The direct variation of x to y implies that x and y increases at the same time, and the formula of x in terms of z is [tex]x = 4z^3[/tex]
The direct proportion of x to y is represented as:
[tex]x\ \alpha\ y^2[/tex]
As an equation, we have:
[tex]x\ =\ ky^2[/tex]
The direct proportion of y to z is represented as:
[tex]y\ \alpha\ z^3[/tex]
As an equation, we have:
[tex]y\ =\ kz^3[/tex]
Square both sides
[tex]y^2 = k^2z^3[/tex]
Substitute [tex]y^2 = k^2z^3[/tex] in [tex]x\ =\ ky^2[/tex]
[tex]x =k^3z^3[/tex]
When z = 2, x = 32.
So, we have:
[tex]32 =k^3 * 2^3[/tex]
Evaluate
[tex]32 =k^3 * 8[/tex]
Divide both sides by 8
[tex]k^3 =4[/tex]
Substitute [tex]k^3 =4[/tex] in [tex]x =k^3z^3[/tex]
[tex]x = 4z^3[/tex]
Hence, the formula of x in terms of z is [tex]x = 4z^3[/tex]
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