Step-by-step explanation:
2w+6w=80
w=10
l=30
![D](https://tex.z-dn.net/?f=D)
is a right triangle with base length 1 and height 8, so the area of
![D](https://tex.z-dn.net/?f=D)
is
![\dfrac12(1)(8)=4](https://tex.z-dn.net/?f=%5Cdfrac12%281%29%288%29%3D4)
.
The average value of
![f(x,y)](https://tex.z-dn.net/?f=f%28x%2Cy%29)
over
![D](https://tex.z-dn.net/?f=D)
is given by the ratio
![\dfrac{\displaystyle\iint_Df(x,y)\,\mathrm dA}{\displaystyle\iint_D\mathrm dA}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cdisplaystyle%5Ciint_Df%28x%2Cy%29%5C%2C%5Cmathrm%20dA%7D%7B%5Cdisplaystyle%5Ciint_D%5Cmathrm%20dA%7D)
The denominator is just the area of
![D](https://tex.z-dn.net/?f=D)
, which we already know. The average value is then simplified to
![\displaystyle\frac74\iint_Dxy\,\mathrm dA](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac74%5Ciint_Dxy%5C%2C%5Cmathrm%20dA)
In the
![x,y](https://tex.z-dn.net/?f=x%2Cy)
-plane, we can describe the region
![D](https://tex.z-dn.net/?f=D)
as all points
![(x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29)
that lie between the lines
![y=0](https://tex.z-dn.net/?f=y%3D0)
and
![y=8x](https://tex.z-dn.net/?f=y%3D8x)
(the lines which coincide with the triangle's base and hypotenuse, respectively), taking
![0\le x\le1](https://tex.z-dn.net/?f=0%5Cle%20x%5Cle1)
. So, the integral is given by, and evaluates to,
![\displaystyle\frac74\int_{x=0}^{x=1}\int_{y=0}^{y=8x}xy\,\mathrm dy\,\mathrm dx=\frac78\int_{x=0}^{x=1}xy^2\bigg|_{y=0}^{y=8x}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac74%5Cint_%7Bx%3D0%7D%5E%7Bx%3D1%7D%5Cint_%7By%3D0%7D%5E%7By%3D8x%7Dxy%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%3D%5Cfrac78%5Cint_%7Bx%3D0%7D%5E%7Bx%3D1%7Dxy%5E2%5Cbigg%7C_%7By%3D0%7D%5E%7By%3D8x%7D%5C%2C%5Cmathrm%20dx)
![=\displaystyle56\int_{x=0}^{x=1}x^3\,\mathrm dx](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle56%5Cint_%7Bx%3D0%7D%5E%7Bx%3D1%7Dx%5E3%5C%2C%5Cmathrm%20dx)
![=14x^4\bigg|_{x=0}^{x=1}](https://tex.z-dn.net/?f=%3D14x%5E4%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%3D1%7D)
Answer:
Nothing further can be done to this topic
Step-by-step explanation:
Answer:
90 miles.
Step-by-step explanation:
Knowing that an inch is equal to 40 miles you can take 40 and multiply it by 2 1/4, thus getting 90. Or, you can break it down. 2 times 40 equals 80. This leaves 1/4 inch left to figure out. If you divide 40 by 4 (figuring out a fourth) you would get 10. Add 80 and 10 and you would have 90 miles.
A sinusoid is one that involves the sine or cosine of one of the variables.
Therefore, the only sinusoid is <span>y=sinx</span>