If y varies jointly as the cube of x, w, and the square of z, what is the effect on w when x, y, and z are doubled?

1 Answer
Jun 1, 2017

Answer:

#w# decreases by a factor of 16.

That is, #w_"new" = 1/16w#

Explanation:

Based on this description, we can create the following equation:

#y = kx^3wz^2#

Where #k# is a constant which doesn't really matter for this particular problem.

The problem asks what happens to #w# when the other variables are doubled, so let's solve for #w# to see what it is originally.

#y = kx^3wz^2#

#y/(kx^3z^2)=w#

Now, the problem asks us to double everything except #w# and see what happens.

#((2y))/(k(2x)^3(2z)^2)=w_"new"#

#(2y)/(k(8x^3)(4z^2))=w_"new"#

#2/(8*4)(y/(kx^3z^2))=w_"new"#

#1/16(y/(kx^3z^2))=w_"new"#

#1/16w = w_"new"#

So #w# decreases by a factor of 16 when the other 3 variables are doubled.

Final Answer