Answer:
![x=\dfrac{1+r}{r}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B1%2Br%7D%7Br%7D)
Step-by-step explanation:
Given equation:
![r=\dfrac{1}{(x-1)}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B1%7D%7B%28x-1%29%7D)
Multiply both sides by (x - 1):
![\implies r(x-1)=\dfrac{1}{(x-1)} \cdot (x-1)](https://tex.z-dn.net/?f=%5Cimplies%20r%28x-1%29%3D%5Cdfrac%7B1%7D%7B%28x-1%29%7D%20%5Ccdot%20%28x-1%29)
![\implies r(x-1)=1](https://tex.z-dn.net/?f=%5Cimplies%20r%28x-1%29%3D1)
Expand the brackets:
![\implies rx-r=1](https://tex.z-dn.net/?f=%5Cimplies%20rx-r%3D1)
Add r to both sides:
![\implies rx-r+r=1+r](https://tex.z-dn.net/?f=%5Cimplies%20rx-r%2Br%3D1%2Br)
![\implies rx=1+r](https://tex.z-dn.net/?f=%5Cimplies%20rx%3D1%2Br)
Divide both sides by r:
![\implies \dfrac{rx}{r}=\dfrac{1+r}{r}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Brx%7D%7Br%7D%3D%5Cdfrac%7B1%2Br%7D%7Br%7D)
![\implies x=\dfrac{1+r}{r}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D%5Cdfrac%7B1%2Br%7D%7Br%7D)
Answer:
3 feet
Step-by-step explanation:
12 inches = 1 foot
36 inches = 36 / 12 = 3 feet
Answer:
![x=8\sqrt{5}](https://tex.z-dn.net/?f=x%3D8%5Csqrt%7B5%7D)
Step-by-step explanation:
I will assume the following:
- You know how to use the quadratic formula
- You know how to simplify radicals
- You know how to use the pythagorean theorem.
The challenge of this exercise comes from using the pythagorean theorem and setting up a few equations.
Given that we have a segment 36 units long and another segment that is 16, it is trivial to get the other segment, 20. Additionally, there are two sides that I want to name so that way I can make a couple of substitutions. I will call these side a and side b. (see attachment 1)
Now comes with setting up three equations. I will start with the two smaller triangles, using side a and side b. See attachments 2 and 3.
Now with the big triangle. I will set up one last equation. See attachment 4.
Given what we know about attachment 2 and 3, we can make two substitutions. See attachment 5. I assume you know how to do the rest and arrive at your only real solution.
Answer:
Andre's
Step-by-step explanation
I think its Andre. I apologize if it is not.