Question

Write pseudocode instructions to carry out each of the following computational operations: a. Determine the area of a triangle given values for the base \(b\) and the height \(h\). b. Compute the interest earned in 1 year given the starting account balance \(B\) and the annual interest rate / and assuming simple interest, that is, no compounding. Also determine the final balance at the end of the year. c. Determine the flying time between two cities given the mileage \(M\) between them and the average speed of the airplane.

Short answer

Pseudocode involves inputting variables, performing calculations, and outputting results for each task.

Step-by-step solution

Calculate Area of Triangle

1. Start.2. Input base \(b\) and height \(h\).3. Calculate area using the formula: \( \text{Area} = \frac{1}{2} \times b \times h \).4. Output the calculated area.5. End.

Compute Simple Interest and Final Balance

1. Start.2. Input the starting balance \(B\) and the annual interest rate \(r\).3. Calculate the interest earned over 1 year using: \( \text{Interest} = B \times r \).4. Calculate the final balance by adding the interest to the starting balance: \( \text{Final Balance} = B + \text{Interest} \).5. Output the interest and final balance.6. End.

Determine Flying Time

1. Start.2. Input the mileage \(M\) and average speed of the airplane \(v\).3. Calculate the flying time using: \( \text{Time} = \frac{M}{v} \).4. Output the flying time.5. End.

Key concepts

Computational Operations

Computational operations are the building blocks of solving mathematical and logical problems through a step-by-step approach. In pseudocode, these operations are written out to help us plan the solution to a problem without worrying about syntax.

These operations include tasks like addition, subtraction, multiplication, and division, which are used to compute a result from given numbers. Consider them as instructions that a computer or programmer follows to get to an answer.

Here's why computational operations matter:

• They streamline complex problems into manageable steps.
• They help visualize the process of arriving at a solution before actual coding.
• They ensure accuracy by systematically breaking down tasks.

By learning to write pseudocode for computational operations, you enhance your problem-solving skills and prepare yourself for actual programming tasks.

Area of Triangle

Finding the area of a triangle is a classic example of applying computational operations in geometry. The area of a triangle can be found using the formula: \[ \text{Area} = \frac{1}{2} \times b \times h \] where \( b \) is the base, and \( h \) is the height of the triangle. This formula is intuitive because it derives from the fact that a triangle is half of a parallelogram.

Steps for Calculating the Area:

• Input values for base, \( b \), and height, \( h \).
• Apply the formula by multiplying the base by the height and then dividing by two.
• Output the result, which gives the area of the triangle in square units.

This simple set of operations allows you to efficiently calculate the area of any triangle, providing you with essential geometry skills.

Simple Interest Calculation

Simple interest is a straightforward method to calculate interest on an initial amount of money, referred to as the principal. It's a linear and easy approach to determining the interest earned over a specific period, typically annually. The formula for calculating simple interest is: \[ \text{Interest} = B \times r \] where \( B \) is the principal amount, and \( r \) is the rate of interest per year, expressed in decimal form.

Key steps in calculating Simple Interest and Final Balance:

• Input the initial balance and the interest rate.
• Use the simple interest formula to compute the interest for one year.
• Calculate the final balance by adding the earned interest to the initial balance.
• Output both the interest earned and the final balance.

This method is beneficial for an array of financial calculations, providing clarity and ease when foreseeing potential earnings on savings.

Flying Time Calculation

Calculating flying time is essential for anyone interested in planning flights. The basic idea is to determine how long it takes to travel a certain distance at a given speed. The formula used to calculate flying time is: \[ \text{Time} = \frac{M}{v} \] where \( M \) is the mileage or distance between the two cities, and \( v \) is the average speed of the airplane.

Steps to Calculate Flying Time:

• Enter the distance between the destinations.
• Input the airplane's average speed.
• Divide the distance by the speed to find the time required for the flight.
• Output the calculated flying time.

Understanding how to compute flying times accurately ensures better planning and sets expectations for travel durations.