If r varies inversely with w -1. If r = 3/50 when w = 3, how do you find r when w is 10?

Question

If r varies inversely with w -1.  If r = 3/50 when w = 3, how do you find r when w is 10?

Eli Assouline · Accepted Answer

undefined To find r when w is 10, we can use the inverse variation equation. First, we need to find the constant of variation, which is denoted as k. In this case, we have r varies inversely with w - 1, so we can write the equation as r = k/(w - 1).

To find k, we can substitute the given values of r and w into the equation. When r = 3/50 and w = 3, we have 3/50 = k/(3 - 1).

Simplifying this equation, we get 3/50 = k/2.

To solve for k, we can cross-multiply: 3 * 2 = 50 * k.

Simplifying further, we have 6 = 50k.

Dividing both sides by 50, we find k = 6/50 = 3/25.

Now that we have the value of k, we can substitute it back into the inverse variation equation and solve for r when w is 10.

Using r = k/(w - 1), we have r = (3/25)/(10 - 1).

Simplifying this equation, we get r = (3/25)/9 = 3/225 = 1/75.

Therefore, when w is 10, r is equal to 1/75.

Avery Alexander · Answer

# r= 3/(25(w-1))#

#r " "alpha" " 1/(w-1)#

Let the constant of variation be #k# then:

#r=k/(w-1)#

Given condition#" "-> 3/50=k/(3-1) -> 3/50=k/2#

Multiply both sides by 2

#k=6/50=3/25#

Thus the equation is #r=3/25xx1/(w-1) -> r= 3/(25(w-1))#