we are given
[tex]y=-0.05x^2+4.5x-6.5[/tex]
where
x is the horizontal distance of the rock in meters, from Landon
y is the height, in meters, of the rock above the ground
we know that when rock lands vertical distance will become 0
so, we set y=0
and then we can solve for x
[tex]y=-0.05x^2+4.5x-6.5=0[/tex]
Multiply both sides by 100
[tex]-0.05x^2\cdot \:100+4.5x\cdot \:100-6.5\cdot \:100=0\cdot \:100[/tex]
[tex]-5x^2+450x-650=0[/tex]
now, we can use quadratic formula
[tex]x=\frac{-450\pm \sqrt{450^2-4\left(-5\right)\left(-650\right)}}{2\left(-5\right)}[/tex]
[tex]x=45-\sqrt{1895},\:x=45+\sqrt{1895}[/tex]
[tex]x=1.4684,x=88.531[/tex]
now, we can find horizontal distance
so, horizontal distance is
[tex]=88.531-1.4684[/tex]
[tex]=87.06m[/tex]..................Answer
