Answer:
![x=5](https://tex.z-dn.net/?f=x%3D5)
![y=8](https://tex.z-dn.net/?f=y%3D8)
![z=-3](https://tex.z-dn.net/?f=z%3D-3)
Step-by-step explanation:
We have been given a parallelogram. We are asked to solve for the values of x and y.
We know that opposite sides of parallelogram are equal, so we can set equation as:
![3x-3=x+7](https://tex.z-dn.net/?f=3x-3%3Dx%2B7)
![3x-x-3=x-x+7](https://tex.z-dn.net/?f=3x-x-3%3Dx-x%2B7)
![2x-3=7](https://tex.z-dn.net/?f=2x-3%3D7)
![2x-3+3=7+3](https://tex.z-dn.net/?f=2x-3%2B3%3D7%2B3)
![2x=10](https://tex.z-dn.net/?f=2x%3D10)
![\frac{2x}{2}=\frac{10}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B10%7D%7B2%7D)
![x=5](https://tex.z-dn.net/?f=x%3D5)
Similarly, we will solve for y.
![2y-6=y+2](https://tex.z-dn.net/?f=2y-6%3Dy%2B2)
![2y-y-6=y-y+2](https://tex.z-dn.net/?f=2y-y-6%3Dy-y%2B2)
![y-6=2](https://tex.z-dn.net/?f=y-6%3D2)
![y-6+6=2+6](https://tex.z-dn.net/?f=y-6%2B6%3D2%2B6)
![y=8](https://tex.z-dn.net/?f=y%3D8)
To solve for z, we will subtract y from x as:
![z=x-y\\z=5-8\\z=-3](https://tex.z-dn.net/?f=z%3Dx-y%5C%5Cz%3D5-8%5C%5Cz%3D-3)
Therefore, the value of z is negative 3.
The formula of an area of a triangle with base
b and height
h:
![A_{\Delta}=\dfrac{bh}{2}](https://tex.z-dn.net/?f=A_%7B%5CDelta%7D%3D%5Cdfrac%7Bbh%7D%7B2%7D)
We have:
![A_{\Delta}=672\ in^2\\b=5x-4\\h=2x](https://tex.z-dn.net/?f=A_%7B%5CDelta%7D%3D672%5C%20in%5E2%5C%5Cb%3D5x-4%5C%5Ch%3D2x)
![Domain:\\5x-4 > 0\to x > 0.8\\x > 0\\therefore\ D:x > 0.8](https://tex.z-dn.net/?f=Domain%3A%5C%5C5x-4%20%3E%200%5Cto%20x%20%3E%200.8%5C%5Cx%20%3E%200%5C%5Ctherefore%5C%20D%3Ax%20%3E%200.8)
Substitute:
Answer: x = 12 in.
Find a particle solution for differential equation in a form
where a is unknown coefficient.
If
then
Substitute these data into the differential equation:
![a\cdot e^x-5\cdot a\cdot e^x+5\cdot a\cdot e^x=3e^x,\\ \\a\cdot e^x=3e^x,\\ \\a=3.](https://tex.z-dn.net/?f=a%5Ccdot%20e%5Ex-5%5Ccdot%20a%5Ccdot%20e%5Ex%2B5%5Ccdot%20a%5Ccdot%20e%5Ex%3D3e%5Ex%2C%5C%5C%20%5C%5Ca%5Ccdot%20e%5Ex%3D3e%5Ex%2C%5C%5C%20%5C%5Ca%3D3.)
Thereofre, the particle solution for differential equation is
![y_p=3e^x.](https://tex.z-dn.net/?f=y_p%3D3e%5Ex.)
Answer:
111000 the ones have a greater value and then we can add the zeros