Math homework problem due tonight!

[Sarah_Alyse]

This is the question:
H is jointly proportional to the squares of L and W. If L=2 and W=1/3, then H=36. Find the constant of proportionality, k, and write the equation.

This is the work that I did.. not confident it is right..i dont know how to make the little two so im putting (squared)
H=KL(squared)W(squared)
36= (K) (2)squared (1/3)squared
4 times .1111
36= .444K
81=K

 

[chrisr]

Correct.

It's simpler to stick with fractions...

\(\displaystyle H=kL^2W^2\)

\(\displaystyle 36=k(2^2)(\frac{1}{3})^2=\frac{4k}{9}\)

\(\displaystyle k=\frac{36(9)}{4}=9^2\)

\(\displaystyle H=(9LW)^2\)