(a) The integral is equal to the area of the triangle; it has height 20 and base 10, so the area is 20*10/2 = 100.
(b) The integral is equal to the area of the semicircle with radius 10. It's also under the horizontal axis, so the area is negative. The semicircle has area , so the integral is -50π.
(c) First compute
which is the area of the triangle on the right. It has height and base 5, so its area is 25/2.
Then split up the desired integral as
and plug in the integral values you know:
Answer:
1980
We can choose 2 men from 9 in 36 in ways.
We can choose 2 women from 11 in 55 ways.
For any arrangement of 2 men there are 55 ways of combining them with 2 women => 55 * 36 = 1980 total ways.
If you're wondering how i got the numbers i used the combination formula:
C(n, k) =
Given:
Side length = 12 in
To find:
The area of the regular polygon.
Solution:
Number of sides (n) = 6
Let us find the apothem using formula:
where s is side length and n is number of sides.
Area of the regular polygon:
in²
The area of the regular polygon is 374.1 in².