Answer:
15 students
Step-by-step explanation:
No. of boys students = No. of all students - No. of girls
no. of boys =50-15 = 35 boys
the boys that will play the match are 2/7 of boys = (2/7)x35 = 10 boys
and the girls that will play the match are 5 girls
so, no of students chosen to play = 5+10=15 students
Answer:
Step-by-step explanation:
3n+2)! / (3n-3)! = (3n+2)*(3n+1)*(3n)*(3n-1)*(3n-2)*(3n-3)! divided by (3n-3)! which becomes:
23! / 18! = (23 * 22 * 21 * 20 * 19 * 18! divided by 18! which becomes:
(23 * 22 * 21 * 20 * 19)
the result is 4037880
i used my ti-84 to take 23! and divide it by 18! and i got 4037880.
this confirms the solution is correct.
Area of a square = L * L
As you know 17 * 17 = 289
So length of one side of square equals 17
Answer:
Step-by-step explanation:
From the image attached below;
We need to calculate the limits of x and y to find the double integral
We will notice that y varies from 1 to 2
The line equation for (0,1),(1,2) is:
y - 1 = x
The line equtaion for (1,2),(4,1) is:
-3(y-2) = (x -1)
-3y + 6 = x - 1
-x = 3y - 6 - 1
-x = 3y - 7
x = -3y + 7
This implies that x varies from y - 1 to -3y + 7
Now, the region D = {(x,y) | 1 ≤ y ≤ 2, y - 1 ≤ x ≤ -3y + 7}
The double integral can now be calculated as:
![\iint _D y^2 dA= \int ^2_1 \bigg[ 2xy ^2 \bigg]^{-3y+7}_{y-1} \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cbigg%5B%202xy%20%5E2%20%5Cbigg%5D%5E%7B-3y%2B7%7D_%7By-1%7D%20%20%5C%20dy)
![\iint _D y^2 dA= \int ^2_1 \bigg[2(-3y+7)y^2-2(y-1)y^2 \bigg ] \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cbigg%5B2%28-3y%2B7%29y%5E2-2%28y-1%29y%5E2%20%5Cbigg%20%5D%20%20%5C%20dy)
![\iint _D y^2 dA= \int ^2_1 \bigg[-6y^3 +14y^2 -2y^3 +2y^2 \bigg ] \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cbigg%5B-6y%5E3%20%2B14y%5E2%20-2y%5E3%20%2B2y%5E2%20%5Cbigg%20%5D%20%20%5C%20dy)
![\iint _D y^2 dA= \int ^2_1 \bigg[-8y^3 +16y^2 \bigg ] \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cbigg%5B-8y%5E3%20%2B16y%5E2%20%20%5Cbigg%20%5D%20%20%5C%20dy)
![\iint _D y^2 dA= \bigg[-8(\dfrac{y^4}{4}) +16(\dfrac{y^3}{3})\bigg ] ^2_1](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cbigg%5B-8%28%5Cdfrac%7By%5E4%7D%7B4%7D%29%20%20%2B16%28%5Cdfrac%7By%5E3%7D%7B3%7D%29%5Cbigg%20%5D%20%5E2_1)
![\iint _D y^2 dA= \bigg[-8(\dfrac{16}{4}-\dfrac{1}{4}) +16(\dfrac{8}{3}-\dfrac{1}{3})\bigg ]](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cbigg%5B-8%28%5Cdfrac%7B16%7D%7B4%7D-%5Cdfrac%7B1%7D%7B4%7D%29%20%20%2B16%28%5Cdfrac%7B8%7D%7B3%7D-%5Cdfrac%7B1%7D%7B3%7D%29%5Cbigg%20%5D)
![\iint _D y^2 dA= \bigg[-8(\dfrac{15}{4}) +16(\dfrac{7}{3})\bigg ]](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cbigg%5B-8%28%5Cdfrac%7B15%7D%7B4%7D%29%20%20%2B16%28%5Cdfrac%7B7%7D%7B3%7D%29%5Cbigg%20%5D)
