Answer to Question #279829 in Algebra for Nickle

Question

The curve formed by a rope bridge can be modeled by the relation y = x^2 - 11x + 10, where "x" is the horizontal distance in metres and "y" is the height in metres. What is the horizontal distance from one end of the bridge to the other end?

show me how

Answer 1

$$y=0=>x^2 - 11x + 10=0$$

$$(x-1)(x-10)=0$$

$$x_1=1, x_2=10$$

$$distance=d=x_2-x_1=10-1=9(m)$$

The horizontal distance from one end of the bridge to the other end is $9$ metres.