MS 101 Alg & Trig test three • 18 June 2015 • Name:

1. A tennis ball was dropped and the bounce heights for consecutive bounces were measured.
   

   Bounce number	Bounce height
   0	1987
   1	1093
   2	601
   3	331
   4	182
   5	100

   1. Add an EXPONENTIAL trend line and equation to the graph. Write the exponential equation below:
   2. __________ Based on the exponential equation in a, what will be the height of bounce number six?
   3. __________ On what bounce number will the bounce height be 17?
   4. __________ According to the International Tennis Federation a tennis ball used in tournament play must meet certain rebound (bounce) specifications. A ball dropped from a 100 inches must rebound between 53 and 58 inches. After bounce five the tennis ball fell from 100 inches. Does the bounce height calculated in b meet specification?
2. Sketch a graph of $y=\frac{9}{(1+e^{-3x})}$ for x = -3 to 3
   
3. In the Tennis Industry Magazine article Racquet Handle Weighting and Maneuverability Rod Cross notes that, "Inspection of 320 different racquets ... shows that almost every light racquet is head heavy and every heavy racquet is head light." The article goes on to discuss the reasons tennis racquets are designed this way. The following table derives from the article.
   

   Weight (gm)	Balance (cm)
   245	40
   260	38
   282	35.5
   308	33.5
   348	31.7

   1. Add a LOGARITHMIC trend line and equation to the graph. Write the logarithmic equation below:
   2. ____________ Based on the logarithmic equation in a, calculate the balance for a weight of 328 gm.
   3. ____________ Based on the logarithmic equation in part a, calculate the weight for a balance of 39 cm.
4. Calculate or solve for x the following expressions and equations.
   1. ____________ ${log}_8\left(64\right)$
   2. ____________ log (10,000,000)
   3. ____________ e⁰
   4. ____________ ln x = 2.079442
   5. ____________ $8^x=64$
   6. ____________ $\frac{1}{3}log\left(x\right)=2$
   7. ____________ ${(cos\mathrm{45°})}^2+{(sin\mathrm{45°})}^2$
   8. ____________ 16 cos(45°) sin(45°)
   9. ____________ $5e^{\left(\frac{x}{8}\right)}=6.42013$
5. _________ Using a 44 foot long rope, Seagal in the center, Tammy walking in a circle with the rope taut, would measure a length of 295 feet. Calculate the value of pi based on this data.
6. _________ Convert 30° to radians expressed as π over a number.
7. _________ Convert 45° to radians expressed as π over a number.
8. _________ Convert 315° to radians expressed as π over a number.
9. _________ Convert $\frac{\mathrm{\pi }}{3}$ radians to degrees.
10. _________ Convert $\frac{5\mathrm{\pi }}{4}$ radians to degrees.
11. _________ Calculate: 283 cos(30°)
12. _________ Calculate: 283 sin(45°)
13. _________ Calculate: 283 cos(45°)
14. _________ Determine the arc length for a $\frac{\mathrm{\pi }}{4}$ arc with a radius of 100.
15. _________ Determine the angle in radians for a radius of 50 and an arc length of 105. The angle can be expressed as a decimal.
16. Suppose I want to inscribe a square inside a circle with a radius of 283. What will be the SVG coordinates of the four corners a, b, c, d? The center of the circle is at (0,0). Try to remember that the y-axis is "upside-down."
    
    1. ( ________ , _________ )
    2. ( ________ , _________ )
    3. ( ________ , _________ )
    4. ( ________ , _________ )