8.6 * 7.5 divided by 2 is 32.25
Answer: 164
Step-by-step explanation:
1) y-2=x 2) y+1=x 3) 6x+3y=6 4) 3x-y=-2
2x+y=8 2x-y=0 2x+y=2 y=2x+3
Answer:
Option B. x = 13
Step-by-step explanation:
In this question, we shall give a separate diagram which will help us to further understand the question.
Please see attached photo for further details.
To find the value of x we shall use the pythagoras theory as illustrated below:
x is the longest side Therefore,
x² = 12² + 5²
x² = 144 + 25
x² = 169
Take the square root of both side
x = √169
x = 13
Therefore, the value of x 13.
![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:
a
Step-by-step explanation:
dont have a rectangler prism.