SOLUTION: Hi this is a word problem: Suppose z varies directly as x and inversely as the square of y. if z = 1/4 when x = 6 and y = 8, find z when x = 9 and y = 2. This is something tha

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi this is a word problem: Suppose z varies directly as x and inversely as the square of y. if z = 1/4 when x = 6 and y = 8, find z when x = 9 and y = 2. This is something tha      Log On


   

Question 110874This question is from textbook College Algebra
: Hi this is a word problem: Suppose z varies directly as x and inversely as the square of y. if z = 1/4 when x = 6 and y = 8, find z when x = 9 and y = 2.
This is something that I have attempted and I know I am way off:
1/4 = (k)6/8^2 k/64 1/4 = k/64 16 = k
z = (16(9)/2^2 144/4 = 36
Yeah way off base!!!
Thanks This question is from textbook College Algebra

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
z = 1/4 when x = 6 and y = 8. Find k[1]and k[2]
z%5B1%5D+=+k%5B1%5Dx%5B1%5D
z%5B1%5D+=+k%5B1%5D%2A6
k%5B1%5D+=+z%5B1%5D+%2F+6
------------------
z%5B1%5D+=+k%5B2%5D%2A%281%2F%28y%5B1%5D%29%5E2%29
z%5B1%5D+=+k%5B2%5D%2A%281%2F%288%5E2%29%29
k%5B2%5D+=+64%2Az%5B1%5D
------------------
k%5B1%5D+=+%281%2F4%29+%2F+6
k%5B1%5D+=+1%2F24
-------------------
k%5B2%5D+=+64%2A%281%2F4%29
k%5B2%5D+=+16
-------------------
Find z when x = 9 and y = 2
z%5B2%5D+=+k%5B1%5D%2Ax%5B2%5D
z%5B2%5D+=+%281%2F24%29%2A9
z%5B2%5D+=+3%2F8 answer
--------------------
z%5B3%5D+=+k%5B2%5D%2A%281%2F%28y%5B2%5D%29%5E2%29
z%5B3%5D+=+16%2A%281%2F4%29
z%5B3%5D+=+4
--------------------
z = 3/8 when x = 9, and z = 4 when y = 2
unless I goofed