Inverse Variation: If y varies inversely with the square of x, and y is 4 when x is 16, find y when x is 64.

Question

Inverse Variation.

Answer 1

For y to vary inversely with x², first write a general equation:

 

y = A/x²

 

4 = A/(16)²

 

A = ?

 

Solve for A, then plug in x = 64 to your function.

Answer 2

y=k/x²

4=k/16²

4*16²=k

4*256=k

k=1024

y=1024/x²

y=1024/64²

y=1024/4096

simplify the fraction...

1024/4096=512/2048=256/1024=128/512=64/256=32/128=16/64=8/32=1/4

y=1/4

note: you should be able to simplify the fraction by dividing both terms by 4 to begin with...

1024/4096=256/1024

divide by 4 again

256/1024=64/256

divide by 4 or 8

64/256=16/64

divide by 16

16/64=1/4

Answer 3

y = k/x²

 

4 = k/16²

 

k = 16²(4) = 1024

 

y = 1024/x²

 

x = 64 ⇒ y = 1024/64² = 0.25