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# Inverse proportion problem

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You are given that \(x\) is directly proportional to \(y^3 \)  , and \(y \)  is inversely proportional to z . If the value of x is 3 when z is 12 , what is the value of x when 75  is equal to z? Express your answer as a common fraction.

Feb 11, 2019
edited by vindou  Feb 11, 2019

#3
+2

So   x = k y^3     but y = c/z        we can combine these by substituting in for y

x = k (c/z^3)   = kc/z^3      we can combine the constants k and c in to one constant k

x = k/z^3       when z = 12  x = 3    solve for k

3 = k /(12^3)      so k = 5184

when z= 75        x = 5184/75^3 =   5184/421875 =       192/15625

Feb 12, 2019

#1
+1

Read your question......you left off the really important relationship between y  and z.

Feb 11, 2019
#2
+1

ah sorry

vindou  Feb 11, 2019
#3
+2

So   x = k y^3     but y = c/z        we can combine these by substituting in for y

x = k (c/z^3)   = kc/z^3      we can combine the constants k and c in to one constant k

x = k/z^3       when z = 12  x = 3    solve for k

3 = k /(12^3)      so k = 5184

when z= 75        x = 5184/75^3 =   5184/421875 =       192/15625

ElectricPavlov  Feb 12, 2019
#4
+1

Thank you!

vindou  Feb 13, 2019