Landon is standing in a hole that is 6.5 m deep. He throws a rock, and it goes up into the air, out of the hole, and then lands on the ground above. The path of the rock can be modeled by the equation y equals negative 0.05x^2+4.5x-6.5, where x is the horizontal distance of the rock, in meters, from Landon and y is the height, in meters, of the rock above the ground. How far horizontally from Landon will the rock land? Round your answer to the nearest hundredth of a meter.

Question

Mathematics

Emilio Ortiz

31 July, 19:58

Landon is standing in a hole that is 6.5 m deep. He throws a rock, and it goes up into the air, out of the hole, and then lands on the ground above. The path of the rock can be modeled by the equation y equals negative 0.05x^2+4.5x-6.5, where x is the horizontal distance of the rock, in meters, from Landon and y is the height, in meters, of the rock above the ground. How far horizontally from Landon will the rock land? Round your answer to the nearest hundredth of a meter.

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Answers (1)

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Mcclain · Answer 1

Given the model for the rock is:

f (x) = 0.05x^2+4.5x-6.5

to evaluate the horizontal distance we find the x-intercept of the function.

We shall have:

f (x) = 0.05x^2+4.5x-6.5

at x-intercept, f (x) = 0

thus

equation the function to x and solving for x we get:

0.05x^2+4.5x-6.5=0

the value of x will be:

x=-91.422 or x=1.42198

thus the horizontal distance will be 1.42198 m