Question

Question on answer

og question:The pythagorean theorem of baseball is a formula for approximating a team's ratio of wins to games played. let R be the number of runs the team scores during the season, A be the number of run allowed to opponents, W be the # of wins, G be the total of games played. Then the formula W/G≈ R^2/R^2 + A^2 approximates the teams' ratio of wins to games played.

A. solve the formula for A in terms of w, g, and R


I just dont see how you went from (R^2 + A^2 = R^2 * g/w. ) to this =
A^2 = R^2 (g/w - 1)

because would you just subtract/cancel r^2 away?

Thank you

Answer 1

Don't know what the original question was, can't look for it since you did not
give yourself a name, and you didn't indicate who the tutor was ....


Depends if you meant:
W/G≈ R^2/R^2 + A^2 as you typed it, or

W/G≈ R^2/(R^2 + A^2) which makes more sense , since in the original it would
immediately reduce to
W/G≈ 1 + A^2
so....

W/G≈ R^2/(R^2 + A^2)
W(R^2 + A^2) = G R^2 , I cross-multiplied
divide both sides by W
R^2 + A^2 = G R^2/W
subtract R^2 from both sides
A^2 = GR^2/W - R^2 = R^2(G/W - 1)
A = √(R^2(G/W - 1))

looks like the explanation lies in the 2nd last line