Answer:
The ball will be the 7 ft high at 2 different times.
Step-by-step explanation:
The height in meters of the ball is given by the following equation:
[tex]h(t) = -16t^2 + 25t[/tex]
7 feet high
The height, by the equation, is given in meters, so we have to work in meters. Since each feet has 0,3048 meters, 7 feet have have 2.1336 meters. So, we have to solve the following equation
[tex]2,1336 = -16t^2 + 25t[/tex]
[tex]16t^2 - 25t + 2,1336 = 0[/tex]
At how many different times will the ball be 7 ft. High?
We have to find the number of solutions for the equation above.
It is given according to the value of [tex]\Delta = b^2 - 4ac[/tex]. If it is positive, there are two solutions, zero one solution and negative no solutions.
In this equation [tex]a = 16, b = -25, c = 2.1336[/tex]. So
[tex]\Delta = b^2 - 4ac = (-25)^2 - 4*16*2.1336 = 488[/tex]
Since the coefficient is positive, the ball will be the 7 ft high at 2 different times.
