Inverse proportions?

Question

Suppose that y is inversely proportional to square root of x.

Find the constant of proportionality k if y = 12 when x = 16.

k = 

Using the k from above write the variation equation in terms of x.

y =   

Using the k from above find y given that x = 20.

y = 

If needed, round answer to 3 decimal places.

Enter DNE for Does Not Exist, oo for Infinity

Answer 1

y =k/sqrx

12 = k/sqr16 = k/4

k = 4(12) = 48 = the constant of proportionality

y = 48/sqrx

if x= 20

y = 48/sqr20 = 48(sqr20)/20 = (12/5)sqr20 = 2.4sqr20

= about 10.733