Answer:
The time taken by the ball to reach the ground is 7 seconds.
Step-by-step explanation:
Given : A ball is thrown in the air from a ledge. Its height in feet is represented by [tex]f(x) = -16(x^2-6x-7)[/tex], where x is the number of seconds since the ball has been thrown. The height of the ball is 0 feet when it hits the ground.
To find : How many seconds does it take the ball to reach the ground?
Solution :
The function
[tex]f(x) = -16(x^2-6x-7)[/tex] represent the height of the ball.
Where, x is the number of seconds.
We have given that the height of the ball is 0 feet when it hits the ground
and we to find the seconds does it take the ball to reach the ground.
i.e., we have to take f(x)=0 and find x.
[tex]0= -16(x^2-6x-7)[/tex]
[tex]x^2-6x-7=0[/tex]
Applying middle term split,
[tex]x^2-7x+x-7=0[/tex]
[tex]x(x-7)+1(x-7)=0[/tex]
[tex](x-7)(x+1)=0[/tex]
[tex]x=7,-1[/tex]
x=-1 is rejected as time is not negative.
x=7 is accepted.
Therefore, The time taken by the ball to reach the ground is 7 seconds.
