Numbers Exercises#

Section Title: Numbers Exercises

Question-1: Triple Root#

In a single line of code, compute \(\sqrt{\sqrt{\sqrt{625}}}\) and round it to the nearest hundredth.

Question-2: Log Expression#

In at most two lines of code, compute \(\displaystyle |ln( 2^{sin(|-100|)})|\) and round it to the nearest hundredth.

Question-3: Function Evaluation#

Write a program that prompts the user for three numbers using three input functions. Assign the entered values to variables with the names x, y, and z.

  • Find \(\displaystyle f(x, y,z) = \frac{5xy}{2+x^2}+\frac{x+y+z}{y^4+x^2y^2}\)

  • Round this value to the nearest hundredth and print the result in the following format.

  • Sample Output:
    x: 1
    y: 2
    z: 3
    f(1,2,3)=3.63

Question-4: Height Conversion#

Write a program that prompts the user to enter their height using two input() functions for the feet and inch parts separately.

  • Assign the entered values to variables named feet and inch.

  • Convert the given height into centimeters using the following conversion formulas: 1 foot = 12 inches and 1 inch = 2.54 cm

  • Sample Output:
    Enter the feet part of your height: 6
    Enter the inch part of your height: 4
    6 feet and 4 inches = 193.04 cm

Question-5: Digit Pair Swap#

Write a program that prompts the user for a 4-digit positive number. Swap the first two digits of the given number with the last two digits and print it.

  • Do not use string indexing that will be covered in the next chapter.

  • Example 1: If the given number is 1234, then print 3412.

    • Print format: 1234 —- swap—> 3412

  • Example 2: If the given number is 6789, then print 8967.

    • Print format: 6789 —- swap—> 8967

Question-6: Distance#

In a coordinate plane, each point is represented by its x and y components in the form of \((x,y)\).
The distance between two points \(P=(x_1,y_1)\) and \(Q=(x_2,y_2)\) is given by the following distance formula:

  • \(\displaystyle dist(P,Q) = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Write a program that prompts the user for the x and y components of a point using two input() functions and computes the distance between the given point and the point \((-5,6)\).

  • Round the distance to the nearest hundredth.

Sample Output:
Enter the x-component of the point: -2
Enter the y-component of the point: 10
The distance between (-5,6) and (-2.0,10.0) is 5.0

Question-7: Midpoint#

In a coordinate plane, each point is represented by its x and y components in the form of \((x,y)\).
The midpoint \((x_m, y_m)\) between two points \(P=(x_1,y_1)\) and \(Q=(x_2,y_2)\) is given by the following midpoint formula:

  • \(\displaystyle x_m = \frac{x_2+x_1}{2}, y_m = \frac{y_2+y_1}{2}\)

Write a program that prompts the user for the x and y components of a point using two input() functions, and computes the x and y components of the midpoint between the given point and the point \((-5,6)\)

Sample Output:
Enter the x-component of the point: 3
Enter the y-component of the point: 5
The midpoint between (-5,6) and (3.0,5.0) is (-1.0,5.5).

Question-8: Pythagorean#

The Pythagorean Theorem states that for a right triangle with sides \(a\), \(b\), and \(c\) where \(c\) is the hypotenuse: \(\displaystyle c = \sqrt{a^2+b^2}.\)

  • Write a program that prompts the user for the sides of a right triangle using two input() functions, and computes the length of the hypotenuse.

  • Round the hypotenuse to the nearest hundredth.

Sample Output:
Enter the length of the first side: 4
Enter the length of the second side: 8
The length of the hypotenuse: 8.94

Question-9: Degrees to Radians#

An angle in degrees is converted to radians using the following formula: \(\displaystyle R = \frac{\pi}{180} \cdot D\).

  • Write a program that prompts the user for an angle in degrees using an input() function, converts it to radians, and rounds it to the nearest hundredth.

  • Use the conversion formula provided above, and also the math.radians() function to compare the results.

Sample Output:
Enter the angle in degrees: 120
120.0 degrees is 2.09 using the formula.
120.0 degrees is 2.09 using the math.radians() functions.

Question-10: Law of Cosines#

The Law of Cosines states that for a triangle with sides \(a\), \(b\), and the angle \(\gamma\) between these two sides:

\(\displaystyle c = \sqrt{a^2+b^2-2ab \cdot \cos(\gamma)}\),

where \(c\) is the length of the third side of the triangle corresponding to the angle \(\gamma\).

  • Write a program that prompts the user for two sides of a triangle and the angle between them in degrees using three input() functions, and computes the length of the third side \(c\).

  • Round \(c\) to the nearest hundredth.

  • The math.cos() function takes the angle in radians. You need to convert the given angle in degrees to radians before using it.

Sample Output:
Enter the length of the first side : 6
Enter the length of the second side : 3
Enter the angle between these two sides in degrees: 70
The length of the third side: 5.72

Question-11: Rational Function#

Write a program that prompts the user for a number. Assign the entered value to variable with the name x.

  • Find \(\displaystyle f(x) = \frac{x^3-2x}{x+6}\)

  • Round this value to the nearest hundredth and print the result in the following format.

  • Sample Output:
    x: 10
    f(10)=61.25

Question-12: Change Maker#

Write a program that prompts the user for an integer amount of money in cents. Your program should calculate how many:

  • 100-cent coins

  • 25-cent coins

  • 10-cent coins

  • 5-cent coins

  • 1-cent coins are needed to represent that amount using the largest possible coins first.
    Then print the number of each type of coin on separate lines.

Question-13: Weighted Average#

Write a program that prompts the user for:

  • the first grade

  • the weight of the first grade

  • the second grade

  • the weight of the second grade

The program should calculate the weighted average using the formula:

\(\displaystyle average = \frac{(g_1 \times w_1) + (g_2 \times w_2)}{w_1 + w_2}\)

Then print the weighted average rounded to two decimal places.

Solution

Question-14: Nearest Integer#

Write a program that prompts the user for a positive floating-point number.

Your program should compute the nearest integer value to the given number without using the round() function.

Then print the result.

Question-15: Digit Rotation#

Write a program that prompts the user for a 3-digit positive integer.

Your program should rotate the digits one position to the right.

  • The last digit becomes the first digit.

  • The other digits shift one place to the right.

Do not use string operations.

Print the result in the following format:

  • original_number —- rotate —> rotated_number

Question-16: Time Difference#

Write a program that prompts the user to enter:

  • the starting time in hours

  • the starting time in minutes

  • the ending time in hours

  • the ending time in minutes

Assume all values are valid and represent times on the same day.

Your program should:

  • Convert both times into total minutes.

  • Compute the difference in minutes.

  • Convert the difference back into hours and minutes.

Print the result in the format shown below.

  • Time difference: XX hours and XX minutes.