Landon is standing in a hole that is 6.5 ft deep. He throws a rock, and it goes up into the air, out of the hole,

Question

and then lands on the ground above. The path of the rock can be modeled by the equation y = 0.005x +
0.42x 6.5, where x is the horizontal distance of the rock, in feet, from Landon and y is the height, in feet, of
the rock above the ground. How far horizontally from Landon will the rock land?
a. 63.54 ft c. 10.23 ft
b. 20.46 ft d. 31.77 ft

Answer 1

To find where the rock will land, we need to find the point where y = 0 (i.e. the height of the rock is 0, indicating it has landed on the ground).

0 = 0.005x + 0.42x - 6.5

Combining like terms:

0.425x - 6.5 = 0

Adding 6.5 to both sides:

0.425x = 6.5

Dividing by 0.425:

x = 15.29

Therefore, the rock will land 15.29 feet horizontally from Landon.

The closest answer choice is (c) 10.23 ft, which is not correct.