Suppose that y^3 varies inversely with . If y=2 when z=1, find the value of z when y=4. Express your answer in simplest fractional

If  y³  varies inversely with  z^1/3,  then you can use the formula:  y³  =  a / z^1/3  where a is the proportionality constant.

 

To find the value of a, use the information that  y = 2  when  z = 1:     

     --->     y³  =  a / z^1/3     --->     (2)³ =  a / (1)^1/3     --->      8  =  a / 1     --->     8 = a

 

So, the formula is:  y³  =  8 / z^1/3  

     --->     find the value of  z  when  y = 4     --->     (4)³  =  8 / z^1/3     --->    64  =  8 / z^1/3​  

     --->     multiply both sides by  z^1/3     --->     64z^1/3  =  8

     --->     divide both sides by  64    --->     z^1/3  =  8/64     --->     z^1/3  =  1/8

     --->     cube both sides     z  =  1/512