Question

Write each of the following as a C++ expression. a. 32 times a plus b b. The character that represents 8 c. The string that represents the name Jullie Nelson. d. \(\left(b^{2}-4 a c\right) / 2 a\) e. \(\quad(a+b) / c(e f)-g h\) f. \(\left(-b+\left(b^{2}-4 a c\right)\right) / 2 a\)

Short answer

a. `32 * a + b`, b. `'8'`, c. `"Jullie Nelson"`, d. `(b * b - 4 * a * c) / (2 * a)`, e. `((a + b) / (c * e * f)) - (g * h)`, f. `(-b + sqrt(b * b - 4 * a * c)) / (2 * a)`.

Step-by-step solution

Translate Mathematical Phrase to Expression (a)

For the expression '32 times a plus b', multiply the variable 'a' by 32, then add 'b'. The C++ expression is: `32 * a + b`.

Translate Character Representation to Expression (b)

For the character that represents 8, simply use single quotes in C++ to define a character. The C++ expression is: `'8'`.

Translate String Representation to Expression (c)

To define a string that represents the name 'Jullie Nelson', use double quotes in C++. The C++ expression is: `"Jullie Nelson"`.

Translate Quadratic Formula Component to Expression (d)

The formula \(\left(b^{2}-4 a c\right) / 2 a\) in C++ needs proper parentheses to ensure the correct order of operations. Use the expression:`(b * b - 4 * a * c) / (2 * a)`.

Translate Mathematical Phrase to Expression (e)

The phrase \((a+b) / c(e f)-g h\) can be written in C++ by grouping operations properly using parentheses for clarity:`((a + b) / (c * e * f)) - (g * h)`.

Solve Quadratic Formula Expression (f)

This expression represents the quadratic formula's simplification \(-b+\left(b^{2}-4 a c\right) / 2 a\). To translate this to a C++ expression, use:`(-b + sqrt(b * b - 4 * a * c)) / (2 * a)`.Note: This assumes inclusion of the math library for the `sqrt` function.

Key concepts

C++ Arithmetic Operators

In C++, arithmetic operators are used to perform basic mathematical operations on variables and constants. These operators include addition, subtraction, multiplication, and division. For example:

• + for addition
• - for subtraction
• * for multiplication
• / for division

These operators follow the rules of precedence, which means certain operators will execute before others unless overridden by parentheses. For instance, in the expression `32 * a + b`, the multiplication part `32 * a` is computed before adding `b` to the result.
Using parentheses can change the order in which calculations are performed. For example, to ensure addition occurs before multiplication, you might write `(a + b) * c`.

C++ Character Literals

In C++, character literals are used to represent single characters enclosed in single quotes, such as `'8'`. These characters are part of the basic data type, `char`, which can store any single character. Here's what you need to know:

• Character literals are enclosed in single quotes, like `'A'` or `'8'`.
• They can be any letter, number, or symbol.
• Internally, characters are stored as numbers using the ASCII encoding, where, for example, `'8'` is stored as 56.

Character literals are distinct from string literals in C++, which are enclosed in double quotes and represent sequences of characters.

C++ String Literals

String literals in C++ are sequences of characters enclosed in double quotes, such as "Jullie Nelson". They are one of the most commonly used data types when working with text. Here are some key points about string literals:

• Strings are enclosed in double quotes.
• They can be assigned to variables of type std::string.
• Strings support operations like concatenation and comparison.

C++ provides a std::string class which allows for handling strings more flexibly through various functions and operators. Unlike character literals, which represent single characters, strings can store multiple characters, including letters, spaces, numbers, and symbols.

C++ Mathematical Expressions

Mathematical expressions in C++ involve a combination of operands (such as variables and constants) and operators (like `+`, `-`, `*`, and `/`). These expressions allow us to perform calculations and assign results to variables. For instance:

• The expression (b * b - 4 * a * c) / (2 * a) calculates one part of the quadratic formula using proper grouping to follow order of operations.
• Mixed operators use standard precedence rules, but parentheses can be used to override these rules for desired operation order.
• C++ also allows the use of functions, such as sqrt() from the `` library, to perform more complex calculations.

In programming, ensuring correct precedence using parentheses is crucial for accurate results, as seen in many algebraic expressions. Understanding how each operator and function interacts within an expression is key for evaluating mathematical equations correctly in C++.