Very easy proportions question

[iamthewalrus]

hey its been a while since i had to do proportions so i was wondering if someone could show me how to solve a problem like this: if x increases by a factor of square root of 2, y decreases by 2, how are x and y related. just by looking at it, i can see that y = 1/x^2 but can someone show me a formal solution, i can't seem to come up with one!

ty.

 

[symbolipoint]

Best translation seems to be, directly as:

x*(2^(1/2))=y*(1/2)

But your provided wording may not exactly fit the proportion idea. Anyway, you should transcribe into conventional notation that you can more easily recognize (lack of typesetting here).

 

[iamthewalrus]

hi i tried the approach you suggested but when you solve for y in terms of x using that equation, you get

y = sqrt(2)/x which basically tells me y is inversely proportional to x whereas it is clear y is inversely proportional the square of x...

 

[symbolipoint]

iamthewalrus, possibly I mishandled the original translation. I will rethink this but someone else will probably respond before I do.

 

[Varnick]

IamtheWalrus, if you use Symbolipont's relationship, you should find that

$$y = 2\sqrt{2} x$$

Is this more helpful?

 

[iamthewalrus]

hi Varnick, thanks for your reply and you're right that's what symbolipoint's equation implies but it's not the correct answer. firstly, if y goes down when x goes up, wouldn't that suggest already some type of inverse relationship? the right answer is supposed to be y = 1/x^2 which seems to be more consistent with the conditions I initially stated.

 

[Varnick]

Where have you got this answer from? It does not appear to be consistent with your initial post (your first post would describe a relationship between y and x, not y and x squared).

V

 

[nothing123]

its from an MCAT question that asked about the relationship between intensity and f-stop of a camera. i just replaced the variables with y and x. and it seems plausible that if x increased by the square root of 2, y would decrease by 2 would describe a relationship where y = 1/x^2. that is, if x increases by sqrt(2), y decreases by [sqrt(2)]^2 = 2. anyways, that was the answer and it appears correct but it did not provide a formal proof for it.

 

[nothing123]

sorry posted on a friends account.