Question

If Z varies directly as y and inversely as square root of x and z = 5, when y =3,x=9. Find the value of z when y=18 and x = 25.

Answer 1

18

Explanation:

`z \alpha y \\z\alpha (1)/(√(x) ) \\z \alpha (y)/(√(x) ) \\z = (ky)/(√(x) ) -------(1)\\\\5 = (3k)/(√(9) ) \\ 5 = (3k)/(3) \\3k = 15\\k = 15/3\\k = 5\\Substitute 5 for k in eq 1\\z = (5y)/(√(x) )\\ z=?\\ y=18 \\ x = 25.\\z = (5y)/(√(x) )\\z = (5(18))/(√(25) )\\z= (90)/(5) \\z = 18`

I hope i am correct