Question

First, how long will it take for the music player to fall to the bottom of the ravine? Solve the equation and find the values of t.


`t = \sqrt{(8t + 24)/(16)}`

Option 1: 1.00 seconds
Option 2: 1.25 seconds
Option 3: 1.50 seconds
Option 4: 1.75 seconds

Answer 1

To find the value of t in the equation t = sqrt((8t + 24)/16), we need to square both sides of the equation, simplify, and solve the resulting quadratic equation. The value of t is 1.00 s.

Step-by-step explanation:

To find the value of t in the equation t = √((8t + 24)/16), we can square both sides of the equation to eliminate the square root. This gives us t^2 = (8t + 24)/16. Next, we can cross multiply to get rid of the fraction, resulting in 16t^2 = 8t + 24. By rearranging the equation and bringing all the terms to one side, we have a quadratic equation 16t^2 - 8t - 24 = 0. We can solve this equation either by factoring or by using the quadratic formula. In this case, the quadratic formula is the most convenient option. By substituting the values into the formula, we find that the solutions are t = 1.00 s and t = -1.50 s. Since time cannot be negative in this context, we discard the negative solution. Therefore, the value of t is 1.00 s.