Answer:
x=-5
Step-by-step explanation:
A vertical line is a line that goes up and down. It has a constant x value
Since the x value is -5
x=-5
The answer is 60,480 cubic centimeters
Answer:
I may be wrong but I believe the answer is y= -2x+1
Answer:
x=![1.22930](https://tex.z-dn.net/?f=1.22930)
Step-by-step explanation:
47(218 x+12 ) =−2(17 −528 x)
Simplify 47(218 x+12 ) : 327(21x+4) 327(21x+4) =−2(17 −528 x)
Multiply both sides by 7(21x+4)
327(21x+4) · 7(21x+4)=−2(17 −528 x)· 7(21x+4)
Simplify, 32=−14(17 −528 x)(21x+4)
Solve 32=−14(17 −528 x)(21x+4): x=32+4√589105 , x=32−4√589105 x=32+4√589105 , x=32−4√589105
The average value of
over the region
is
![\dfrac{\displaystyle\iint_{\mathcal D}f(x,y)\,\mathrm dx\,\mathrm dy}{\displaystyle\iint_{\mathcal D}\mathrm dx\,\mathrm dy](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cdisplaystyle%5Ciint_%7B%5Cmathcal%20D%7Df%28x%2Cy%29%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%7D%7B%5Cdisplaystyle%5Ciint_%7B%5Cmathcal%20D%7D%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy)
We can describe the region
as the set
![\{(x,y)\mid0\le x\le1,\,0\le y\le8x\}](https://tex.z-dn.net/?f=%5C%7B%28x%2Cy%29%5Cmid0%5Cle%20x%5Cle1%2C%5C%2C0%5Cle%20y%5Cle8x%5C%7D)
So the integral in the numerator is
![\displaystyle\iint_{\mathcal D}5xy\,\mathrm dx\,\mathrm dy=5\int_{x=0}^{x=1}\int_{y=0}^{y=8x}xy\,\mathrm dy\,\mathrm dx=40](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%7B%5Cmathcal%20D%7D5xy%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D5%5Cint_%7Bx%3D0%7D%5E%7Bx%3D1%7D%5Cint_%7By%3D0%7D%5E%7By%3D8x%7Dxy%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%3D40)
The integral in the denominator is the same as the area of
, which is a right triangle, so it's easy to compute
![\displaystyle\iint_{\mathcal D}\mathrm dx\,\mathrm dy=\frac12\cdot1\cdot8=4](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%7B%5Cmathcal%20D%7D%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D%5Cfrac12%5Ccdot1%5Ccdot8%3D4)
So the average value is
.