Afootball is kicked toward the goal. the height of the ball is modeled by the function h(t) = -16t2 + 64t where t equals the time in seconds and h(x) represents the height of the ball at time t seconds. what is the axis of symmetry and what does it represent?

t = 2; it takes 2 seconds to reach the maximum height and 2 seconds to fall back to the ground
t = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground
t = 4; it takes 4 seconds to reach the maximum height and 4 seconds to fall back to the ground
t = 4; it takes 4 seconds to reach the maximum height and 8 seconds to fall back to the ground

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

Prove the following(cot0+cosec0)[tex](cot0 + cosec0) { }^{2} = \frac{1 + cos0}{1 - cos0} [/tex]

What number gives you a irrational number when added to 2/5