Y is directly proportional to x and inversely proportional to the square of z and y = 40 when x = 80 and z = 4, how do you find y when x = 7 and z = 16?

##y=7/32## when ##x=7## and ##z=16##

##y## being directly proportional to ##x## and inversely proportional to the square of ##z## means there is a constant ##k## such that ##y=kx/z^2=(kx)/z^2##.

Since ##y=40## when ##x=80## and ##z=4##, it follows that ##40=(80k)/4^2=5k## which implies ##k=8##.

Therefore, ##y=(8x)/z^2##.

Hence, when ##x=7## and ##z=16##, ##y=56/16^2=7/(2*16)=7/32##.