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Hi Anne,

How do I combine these two equations to solve for " a ".

L^2 - r^2 = a^2

r = L x Ac / G

Thanks,

AL

WowGoHere.com

Hi Al, I will be happy to assist you.

First I assume capital A is a different variable than the lower case a you want to solve for.

Because L^2 - r^2 = a^2, taking the square roots of both sides gets

a = sqrt(L^2 - r^2)

what is also known is r= L x Ac/G

substituting this in gets

a = sqrt(L^2 - (L x Ac/G)^2)

Squaring L x Ac/G gets

a = sqrt(L^2 - L^2 x (Ac)^2/G^2)

Factoring out the L^2 and taking the square root of it gets

a = Lsqrt(1 - (Ac)^2/G^2)

I'm keeping Ac in parenthesis because I am unsure if it is one variable or two

1 can be rewritten as G^2/G^2 so the denominator of G^2 can be factored out, and square rooted to get

a = (L/G)sqrt(G^2 - (Ac)^2)

Please let me know if you are unsure how I got this.

I hope this helps

Anne

Algebra

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