Verified answer

√x y = k

(√12) (8) = k

k = 16√3

y = 16√3 / √6

y = 16 / √2

y = 8 √2

RE: If y varies rapidly with x, and y=10 while x=15, discover y while x=6.? If x varies inversely as y and x=2 while y=8, discover x while y=17. If y varies rapidly as x and inversely as z^2, and y=3 while x=2 and z=4, what's the fee of x while y=9 and z=4?

varies inversely means y = k/√x, k constant number

when x = 12, y = 8

8 = k/√12

k = 8√(12) = 16√(3)

y = 16√(3) /√x

when x = 6

y= 16√(3) /√6 = 16/√(2) = 8√(2)

y varies inversely as √x means that y = c/√x for some constant c. You can use the given data that y = 8 when x = 12 to find c.

things that vary inversely to each other have a common product.

So there is a constant c with y sqrt(x) = c

now plug in 8,12

8sqrt(12) = c

ysqrt(6) = c

y = 8sqrt(12)/sqrt(6) = 8sqrt(2)

y=k/sqrt(x)

8=k/sqrt(12)

k=sqrt(12) x 8

when x=6,

y=sqrt(12) (8)/ sqrt(6) (answer)

=3.464(8)/sqrt(6)

11.313

check my calculation.