Answer:
5 ft
Step-by-step explanation:
The triangular face is a right triangle with hypotenuse 13 ft
Use Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
y² + 12² = 13²
y² + 144 = 169 ( subtract 144 from both sides )
y² = 25 ( take the square root of both sides )
y =
= 5
The height of the ramp is 5 ft
Answer:
I would say A lmk if im wrong.
Step-by-step explanation:
![y\ln(x^2+y^2+8)=3](https://tex.z-dn.net/?f=y%5Cln%28x%5E2%2By%5E2%2B8%29%3D3)
Differentiate both sides with respect to
:
![\dfrac{\mathrm dy}{\mathrm dx}\ln(x^2+y^2+8)+y\dfrac{\frac{\mathrm d}{\mathrm dx}[x^2+y^2+8]}{x^2+y^2+8}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cln%28x%5E2%2By%5E2%2B8%29%2By%5Cdfrac%7B%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E2%2By%5E2%2B8%5D%7D%7Bx%5E2%2By%5E2%2B8%7D%3D0)
We have by the chain rule,
![\dfrac{\mathrm d}{\mathrm dx}[x^2+y^2+8]=2x+2y\dfrac{\mathrm dy}{\mathrm dx}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E2%2By%5E2%2B8%5D%3D2x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D)
so that
![\dfrac{\mathrm dy}{\mathrm dx}\left(\ln(x^2+y^2+8)+\dfrac{2y^2}{x^2+y^2+8}\right)=-\dfrac{2xy}{x^2+y^2+8}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cleft%28%5Cln%28x%5E2%2By%5E2%2B8%29%2B%5Cdfrac%7B2y%5E2%7D%7Bx%5E2%2By%5E2%2B8%7D%5Cright%29%3D-%5Cdfrac%7B2xy%7D%7Bx%5E2%2By%5E2%2B8%7D)
![\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{2xy}{(x^2+y^2+8)\left(\ln(x^2+y^2+8)+\frac{2y^2}{x^2+y^2+8}\right)}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D-%5Cdfrac%7B2xy%7D%7B%28x%5E2%2By%5E2%2B8%29%5Cleft%28%5Cln%28x%5E2%2By%5E2%2B8%29%2B%5Cfrac%7B2y%5E2%7D%7Bx%5E2%2By%5E2%2B8%7D%5Cright%29%7D)
![\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{2xy}{(x^2+y^2+8)\ln(x^2+y^2+8)+2y^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D-%5Cdfrac%7B2xy%7D%7B%28x%5E2%2By%5E2%2B8%29%5Cln%28x%5E2%2By%5E2%2B8%29%2B2y%5E2%7D)
Answer:
15 feet per minute.
Step-by-step explanation:
- speed = distance ÷ time
- speed = 450 feet ÷ 30 minutes
- 15 feet per minute = 450 feet ÷ 30 minutes
Answer:
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Step-by-step explanation:
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