Answer:
6^8
Step-by-step explanation:
(6^4)(6^4)
6^8
or something like that
Complete Question:
Alejandro jumped from a cliff into the ocean in Acapulco while vacationing with some friends.
Where t is the time in seconds and h is the height in feet
(a) How long did it take for Alejandro to reach his maximum height
(b) What was the highest point Alejandro reached
(c) Alejandro hits the water after how many seconds
Answer:
(a) 0.5 seconds
(b) 484 feet
(c) 6 seconds
Step-by-step explanation:
Given
Solving (a): Time to reach maximum height
This is the maximum of the function and it is calculated using:
Where
So:
Solving (b): Highest point reached
Time to reach the highest point is 0.5.
So, the highest point is: h(0.5)
Solving (c): Time he hits water.
At this point, h(t) = 0
So;
Factorize
Divide both sides by -16
Expand
Factorize
Time can't be negative.
So:
Make an inequality representing both constraints.
0.5x+y<20
x+y≥24
for a
Question:
A certain vibrating system satisfies the equation u''+γu'+u=0. Find the value of the damping coefficientγfor which the quasi period of the damped motion is 50% greater than the period of the corresponding undamped motion.
Answer: y = √(20/9) = √20/3 = 1.49071
Step-by-step explanation:
u''+γu'+u=0
m =1, k =1, w• = √ (k/m) = 1
The period of undamped motion T, is given by T = 2π/w•, T = 2π/1 = 2π
The quasi period Tq = 2π/quasi frequency
Quasi frequency = ((4km - y^2)^1/2)/2m
Therefore the quasi period Tq = 4πm/((4km - y^2)^1/2)
From the question the quasi period is 50% greater than the period of undamped motion
Therefore Tq = T + (1/2)T = (3/2)T
Thus,
4πm/((4km - y^2)^1/2) = (3/2)(2π)
Where, k =1, m=1,
4π/((4 - y^2)^1/2) = 3π,
(4 - y^2)^1/2 = 4π/3π,
(4 - y^2) = (4/3)^2,
4 - y^2 = 16/9,
y^2 =4 - 16/9,
y^2 = 20/9,
y = √(20/9)
It will take tony 6 hours
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