Question

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

Answer 1

Choice D is correct.

Explanation:

We have given that

If y varies directly as x and z,

y ∝ xz

y = kxz eq(1)

where k is constant of variation.

As given that y = 4 when x = 6 and z = 1

4 = k(6)(1)

4 = k(6)

4 = 6k

k = 4/6

k = 2/3

Putting the value of k in eq(1), we have

y = 2/3xz

Now, we have to find the value of y when x = 7 and z = 4

y = 2/3(7)(4)

y = 56/3

Hence, Choice D is correct.

Answer 2

Answer: option d.

Explanation:

If y varies directly as x and z, the form of the equation is:

`y=kxz`

Where k is the constant of variation.

If y=4 when x=6 and z=1 then substitute these values into the expression and solve for k:

`4=k(6)(1)\\4=6k\\k=(4)/(6)\\\\k=(2)/(3)`

Substitute the value of k into the expression. Then, the equation is:

`y=(2)/(3)xz`

To find the value of y when x=7 and z=4, you must substute these values into the equation. Therefore you obtain:

`y=k=(2)/(3)(7)(4)`

`y(7,4)=(56)/(3)`