Hi  Anne,

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

L^2 - r^2 = a^2

r = L x Ac / G


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



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Anne Losch


Solving equations, graphing, evaluatin equations, factoring, functions, systems of equations, rational equations, exponent, complex numbers, word problems, logarithms, polynomials, and all topics in an Algebra 1, Algebra 2, or College Algebra class


I have a teaching certificate, I have taught Algebra 1 & 2 as well as tutored those subjects and tutored in College Algebra.

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