4.6. Exercises

1. Liz buys three apples, a dozen bananas, and one cantaloupe for $2.36. Bob buys a dozen apples and two cantaloupe for$5.26. Carol buys two bananas and three cantaloupe for $2.77. How much do single pieces of each fruit cost?

In this exercise, you're tasked with determining the individual prices of three different types of fruit based on the total spending of three customers: Liz, Bob, and Carol. To solve this problem, you'll need to set up a system of equations. Each customer's total spending provides a separate equation. For example, if we let the cost of an apple be 'a', a banana 'b', and a cantaloupe 'c', we can form equations based on their total purchases:

• Liz: 3a + 12b + 1c = 2.36
• Bob: 12a + 2c = 5.26
• Carol: 2b + 3c = 2.77

With these equations, you can use methods like substitution or matrix techniques in MATLAB to find the values of a, b, and c, which will give you the cost per fruit.

Think of this as a mystery we need to solve. Imagine a grocery store where customers are buying different amounts of fruit, but we only know how much they spent in total. It's like trying to figure out how much each piece of fruit costs without labels – we have clues (the total amounts) and need to use logic to break it down!

2. Write a function file that converts temperature in degrees Fahrenheit (F) to degrees Centigrade (C). Use input and fprintf commands to display a mix of text and numbers. Recall the conversion formulation, C = 5/9 (F - 32).

This exercise challenges you to create a function in MATLAB that converts Fahrenheit temperatures to Celsius. The formula to make this conversion is C = 5/9 * (F - 32). You'll need to write a function that takes input from the user for the Fahrenheit value, performs the calculation, and then displays the temperature in Celsius using the fprintf command. By effectively utilizing user inputs and formatted output, this exercise combines coding skills with practical applications in temperature measurement.

Imagine you're checking the weather on your favorite weather app, which gives temperatures in Fahrenheit because you're in the U.S. But you're planning a trip to a country that uses Celsius – you'll need to convert it! This function acts like a personal assistant to help you quickly and accurately switch between the two temperature systems.

3. Write a user-defined MATLAB function, with two input and two output arguments that determines the height in centimeters (cm) and mass in kilograms (kg) of a person from his height in inches (in.) and weight in pounds (lb).

(a) Determine in SI units the height and mass of a 5 ft.15 in. person who weighs 180 lb.

(b) Determine your own height and weight in SI units.

In this exercise, you will create a MATLAB function that converts height from inches and weight from pounds to metric SI units: centimeters for height and kilograms for weight. The conversion formulas are:

• Height in cm = Height in inches * 2.54
• Weight in kg = Weight in pounds * 0.453592. Your function should accept the height and weight as inputs and return the converted values as outputs. You'll also be tasked with demonstrating this function by first computing the SI units for a specified individual and then using it to find your own height and weight.

Think of this function as a health tracker that can transform your personal measurements into a format understood worldwide. Whenever you travel abroad or check health guidelines, having your height and weight in metric can be crucial. Imagine you’re preparing for an international athletic competition, and the organizers require your stats to be in metric – this function helps make that conversion effortlessly!

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