if xr=v, v=kr, and rv=~0, which of the following is equal to k?

Question

if xr=v, v=kr, and rv=~0, which of the following is equal to k?

Answer 1

If xr = v, and v = kr, then xr = kr
(Why? Since both expressions equal v, they must be equal to each other. Like if 1 + 2 = 3, and 10 - 7 = 3, 1 + 2 must equal 10  - 7. This is called the transitive property.)

Since xr = kr and r ≠ 0 (if rv ≠ 0, then neither r nor v can be zero), we can divide both sides by r to get
x = k

Answer 2

Given the following information:    (1.)  xr=v

                                                  (2.)  v=kr

                                                  (3.)  rv=~0  

..... find k .

First, use (2.) to solve for k by dividing both sides of the equation by r:

    v=kr   ===>   v/r = kr/r   ===>   k=v/r

Then, notice that when you divide both sides of equation (1.) by r, you arrive at the following:

    xr=v   ===>   xr/r = v/r   ===>   x=v/r

Thus, since k=v/r and x=v/r, k=x.

We can verify the above by looking at (3.) and noticing that when we solve for either r or v we arrive at the following:

   rv=~0   ===>   rv/v = ~0/v   ===>   r= ~0/v 

   rv=~0   ===>   rv/r = ~0/r   ===>   v= ~0/r 

So, v/r= (~0/r) / (~0/v) =  (~0/r) * (v/~0) = (~0v)/(~0r) = v/r, which is true...

...and thus, k=x holds true.