Question

A ball is dropped from a building at the same time a balloon rises from the ground. The heights, in feet, of the ball and balloon above the ground after x seconds are modeled by the functions below. Ball: f(x)=24−16x2Balloon: g(x)=4x After how many seconds are the ball and the balloon at the same height? Use a graphing calculator and round to the nearest hundredth. A. 1.36 B. 4.42 C. 1.11 D. 5.42

Answer 1

Answer:

C.  1.11

Step-by-step explanation:

Ball: f(x) = 24 − 16x^2

Balloon: g(x) = 4x

4x = 24 - 16x^2

16x^2 + 4x - 24 = 0

4x^2 + x - 6 = 0

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \dfrac{-1 \pm \sqrt{1^2 - 4(4)(-6)}}{2(4)}$

$x = \dfrac{-1 \pm \sqrt{1 + 96}}{8}$

$x = \dfrac{-1 \pm \sqrt{97}}{8}$

$x = \dfrac{-1 + \sqrt{97}}{8}$   or   $x = \dfrac{-1 - \sqrt{97}}{8}$

We discard the negative solution.

$x = 1.11$

Answer: C.  1.11