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====== Math 445 Lab #1 ======

These problems are taken from Attaway chapter 1, both 2nd and 3rd editions. Remember, Matlab's //help// function is your friend.

**Problem 1:** Evaluate these expressions in your head and write down the answer. Then evaluate them with Matlab. If you made a mistake, figure out what it was. 

25/4*4

3+4^2

4\12 + 4

3^2

(5-2)*3


**Problem 2:** What is the type of the answers in problem 1?

**Problem 3:** Use //intmin// and //intmax// to determine the range of values that can be stored in the types //uint32// and //unint64//. Express the answers as integers and in scientific notation.

**Problem 4:** Wind chill factor: The WCF conveys how cold it feels with a given air 
temperature T (degrees Farenheit) and wind speed V (miles per hour). A formula
for WCF is

<latex>
  WCF = 35.7 + 0.6 T - 35.7 V^{0.16} + 0.43 \; T \; V^{0.16}
</latex>

Create variables for temperature T and wind speed V and then using this formula,
calculate the WCF for (a) T = 45 F and V = 10 mph and (b) T = 45 F and V = 0 mph.

Bonus: Do you think the Wind Chill Factor is a sensible quantity? Why or why not? If not, can you come up with something better? 


**Problem 5:** Use Matlab help to understand the following questions, and then answer them based on your understanding. Then use Matlab to check your answers. Rethink any questions you answered incorrectly.

 is fix(3.5) == floor(3.5)?

 is fix(3.4) == fix(-3.4)?

 is fix(3.2) == floor(3.2)?

 is fix(-3.2) == floor(-3.2)?

 is fix(-3.2) == ceil(-3.2)?

What is the type of //fix(-3.2) == ceil(-3.2)//?

**Problem 6:** Find Matlab expressions for

 cube root of 19

 3 to the 1.2

 tangent of pi

Evaluate the expressions. Do you notice anything unexpected? Can you explain it?

**Problem 7:** Generate random numbers

 real in range 0-1

 real in range 0-20

 real in range 20-50

 integer in range 0-10

 integer in range 0-11

 integer in range 50-100

**Problem 8:** Get into new Command window and type rand to get a random real number. 
Make a note of the number. Then exit and restart matlab, and repeat. The 
random number should be the same. Exit and restart matlab again. This time,
change the random number seed before generating a new random number. The 
random number should be different this time.

**Problem 9:** Evaluate these expressions in your head, and then check your answers by evaluating them with Matlab. If you made any mistakes, figure out why.

  'b' >= 'c' + 1
  
  3 == 2 + 1
  
  (3 == 2) + 1
  
  xor(5 < 6, 8 > 4)
  
What is the type of each of the answers?

**Problem 10:** The geometric mean g of n numbers $x_1, x_2, \ldots, x_n$ is given by

<latex>
  g = \sqrt[n]{x_1 x_2 \ldots x_n}
</latex>

This is useful, for example, in finding the average rate of return on an investment with varying yearly return. If an investment returns 15% its first year, 5% its second, and 10% its third, the average rate of return is 
 
<latex>
  \sqrt[3]{1.15 \cdot 1.05 \cdot 1.10}
</latex>

Compute the average rate of return, expressed as a percent.
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