created 08/01/99

# Chapter 11 Programming Exercises

## Exercise 1

Write a program that calculates the annual cost of running an appliance. The program will ask the user for the cost per kilowatt-hour and the number of kilowatt-hours the appliance uses in a year:

```Enter cost per kilowatt-hour  in cents
8.42
Enter kilowatt-hours used per year
653
Annual cost: 54.9826
```
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## Exercise 2

When a brick is dropped from a tower, it falls faster and faster until it hits the earth. The speed v is given by

```v = (1/2) g t2
```

Here v is the speed in feet per second, t is the time in seconds, and g is 32.174. Write a program that asks the user for the number of seconds and then prints out the speed.

```Enter the number of seconds
5.4
Speed of the brick: 469.092 feet per second
```

One hundred miles per hour is 146.67 feet per second. Use your program to determine approximately how long it takes the brick to reach that speed.

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## Exercise 3

The base 2 logarithm of a number is defined by:

```log2 X = n  if 2n = X
```

For example

```log2 32 = 5,  because  25 = 32
```
```log2 1024 = 10,  because 210 = 1024
```

Write a program that inputs a number and outputs its base 2 logarithm. Use floating point input. This problem would be easy, but the Math package does not have a base 2 logarithm method. Instead you have to do this:

```log2 X = (loge X) / (loge 2)
```

Here, `loge X` is the natural logarithm of X. Use this function in the Java Math package:

```Math.log( X )
```

When you use this, X must be a double. Write the program so that the user can enter floating point numbers.

```Enter a double:
998.65
Base 2 log of 998.65 is 9.963835330516641
```
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## Exercise 4

The harmonic mean of two numbers is given by:

```H = 2 / ( 1/X + 1/Y )
```

This is sometimes more useful than the more usual average of two numbers. Write a program that inputs two numbers (as floating point) and writes out both the usual average (the arithmetic mean) and the harmonic mean.

```Enter X:
12
Enter Y:
16
Arithmetic mean: 14.0
Harmonic   mean: 13.714285714285715
```
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