Answer to Question #142557 in Algebra for Solana

Question

Latoya throws a ball from the top of a bridge her throat is mauled by the equation y = -0.5x^2+3x+10 and the bridge is modeled by the equation

y = -0.2x + 7, how far does the ball travel horizontally before its first bounce?

Answer 1

The first bound takes place when y and x-coordinates of the ball may be substituted in the equation of the bridge, so

$-0.5x^2+3x+10 = -0.2x+7.$

Simplifying the equality, we get

$x^2-6.4x-6=0.$

$D = 6.4^2+6\cdot4=64.96,\;\; \sqrt{D}\approx 8.06, \;\; x_1 = -0.83, \;\; x_2 = 7.23.$

We should choose the positive root, so x = 7.23 m.