variation question, y=kx^(3/2)?

Question

equation:
y=kx^(3/2)
variables:
y=96
x=16
solve for k.
do i need to divide both sides by 16 first? thanks for the help.

Answer 1

They give us the values of x and y.

Plug those values into the given equation and simplify.

y = kx^(3/2)

96 = k(16)^3/2

You need to reduce 16 raised to the fraction 3/2 as step one.

I'll do that first.

16^(3/2) can also be written as the square root of 16 to the third power.

We have:

16^(3/2) = sqrt({16})^3 = 4x4x4 = 64

So, x= 64.

96 = k64

Next: Divide each side of the equation by 64 to find k.

96/64 = k

6/4 = k

3/2 = k

Guido

Answer 2

You cannot divide by 16, because we have a power of x
You can proceed as follows:
y = k x^ (3/2)

Substitute the known values, 96 = k 16^(3/2)
Then we have,...........96 = 64 k
Solve for k,.................k = 96/ 64 = 1.5

Very easy, even I can do it. Now you learn it.

Answer 3

y = kx^(3/2)

96 = k * (16^(3/2))
96 = k * (sqrt(16))^3
96 = k * 4^3
96 = k * 64
k = (96/64)
k = (3/2)

Answer 4

y=kx^(3/2)
variables:
y=96
x=16
solve for k.

96=k(16)^{3/2}
96=k (64)
96/64 =y
y=3/2

Answer 5

96 = k * 16^(3/2)
=> k = ( 2^5*3 ) / [(2^4)^(3/2)]
=> k = (2^5 * 3 )/(2^6) = 3/2
k = 3/2