The answer is 1761 1/2 (1761.5 in decimal form)
This can solved graphically, using algebraic manipulation or differential calculus.
Plotting the equation will generate a parabola. The vertex represents the point where the ball will reach the maximum height.
The vertex can be determined by completing the square
h = -16t2 + 45t + 5
h - 5 = -16(t2 - 45/16t)
h - 5 - 2025/64 = -16(t2 - 45/16t + 2025/1024)
(-1/16)(h - 2345/64) = (t - 45/32)^2
The vertex is
(45/32,2345/64) or (1.41,36.64)
The maximum height is 36.64 ft
Using calculus, taking the first derivative of the equation and equating to 0
dh/dt = 0 = -32t + 45
t = 45/32
Substituting this value to the equation
h = -16(45/32)^2 + 45(45/32) + 5
h = 36.64 ft
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|-6| + |-3 + (-5)|
6 + |-8|
6 + 8
14
Answer:
Step-by-step explanation:
<u>Recall:</u>
- Sinusoidal Function ->
- Amplitude ->
- Period ->
- Phase Shift ->
- Vertical Shift/Midline ->
<u>Given:</u>
- Amplitude ->
- Period ->
- Phase Shift ->
- Vertical Shift/Midline ->
<u>Conclusion:</u>
The equation that models the situation is
Hope this helped! I've attached a graph of the function so you can understand it better!
