Imagine slicing through a sphere with a plane (sheet ofpaper). The smaller piece produced is called a spherical cap. Its volume is V= πh2(3r−h) /3, where r is the radius of the sphere and h is the thickness of the cap. Find dr/dh for a spherical cap with a volume of 5π/ 3 m3. Evaluate this derivative when r=2 m and h=1 m. What is the expression for dr /dh? And evaluate this derivative when r= 2m and h = 1m.

1. a driveway has a 15° grade. if the driveway is 40 meters long, how much does the driveway rise? (nearest tenth of a meter) 2. a person located 4 miles from a rocket launch site sees a rocket at an angle of elevation of 32°. at that moment, how high is the rocket above the ground? (nearest tenth of a mile) 3.an airplane approaches an airport landing strip with an angle of depression of 12°. if the airplane is flying at an altitude of 20,000 feet, find the distance on the ground that the plane will need to land. (nearest 1,000 feet) 4.two buildings are located on opposite sides of the street, 40 meters apart. the angle of elevation from the top of the shorter building to the top of the taller building is 53°. if the taller building is 300 meters tall, what is the height of the shorter building? (nearest meter) 5.george is 187 cm tall. his son, ralph, is 142 cm tall. who casts the longer shadow. george when the sun is 65° above the horizon, or ralph when the sun is 56° above the horizon? how much longer? (nearest centimeter)

Two different linear functions are shown below with two points given from each function. use slope-intercept form or point-slope form to find the equation of each. linear function a points: (–5, –2), (–5, 7) linear function b points: (7, –5), (–2, –5) function a has: the equation of line a is: function b has: the equation of line b is:

The probability of winning something on a single play at a slot machine is 0.11. after 4 plays on the slot machine, what is the probability of winning at least once