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# Algebra/Combine

Question
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

Volunteer

#### Anne Losch

##### Expertise

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

##### Experience

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

Organizations
NEA, past NCTM, MAA, AMS, and ASCD

Education/Credentials
I hold a B.S. in mathematics and computer science from an accredited university and have gone back to school to get my teacher certificate. I hold more than enough credits for an education minor.

Past/Present Clients
I have worked at tutoring centers including Sylvan Learning and Huntington Learning Center. I have posted answers to mathematical questions on answers.com but would rather volunteer with AllExperts.