy%20-%20%5Cint%5Climits%5E2_o%20%7B%5Cfrac%7By%7D%7B2%5E%7B8%7D%20%7D%20%5E%7B8%7D%20%7D%20%5C%2C%20dy%20%5D)
![v=\pi [\frac{1}{4} \frac{y^{3} }{3} \int\limits^2_0 - \frac{1}{2^{8} } \frac{y^{g} }{g} \int\limits^2_o\\v= \pi [\frac{1}{12} (2^{3} -0)-\frac{1}{2^{8}*9 } (2^{g} -0)]\\v= \pi [\frac{2}{3} -\frac{2}{g} ]\\v= \frac{4}{g} \pi](https://tex.z-dn.net/?f=v%3D%5Cpi%20%5B%5Cfrac%7B1%7D%7B4%7D%20%5Cfrac%7By%5E%7B3%7D%20%7D%7B3%7D%20%20%5Cint%5Climits%5E2_0%20-%20%5Cfrac%7B1%7D%7B2%5E%7B8%7D%20%7D%20%20%5Cfrac%7By%5E%7Bg%7D%20%7D%7Bg%7D%20%5Cint%5Climits%5E2_o%5C%5Cv%3D%20%5Cpi%20%5B%5Cfrac%7B1%7D%7B12%7D%20%282%5E%7B3%7D%20-0%29-%5Cfrac%7B1%7D%7B2%5E%7B8%7D%2A9%20%7D%20%282%5E%7Bg%7D%20-0%29%5D%5C%5Cv%3D%20%5Cpi%20%5B%5Cfrac%7B2%7D%7B3%7D%20-%5Cfrac%7B2%7D%7Bg%7D%20%5D%5C%5Cv%3D%20%5Cfrac%7B4%7D%7Bg%7D%20%5Cpi)
A similar question about finding the volume generated by a given region is answered here: brainly.com/question/3455095
Answer:
54 minutes
Step-by-step explanation:
From the question, we are given;
- A room with dimensions 5.2 m by 4.3 m by 2.9 m
- The exchange air rate is 1200 L/min
We are required to determine the time taken to exchange the air in the room;
First we are going to determine the volume of the room;
Volume of the room = length × width × height
= 5.2 m × 4.3 m × 2.9 m
= 64.844 m³
Then we should know, that 1 m³ = 1000 L
Therefore, we can convert the volume of the room into L
= 64.844 m³ × 1000 L
= 64,844 L
But, the rate is 1200 L/min
Thus, time = Volume ÷ rate
= 64,844 L ÷ 1200 L/min
= 54.0367 minutes
= 54 minutes
Therefore, it would take approximately 54 minutes
Answer:
<u>If P is 30 units and l is 10 units, w is 5 units</u>
Step-by-step explanation:
1. Let's check the information given to resolve the question:
P = 2l + 2w
If P is 30 units and l is 10 units, w is units
2. Replacing with the values:
P = 2l + 2w
30 = 2 (10) + 2w
30 = 20 + 2w
-2w = 20 -30 (Subtracting 2w and - 30 to both sides)
-2w = - 10
2w = 10 (Multiplying by - 1 at both sides)
<u>w = 5 (Dividing by 2 at both sides)</u>
<u>If P is 30 units and l is 10 units, w is 5 units</u>
<u>Note: Same answer than question 13938258</u>