SOLUTION: when y varies directly with the square of a and inversely with the square root of b. If y=6 when a=4 and b=16, find y when a=8 and b=4?

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Question 1174304: when y varies directly with the square of a and inversely with the square root of b. If y=6 when a=4 and b=16, find y when a=8 and b=4?
Found 3 solutions by ankor@dixie-net.com, Edwin McCravy, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
when y varies directly with the square of a and inversely with the square root of b.
y+=+%28ka%5E2%29%2F%28sqrt%28b%29%29
If y=6 when a=4 and b=16
find k
%284%5E2k%29%2Fsqrt%2816%29 = 6
%2816k%29%2F4 = 6
mult by 4
16k = 4*6
k = 24/16
k = 1.5
:
find y when a=8 and b=4?
y = 1.5%288%5E2%29%2Fsqrt%284%29
y = 1.5%2864%29%2Fsqrt%284%29
y = 96%2F2
y = 48
:
Sorry about this unforgivable error!

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
So plug k = 6 in here:

y+=+%28ka%29%2F%28sqrt%28b%29%29 <-- Ankor showed you how to get this

And get

y+=+%286a%29%2F%28sqrt%28b%29%29 

Now plug in a=8 and b=4 and simplify.

Edwin

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Neither response you have received to this point uses the defined variation. The problem says the direct variation is with the square of a, not just a. The starting point for the solution should be

y+=+k%28a%5E2%2Fsqrt%28b%29%29

That of course will change the final answer.

I would solve the problem in a less formal way, by using the defined variations and how the input values change.

a doubles from 4 to 8, a factor of 2. Since y varies directly as the square of a, this increases y by a factor of 2^2=4.

b gets cut from 16 to 4, a factor of 1/4. Since y varies inversely as the square root of b, this changes y by a factor of 1%2Fsqrt%281%2F4%29+=+1%2F%281%2F2%29+=+2.

So the changes in the two input values change the original y value by a factor of 4*2=8.

ANSWER: When a=8 and b=4, the value of y is 6*8 = 48.