The height at t seconds after launch is
s(t) = - 16t² + V₀t
where V₀ = initial launch velocity.
Part a:
When s = 192 ft, and V₀ = 112 ft/s, then
-16t² + 112t = 192
16t² - 112t + 192 = 0
t² - 7t + 12 = 0
(t - 3)(t - 4) = 0
t = 3 s, or t = 4 s
The projectile reaches a height of 192 ft at 3 s on the way up, and at 4 s on the way down.
Part b:
When the projectile reaches the ground, s = 0.
Therefore
-16t² + 112t = 0
-16t(t - 7) = 0
t = 0 or t = 7 s
When t=0, the projectile is launched.
When t = 7 s, the projectile returns to the ground.
Answer: 7 s
Answer:
We have function,

Standard Form of Sinusoid is

Which corresponds to

where a is the amplitude
2pi/b is the period
c is phase shift
d is vertical shift or midline.
In the equation equation, we must factor out 2 so we get

Also remeber a and b is always positive
So now let answer the questions.
a. The period is


So the period is pi radians.
b. Amplitude is

Amplitude is 6.
c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.
So using that<em> rule, our range is [6+3, -6+3]= [9,-3] So our range</em> is [-3,9].
D. Plug in 0 for x.





So the y intercept is (0,-3)
E. To find phase shift, set x-c=0 to solve for phase shift.


Negative means to the left, so the phase shift is pi/4 units to the left.
f. Period is PI, so use interval [0,2pi].
Look at the graph above,
Answer:
~
Step-by-step explanation:
There isn't enough context information to solve the following problem.
Answer:
D) 4
Step-by-step explanation:
−9 + 12 + (unknown) + −8 = −1
<em>Start by going through and testing each option</em>
−9 + 12 + 2 + −8 =
3 + 2 + −8 =
5 + −8 =
−3
−3 ≠ −1
<em>A) 2 is not possible.</em>
−9 + 12 + −2 + −8 =
3 + −2 + −8 =
1 + −8 =
−7
−7 ≠ −1
<em>B) </em>−<em>2 is not possible.</em>
−9 + 12 + −4 + −8 =
3 + −4 + −8 =
−1 + −8 =
−9
−9 ≠ −1
<em>C) </em>−4<em> is not possible.</em>
<em>From this, D is looking like the answer. But to be sure, test it.</em>
−9 + 12 + 4 + −8 =
3 + 4 + −8 =
7 + −8 =
−1
−1 = −1
<em>D) 4 is the answer.</em>