Question

Solve the problem. Show how you used a real number line to solve the polynomial inequality. An arrow is fired straight up from the ground with an initial velocity of 240 feet per second. Its height, s(t), in feet t any time t is given by the function s(t) = -16t2 + 240t. Find the interval of time for which the height of the arrow is greater than 116 feet.

A. t ∈ (-[infinity], -7.5)
B. t ∈ (-7.5, 7.5)
C. t ∈ (7.5, [infinity])
D. None

Answer 1

To solve the inequality, we need to find the values of t for which the height of the arrow is greater than 116 feet. By graphing or using the quadratic formula, we find that the interval of time for which the height of the arrow is greater than 116 feet is t ∈ (1.25, 14.75).

Step-by-step explanation:

To solve the inequality, we need to find the values of t for which the height of the arrow is greater than 116 feet. We can do this by setting the function s(t) = -16t^2 + 240t greater than 116 and solving for t.

-16t^2 + 240t > 116

We can rearrange this equation to have 0 on one side:

-16t^2 + 240t - 116 > 0

Next, we can graph the quadratic equation on a real number line. The solution will be the interval(s) where the graph is above the x-axis (greater than 116). The two points where the graph intersects the x-axis will be the endpoints of the interval.

By graphing or using the quadratic formula, we find that the two solutions are approximately t ≈ 1.25 and t ≈ 14.75. Therefore, the interval of time for which the height of the arrow is greater than 116 feet is t ∈ (1.25, 14.75).