MS 101 Alg & Trig test three • 20 June 2013 • Name:

1. A keyboard has 95 characters available for use in passwords:
   
   ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789-= ~!@#$%^&*()_+ ;',./:"<>?[]\{}|.
   
   The strength of a random password as measured by the information entropy. The formula for a random password's information entropy, H, is given by the function:
   
   H = (Length of the password ) log₂(Number of characters available)
   H = L log₂N
   
   where H is reported in bits of entropy. Note that the log is the base 2 logarithm.
   1. H = _____________ bits. For a random password with a length of eight (L = 8) which uses lowercase, uppercase, numbers, and symbols (number of possible characters N to choose from is 95), calculate the bits of entropy.
      
   2. L = _____________ Some IT pundits recommend that random passwords have 72 bits of entropy. Use the function above with an N equal to 95 characters. Calculate the length L necessary to obtain H = 72 bits of entropy.
   3. L = _____________ Most computer users only use lowercase and uppercase letters, which is only 52 possible characters for their password. With N equal to 52 characters, Calculate the length L necessary to obtain H = 72 bits of entropy.
   4. _____________ What is the length in characters of the passwords you usually use? [open answer].
2. The chart depicts a baby weight function for a baby that grew at
   f(x) = 16.07 ln(x) − 27.51 where x is the months since conception and f(x) is the weight in pounds. Birth is at x = 9 months. The y-axis is the weight of the baby in pounds.
   1. ____________ Calculate the birth weight of the baby by evaluating the growth function at x = 9 months.
   2. ____________ Calculate the weight of the baby at x = 21 months (one year post birth).
   
   Either make the calculation or solve for x as appropriate. Round answers to two decimal places.
   
3. ____________ ln e
4. ____________ log 1000
5. ____________ e^1.79176
6. ____________ log_x100 = 2
7. ____________ 5 ln (3x) = 19.0333125
8. ____________ ln(3) + ln(7) = ln(x)
9. ____________ log₂(2)+log₂(4)+log₂(16)+log₇(823543)+14

10. Distance	Sound volume
    10	100
    20	60
    30	40
    50	20
    80	0

    Attenuation is essentially the ability of a sound to lower in volume as the player moves away from the source of the sound. The rate at which this volume fade occurs is based on a mathematical model. The logarithmic attentuation model is good for sounds that need more exact 3D positionalization. Also good for making sounds 'pop' at a close distance; good for incoming missiles and projectiles as well. – Adapted from: EpicGames
    
    Use a spreadsheet to plot the logarithmic sound attenuation model. Add a logarithmic trend line and equation.
    1. Write the logarithmic function:
    2. _________ Use the logarithmic function to calculate the volume for a distance of 65.
    3. _________ Use the logarithmic function to calculate the distance for a volume of 80.
11. _________ Convert π/4 radians to degrees.
12. _________ Convert 30° to radians expressed as π over a number.
13. _________ Calculate the arc length s for a π/4 radian arc with a radius r of 10 meters.
14. _________ The angles inside a triangle add up to 180° If a right triangle has one acute angle of 30°, what is the angle of the other acute angle?
15. _________ Calculate: 200 sin(45°)
16. _________ Calculate: 200 cos(45°)
17. Suppose I want to inscribe a square inside a circle with a radius of 200. What will be the SVG coordinates of the four corners?
    1. ( ________ , _________ )
    2. ( ________ , _________ )
    3. ( ________ , _________ )
    4. ( ________ , _________ )