Question

Suppose that you have the following conditional expression. (Assume that all the variables are properly declared.) \((0<\text { backyard } \& \& \text { backyard }<=5000)\) ? fertilizingCharges \(=40.00\) \(: \text { fertilizingCharges }=40.00+\text { (backyard }-5000) \star 0.01\) a. What is the value of fertilizingCharges if the value of backyard is \(3000 ?\) b. What is the value of fertilizingCharges if the value of backyard is \(5000 ?\) c. What is the value of fertilizingCharges if the value of backyard is \(6500 ?\)

Short answer

a) 40.00 b) 40.00 c) 55.00

Step-by-step solution

Evaluate the Condition for Each Case

The conditional expression is \[ (0 < \text{backyard} \&\& \text{backyard} \leq 5000) ? \text{fertilizingCharges} = 40.00 : \text{fertilizingCharges} = 40.00 + (\text{backyard} - 5000) \times 0.01 \]We need to evaluate the condition \[ 0 < \text{backyard} \leq 5000 \]for each given value of `backyard` (3000, 5000, 6500).

Calculate fertilizingCharges for backyard = 3000

Substitute backyard = 3000 into the condition:\[ 0 < 3000 \leq 5000 \]This is true, so we use fertilizingCharges = 40.00.

Calculate fertilizingCharges for backyard = 5000

Substitute backyard = 5000 into the condition:\[ 0 < 5000 \leq 5000 \]This is true, so we use fertilizingCharges = 40.00.

Calculate fertilizingCharges for backyard = 6500

Substitute backyard = 6500 into the condition:\[ 0 < 6500 \leq 5000 \]This is false, so we use \[ \text{fertilizingCharges} = 40.00 + (6500 - 5000) \times 0.01 = 40.00 + 15 = 55.00 \]

Key concepts

C++ programming

C++ is a powerful, high-level programming language that blends procedural, object-oriented, and generic programming features. It's widely used for system/software development, game development, and real-time simulations. Understanding C++ starts with mastering its syntax and basic concepts which provide a foundation for more complex topics.
When programming in C++, you usually start by defining variables, which are containers for storing data values of various types like `int` for integers, `double` for decimal numbers, or `bool` for boolean values. C++ offers various control structures to help decide the flow of a program, and handles both high-level abstraction and the ability to manipulate hardware resources, making it a versatile choice for different applications.
Programs in C++ generally consist of functions. The main function `main()` is the entry point of every C++ program. Here is where execution starts and ends. As you progress, you'll also encounter libraries like the Standard Template Library (STL) which offers a plethora of functions and classes designed to handle data structures like vectors, lists, and maps efficiently.

conditional operator

In C++, the conditional operator, also known as the ternary operator, is a shorthand way to perform conditional evaluations. It's represented by a `?` and `:`. This operator is highly useful for making quick decisions based on conditions within a single line of code, simplifying `if-else` statements.
The syntax for a conditional operator is:

• condition ? expression_if_true : expression_if_false;

The operator evaluates the `condition`. If the condition evaluates to `true`, it executes `expression_if_true`, otherwise it executes `expression_if_false`.
Consider the expression:

• `(0 < backyard && backyard <= 5000) ? fertilizingCharges = 40.00 : fertilizingCharges = 40.00 + (backyard - 5000) * 0.01;`

Here, if `backyard` is between 0 and 5000, `fertilizingCharges` is set to 40.00. Otherwise, it calculates extra charges using the formula `40.00 + (backyard - 5000) * 0.01`. This makes it easy to manage multiple outcomes without lengthy code.

basic arithmetic operations

Basic arithmetic operations are crucial in C++ programming as they enable computation of numeric data. C++ supports:

• `+` for addition
• `-` for subtraction
• `*` for multiplication
• `/` for division
• `%` for modulus (to find remainders)

These operators perform calculations that are core to a vast array of programming tasks.
In the conditional expression discussed, multiplication and subtraction are used in the formula `fertilizingCharges = 40.00 + (backyard - 5000) * 0.01`. This computes additional charges depending on the size of `backyard`. - The `subtraction` operation `(backyard - 5000)` calculates the extra amount of area above 5000 square feet.
- The multiplication `* 0.01` determines the monetary charge associated with the extra area.

• This showcases how arithmetic operations are integrated into solving real-world problems using C++.

control structures

Control structures in C++ programming are essential for directing the flow of a program. They enable decision making (like `if`, `else`) and are fundamental for loops (`for`, `while`, `do-while`) and switching (`switch-case`) execution based on conditions.
For conditional operations, control structures help determine which set of statements to execute based on logical tests like `&&` and `||`, which represent logical AND and OR, respectively. In the exercise, `&&` checks whether both conditions `0 < backyard` and `backyard <= 5000` are true. This boolean logic ensures the program only executes certain segments if the conditions are met.
Control structures create flexible and dynamic code, allowing for robust applications. They make your programs adaptable, letting you build everything from simple decision-based tasks to complex applications responding to various inputs and states.