Respuesta :
Answer:
see explanation
Step-by-step explanation:
Given
h(t) = - 16t² + 48t + 160
(a)
To find the zeros equate h(t) to zero, that is
- 16t² + 48t + 160 = 0 ( divide through by - 16 )
t² - 3t - 10 = 0 ← in standard form
(t - 5)(t + 2) = 0 ← in factored form
Equate each factor to zero and solve for t
t - 5 = 0 ⇒ t = 5
t + 2 = 0 ⇒ t = - 2
However t > 0 ⇒ t = 5 is when the rock hits the ocean
(b)
Equate h(t) to 160
- 16t² + 48t + 160 = 160 ( subtract 160 from both sides )
- 16t² + 48t = 0 ( divide through by - 16 )
t² - 3t = 0 ← factor out t from each term
t(t - 3) = 0
t = 0 ← time when rock was thrown from the top of the trail
t - 3 = 0 ⇒ t = 3
The rock is 160 ft above the ocean at 0 seconds and 3 seconds
(c)
Substitute t = 1.5 into h(t)
h(1.5) = - 16(1.5)² + 48(1.5) + 160 = - 36 + 72 + 160 = 196
The rock is 196 ft above the ocean at 1.5 seconds
The rock will hit the ocean at t = 5 seconds, the rock will be 160 feet above the ocean at t = 0 and t = 3 seconds, and the height of the rock at t=1.5 seconds is 196 feet and this can be determined by using the given data.
Given :
- Genevieve is going to throw a rock from the top of a trail overlooking the ocean.
- When she throws the rock upward from 160 feet above the ocean, the function h(t) =−16[tex]\rm t^2[/tex]+48t+160 models the height, h, of the rock above the ocean as a function of time, t.
A) To evaluate the zeros of the given function equate h(t) equal to zero.
[tex]\rm -16t^2+48t+160 = 0[/tex]
[tex]\rm 16t^2 - 48t-160=0[/tex]
[tex]\rm 16(t^2+3t+10)=0[/tex]
[tex]\rm 16(t^2-5t+2t-10)=0[/tex]
16(t - 5)(t + 2) = 0
t = -2, 5
Time 't' is never negative. So, the rock will hit the ocean at t = 5 seconds.
B) Now, equate h(t) to 160.
[tex]\rm 160 = -16t^2 + 48t +160[/tex]
[tex]\rm 16t^2-48t=0[/tex]
16t(t - 3) = 0
t = 0 , 3
The rock will be 160 feet above the ocean at t = 0 and t = 3 seconds.
C) Put (t = 1.5) in the given function h(t).
[tex]\rm h(1.5) = -16(1.5^2)+48(1.5)+160[/tex]
h(1.5) = -36 + 72 + 160
h(1.5) = 196 feet
So, the height of the rock at t=1.5 seconds is 196 feet.
For more information, refer to the link given below:
https://brainly.com/question/21835898
