YOUR ASSIGNMENT: Ball Bounce You have chosen one ball; now you will predict how high it bounces on the 10th bounce.

In this assignment, you may work alone, with a partner, or in a small group. Discuss the results of your work and/or any lingering questions with your teacher.

1. Circle the ball you chose. (1 point)

Basketball Tennis ball Table-tennis ball

Writing an Equation

2. Assume that the ball rebounds the same percentage on each bounce. Using the initial drop height and the height after the first bounce, find the common ratio, r.
Note: Round r to three decimal places. Use this formula:

(3 points: 2 points for showing your work, 1 point for the answer)

r =

3. State the general version of the recursive formula. (1 point)

4. Find the recursive formula for the height of your ball. Remember that the 1st term, a1, is the height of the ball on the first bounce.(2 points)

5. Fill out the following table for your ball's height after the first 3 bounces. Note: Let n = bounce number. The height on the 1st bounce, n = 1, is given. (2 points:)
Bounce n Height
First bounce 1 Basketball: 54 inches
Tennis ball: 58 inches
Table-tennis ball: 26 cm
Second bounce 2

Third bounce 3

6. Write the explicit formula for the geometric sequence of the height of the ball on the nth bounce. Use the formula an = a1 • rn – 1. Remember that the 1st term, a1, is the height of the ball on the first bounce. (2 points)

Solving the Problem

7. Using the explicit formula, find the height of the ball on the 10th bounce. (4 points: 2 points for showing your work, 2 points for the answer)

Taking Time to Reflect

8. What are some factors that could affect the ball's bounce? Why might a ball bounce higher or lower than the regulated height? (1 point)

9. For the sport you chose, why would it matter if a player used a ball that bounced higher than the regulation? (1 point)

Consider the integral: 4 0 16 − y2 − 16 − y2 4 1 x2 + y2 dz dx dy . (a) describe w. use the standard view of the x, y, and z axes. front half of a cone with a rounded top. full cone with a flat top. right half of a cone with a flat top. front half of a cone with a flat top. right half of a cone with a rounded top.

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

Use the elimination method to solve the systems of equations.choose the correct ordered pair. 7x+4y=39