Answer:
The ball reaches a height of 126.58 ft after 2.8125 seconds
Step-by-step explanation:
The maximum height of a parabola can always be found by looking for the vertex. You can find the x value (or in this case the t value) of a vertex by using -b/2a in which a is the coefficient of x^2 and b is the coefficient of x.
-b/2a
-(90)/2(-16)
-90/-32
2.8125 seconds
Now to find the height, we input that value in for t
h = -16t^2 + 90t
h = -16(2.8125)^2 + 90(2.8125)
126.58 feet
Ball takes 2.8 seconds to reach maximum height
Maximum height of the ball is 126.56 feet
Domain : [tex]\left(0 \:,\:\infty \:\right)[/tex]
Range: [tex]\:[0\:,\:\frac{2025}{16}][/tex]
Given :
The equation h(t) = -16t^2+90t gives the height h of the ball after t seconds
Explanation :
To find the time when the ball reaches maximum height we use formula
[tex]t=\frac{-b}{2a}[/tex]
From the given height equation , the value of a=-16 and b= 90
Replace it in the formula to find out 't'
[tex]t=\frac{-b}{2a} =\frac{-90}{2(-16)} =\frac{45}{16}=2.8 \; seconds[/tex]
It takes 2.8 seconds to reach maximum height
Now we plug in the value of 't' in h(t) to find out maximum height
[tex]h(t)=-16x^2+90x\\h(t)=-16(\frac{45}{16})^2+90(\frac{45}{16})\\H(\frac{45}{16})=\frac{2025}{16}[/tex]
Maximum height is 126.56 feet
Domain are the 't' values for which the function is defined
't' represents seconds that cannot be 0
so domain is t>0
[tex]\left(0 \:,\:\infty \:\right)[/tex]
Range is the height that cannot be negative and it reaches maximum height
So range is h(t)>=0 and less than 126.56 feet
[tex]Range:\\ \:[0\:,\:\frac{2025}{16}][/tex]
Learn more : brainly.com/question/22883684
