kyle throws a baseball into the air and the height of the ball, h meters, above the ground after t seconds is represented by the equation h=-4t^2+32t
between which 2 times is the ball higher than 48 meters
if you solve -4t^2+32t = 48
you get t = 2,6
so, what do you think?
To find the times at which the ball is higher than 48 meters, we need to solve the equation h = -4t^2 + 32t > 48.
First, we rewrite the inequality as -4t^2 + 32t - 48 > 0.
Next, we divide the inequality by -4 to simplify it: t^2 - 8t + 12 < 0.
To solve this quadratic inequality, we factor it by finding two values whose sum is -8 and whose product is 12. In this case, the values are -2 and -6.
So, the factored form of the inequality becomes (t - 2)(t - 6) < 0.
To determine the solution, we set each factor less than zero and solve for t:
1. t - 2 < 0
t < 2
2. t - 6 < 0
t < 6
So, the ball is higher than 48 meters between t = 2 seconds and t = 6 seconds.