Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.
2 answers:
Answer: option d.
Step-by-step explanation:
If <em>y </em>varies directly as <em>x</em> and <em>z</em>, the form of the equation is:

Where<em> k</em> is the constant of variation.
If y=4 when x=6 and z=1 then substitute these values into the expression and solve for <em>k:</em>

<em> </em>Substitute the value of <em>k</em> into the expression. Then, the equation is:

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


<em> </em>
Answer:
Choice D is correct.
Step-by-step 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.
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