Amonte carlo analysis can be used for optimization. for example, the trajectory of a ball can be computed with 2 |(p14.35) x+yo 2 cos20o y=(tan0o)x where y the height (m), go = the initial angle (radians), the initial velocity (m/s), g 9.81 m/s, and yo vo = 25 m/s, and oo = 50", determine the maximum height and the corresponding x distance (a) analytically with calcu- lus and (b) numerically with monte carlo simulation. for the latter, develop a script that generates a vector of 10,000 uniformly-distributed values of x between 0 and 60 m. use this vector and eq. p14.35 to generate a vector of heights. then, employ the max function to determine the maximum height and the associated x distance the gravitational constant 1 m, the initial height (m).

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day