Homework Soursey varies directly as the cube of x and inversely as the squa
y varies directly as the cube of x and inversely as the square of z. If y= 16 when x= 5 and z= 18, find yy when x= 12 and z= 5. Round the answer to the nearest hundredth.
Solution
Since y varies directly as the cube of x and inversely as the square of z, we have y = px3 ...(1) and y = q/z2 ,,,(2) where p and q are constants of proportionality. Since y = 16 when x = 5 and z = 18, on substituting these values of x and y in the 1st equation , and y and z in the 2nd equation, we have 16 = p*(5)2 , or, 25p = 16 so that p = 16/25 and, 16 = q/ (18)2 or, q = 16*(18)2 or, q = 5184. Then y = 16/25 x3 and y = 5184/z2. Then y = (16/25 )x3 (5184/z2) = = 16*5184/25)( x3 / z2). Thus, when x = 12 and z =5, we have yy =(16*5184/25)[ (12)3 / (5)2 ] =(82944/25)(1728/25) = 143327232/625 = 229.32 ( on rounding off to the nearest hundredth)
