The answer would be x = -7.
Hope this helps!
It should be 126in 10.5ft and 3.5 yards. First convert to inches then divide by 12 for feet then divide by 3 for yards.
ANSWER: y=4/3x-7
Reasoning: slope is 4/3 (change in y over change in x)
The y intercept is a -7
Then you just fill in the equation
Answer:
![\mathbf{\iint _D y^2 dA= \dfrac{22}{3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cdfrac%7B22%7D%7B3%7D%7D)
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 = \dfrac{2-1}{1-0}(x-0)](https://tex.z-dn.net/?f=y-1%20%3D%20%5Cdfrac%7B2-1%7D%7B1-0%7D%28x-0%29)
y - 1 = x
The line equtaion for (1,2),(4,1) is:
![y-2 = \dfrac{1-2}{4-1}(x-1) \\ \\ y-2 = -\dfrac{1}{3}(x-1)](https://tex.z-dn.net/?f=y-2%20%3D%20%5Cdfrac%7B1-2%7D%7B4-1%7D%28x-1%29%20%5C%5C%20%5C%5C%20y-2%20%3D%20-%5Cdfrac%7B1%7D%7B3%7D%28x-1%29)
-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 \int ^{-3y +7}_{y-1} \ 2y ^2 \ dx \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cint%20%5E%7B-3y%20%2B7%7D_%7By-1%7D%20%5C%202y%20%5E2%20%20%5C%20dx%20%5C%20dy)
![\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)
![\iint _D y^2 dA= -30 + \dfrac{112}{3}](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%20-30%20%2B%20%5Cdfrac%7B112%7D%7B3%7D)
![\iint _D y^2 dA= \dfrac{-90+112}{3}](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cdfrac%7B-90%2B112%7D%7B3%7D)
![\mathbf{\iint _D y^2 dA= \dfrac{22}{3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cdfrac%7B22%7D%7B3%7D%7D)
Answer:
he missed 11 shots
Step-by-step explanation:
if you are trying to find how many the basketball player didnt make you will do this
24 - 13 = 11
he didnt make 11 shots
hope this helps!!!