Question

Write an if/then/else primitive to do each of the following operations: a. Compute and display the value \(x \div y\) if the value of \(y\) is not 0 . If \(y\) does have the value 0 , then display the message 'Unable to perform the division'. b. Compute the area and circumference of a circle given the radius \(r\) if the radius is greater than or equal to \(1.0\); otherwise, you should compute only the circumference.

Short answer

For (a), check \(y\) and divide if not 0; otherwise, show error. For (b), compute area and circumference if \(r \geq 1.0\), else just the circumference.

Step-by-step solution

Check if division is possible

Start by checking if the divisor, \(y\), is not zero. If \(y eq 0\), then proceed to compute the division.

Perform division

If \(y\) is not zero, calculate the division \(x \div y\). Display the result of this division operation.

Handle division error

If \(y = 0\), output the message: 'Unable to perform the division' because division by zero is undefined.

Check radius for area and circumference

Evaluate if the radius \(r\) is greater than or equal to 1.0. When \(r \geq 1.0\), proceed to compute both the area and circumference.

Calculate area and circumference

For \(r \geq 1.0\), use the formulas: Area \(= \pi r^2\) and Circumference \(= 2\pi r\). Calculate both values and display them.

Calculate only circumference for small radius

If the radius is less than 1.0, only compute the circumference using the formula: Circumference \(= 2\pi r\). Display the circumference.

Key concepts

Division by Zero

When performing division, one must always be wary of dividing by zero. This is because division by zero is undefined within mathematics. The division operation essentially asks how many times the divisor fits into the dividend. In the case of dividing by zero, the divisor does not have any real value that fits into the dividend, making it impossible to perform.

To handle situations where division by zero might occur, programming languages use control statements like `if-else`. If the divisor is not zero, the division can proceed. Otherwise, a message like "Unable to perform the division" is displayed to inform the user of the impossibility of this arithmetic operation. This prevents the program from crashing and allows it to handle unexpected inputs gracefully.

It's important to always anticipate the potential for division by zero, especially if user input or dynamic data is involved, as this could lead to runtime errors.

Arithmetic Operations

Arithmetic operations are fundamental to mathematics and programming alike. These operations include addition, subtraction, multiplication, and division. Each has its own rules and order of operations, often memorized through the PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) acronym.

In programming, these operations are used to perform calculations and manipulate data. Knowing how to implement these correctly is crucial. For example, when performing the division of two numbers, it's essential to check conditions such as ensuring the divisor is not zero to avoid errors. Programming constructs like loops and conditional statements (e.g., `if` and `else`) help manage these conditions and guide the program flow.

Additionally, arithmetic operations can be part of geometric calculations or any mathematical computations required in a program. Understanding and implementing them correctly can significantly impact program effectiveness and efficiency.

Geometric Calculations

Geometric calculations involve the computation of measurements such as area, perimeter, and volume in various shapes and figures. These calculations often rely on specific formulas. For a circle, the important measurements include area and circumference.

- **Area of a circle** is calculated using the formula: \, \[ \text{Area} = \pi r^2 \] where \( r \) is the radius of the circle.
- **Circumference of a circle** uses the formula: \, \[ \text{Circumference} = 2\pi r \] which also depends on the radius.
When the radius of a circle is greater or equal to 1.0, both the area and circumference are computed to provide a full understanding of the circle's size. However, when dealing with a smaller radius, sometimes only circumference is needed to limit computational requirements or meet specific problem conditions.

Geometric calculations generally have wide applications, such as in engineering, architecture, and various branches of science, emphasizing the importance of understanding these mathematical concepts.