Question

Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.

If y varies directly as x and as the square of z, and when x = 5 and z = 1, find y when x = 1 and z = 4.
A) 1
B) 5
C) 25
D) 125

Answer 1

The constant of variation is 6. The equation for the statement is y = 6xz^2. When x = 1 and z = 4, y = 96.

Step-by-step explanation:

To find the constant of variation and write an equation for the statement, we can use the formula for direct variation:

y = kx

In this case, y varies directly as x and as the square of z, so the equation becomes:

y = kxz^2

To find the constant of variation, we can substitute the given values of x and z into the equation when x = 5 and z = 1:

y = k(5)(1^2)

Simplifying, we have:

y = 5k

Now we can solve for k by substituting the values of y and x:

30 = 5k

Solving for k, we get:

k = 6

Now that we have the value of k, we can substitute the given values of x and z when x = 1 and z = 4 into the equation:

y = 6(1)(4^2)

Simplifying, we get:

y = 6(1)(16)

y = 96