Answer:
The height of the prism measures 22 meters
The volume of the prism measures 10,890 cubic meters.
Step-by-step explanation:
The height is twice the width of the prism.
The prism's width is 11 meters.
2 x 11 = 22
The volume of a rectangular prism is calculated as:
V = l x w x h
So, the volume is:
V = 45 x 11 x 22
The volume is 10,890 cubic meters.
Hope this helps!
<span>9, 12, 19, 30, ...
</span>formula for the nth term is;
<span>2n^2 + 3n - 10</span>
Multiplying both sides by
gives
![xy^2\dfrac{\mathrm dy}{\mathrm dx}+y^3=1](https://tex.z-dn.net/?f=xy%5E2%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%2By%5E3%3D1)
so that substituting
and hence
gives the linear ODE,
![\dfrac x3\dfrac{\mathrm dv}{\mathrm dx}+v=1](https://tex.z-dn.net/?f=%5Cdfrac%20x3%5Cdfrac%7B%5Cmathrm%20dv%7D%7B%5Cmathrm%20dx%7D%2Bv%3D1)
Now multiply both sides by
to get
![x^3\dfrac{\mathrm dv}{\mathrm dx}+3x^2v=3x^2](https://tex.z-dn.net/?f=x%5E3%5Cdfrac%7B%5Cmathrm%20dv%7D%7B%5Cmathrm%20dx%7D%2B3x%5E2v%3D3x%5E2)
so that the left side condenses into the derivative of a product.
![\dfrac{\mathrm d}{\mathrm dx}[x^3v]=3x^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E3v%5D%3D3x%5E2)
Integrate both sides, then solve for
, then for
:
![x^3v=\displaystyle\int3x^2\,\mathrm dx](https://tex.z-dn.net/?f=x%5E3v%3D%5Cdisplaystyle%5Cint3x%5E2%5C%2C%5Cmathrm%20dx)
![x^3v=x^3+C](https://tex.z-dn.net/?f=x%5E3v%3Dx%5E3%2BC)
![v=1+\dfrac C{x^3}](https://tex.z-dn.net/?f=v%3D1%2B%5Cdfrac%20C%7Bx%5E3%7D)
![y^3=1+\dfrac C{x^3}](https://tex.z-dn.net/?f=y%5E3%3D1%2B%5Cdfrac%20C%7Bx%5E3%7D)
![\boxed{y=\sqrt[3]{1+\dfrac C{x^3}}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D%5Csqrt%5B3%5D%7B1%2B%5Cdfrac%20C%7Bx%5E3%7D%7D%7D)
The discount price if the discount is 15% would be... $198.
Hope I could help! :)