The variable z is directly proportional to x, and inversely proportional to y. when x is 16 and y is 17, z has the value 11.294117647059. what is the value of z when x= 22, and y= 26

Lets suppose k is the constant of proportionality.

z = k * x / y

when x is 16 and y is 17, z has the value 11.294117647059

11.294117647059 = k * 16/17

Multiplying 17 on both sides

11.294117647059 * 17 = k * 16

192 = k * 16

Dividing 16 on both sides

192/16 = k

k = 12

Now when x= 22, and y= 26

z = k * x/y

z = 12 * 22 / 26

z = 10.1538461538 : Answer

Hope it will help :)

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

b, i believe, but not sure.