A year with 366 days is called a leap year. Leap years are necessary to keep the calendar synchronized with the sun because the earth revolves around the sun once every 365.25 days. Actually, that figure is not entirely precise, and for all dates after 1582 the Gregorian correction applies. Usually years that are divisible by 4 are leap years, for example 1996. However, years that are divisible by 100 (for example, 1900) are not leap years, but years that are divisible by 400 are leap years (for example, 2000). Write a
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- The equation of a line in standard form is ax + by = c , wherein both aand b cannot be zero, and a, b, and c are real numbers. If b≠0, then –a/b is the slope of the line. If a = 0, then it is a horizontal line, and if b = 0, then it is a vertical line. The slope of a vertical line is undefined. Two lines are parallel if they have the same slope or both are vertical lines. Two lines are perpendicular if either one of the lines is horizontal and the other is vertical or the product of their slopes is –1. Design the class lineType to store a line. To store a line, you need to store the values of a (coefficient of x), b (coefficient of y), and c. Your class must contain the following operations: If a line is nonvertical, then determine its slope. Determine if two lines are equal. (Two lines a₁x + b₁y = c₁ and a₂x + b₂y = c₂ are equal if either a₁ = a₂, b₁ = b₂, and c₁ = c₂, or a₁ = ka₂, b₁ = kb₂ and c₁ = kc₂, and for some real number k.) Determine if two lines are parallel. Determine if…arrow_forwardIn the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product. Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as: C = (5/9)*(F - 32), where F is the Fahrenheit temperature and C is the Celsius temperature. If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer? Our input is 77. C = (5/9)*(77 - 32) C = (5/9)*(45) C = 25 The equivalent temperature is 25 degrees Celsius. To complete the Discussion activity, please do the following: Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above). Arm length is a function of height. The circumference of a circle is a function of diameter. The height of…arrow_forwardA right triangle can have sides that are all integers. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. These three sides must satisfy the relationship that the sum of the squares of two of the sides is equal to the square of the hypotenuse. Write a program to find all Pythagorean triples for side1, side2, and the hypotenuse all no larger than 30. Use a triple-nested for loop that simply tries all possibilities. Using Files in c programming language and comment all your steps pleasearrow_forward
- Many companies use telephone numbers like 555-GET-FOOD so the number is easier for their customers to remember. On a standard telephone, the alphabetic letters are mapped to numbers in the following fashion: A, B, and C 2 D, E, and F 3 G, H, and I 4 J, K, and L 5 M, N, and O 6 P, Q, R, and S 7 T, U, and V 8 W, X, Y, and Z 9 Write a program that asks the user to enter a 10-character telephone number in the format XXX-XXX-XXXX. The application should display the telephone number with any alphabetic characters that appeared in the original translated to their numeric equivalent. For example, if the user enters 555-GET-FOOD the application should display 555-438-3663. Gaddis Tony. Starting Out with Python (2-downloads) (p. 367). Pearson Education. Kindle Edition.arrow_forwardWhen you use a mortgage to purchase a home, the lending institution effectively owns the home. You buy back part ownership in the home with each monthly payment. The part you have bought back is your equity in the home. If the mortgage amount is P dollars, the monthly interest rate is r as a decimal, and the term of the mortgage is t months, then your equity after k payments is E(k) = P((1 + r)k − 1) (1 + r)t − 1 dollars. In this exercise, assume that the mortgage amount is $200,000, the APR is 6% so r = .06/12 and the term of the loan is 30 years (360 months). (a) Find a formula for the equity. (b) Make a graph of the equity over 360 months, the term of the loan. (c) Does the graph show that you have half-ownership in the home halfway through the term of the mortgage? Halfway through the term of the mortgage corresponds to k1 = _______ payments. From the graph, we see that E(k1) is ________ half of the mortgage amount, so we _______ have half-ownership in the home…arrow_forwardMany companies use telephone numbers like 555-GET-FOOD so the number is easier for their customers to remember. On a standard telephone, the alphabetic letters are mapped to numbers in the following fashion:A, B, and C = 2D, E, and F = 3G, H, and I = 4J, K, and L = 5M, N, and O = 6P, Q, R, and S = 7T, U, and V = 8W, X, Y, and Z = 9Create an application that lets the user enter a 10-character telephone number in the format XXX-XXX-XXXX. The application should display the telephone number with any alphabetic characters that appeared in the original translated to their numeric equivalent. For example, if the user enters 555-GET-FOOD, the application should display 555-438-3663.arrow_forward
- Suppose you save $100 each month in a savings account with annual interest rate 3.75%. Thus, the monthly interest rate is 0.0375/12 = 0.003125. After the first month, the value in the account becomes 100 * (1 + 0.003125) = 100.3125, after the second month, the value in the account becomes (100 + 100.3125) * (1 + 0.003125) = 200.938, after the third month, the value in the account becomes (100 + 200.938) * (1 + 0.003125) = 301.878 and so on. Write a Java program that prompts the user to enter a monthly saving amount and displays the account value after the sixth month. (You will use a loop to simplify the code and display the account value for any month.) Sample Output:Enter the monthly saving amount: 100After the first month, the account value is 100.3125After the second month, the account value is 200.9384765625After the third month, the account value is 301.8789093017578Note: The computation should be until 12 months.arrow_forwardUsing Paython Write a program that asks a student for his grade (out of 100) in 3 exams and then print out his final grade (out of 100), given that the weight of the first exam is 30%, the second 30%, and the third 40%.Example Input:Exam1: 70Exam2: 80Exam3: 90Example Output:Total Grade = 81Explanation: 0.3 * 70 + 0.3 * 80 + 0.4 * 90 = 81arrow_forwardWrite a program that inputs a number and checks whether it is a perfect number or not. A perfect number is the number that is numerically equal to the sum of its divisors. For example, 6 is a perfect number because the divisors of 6 are 1, 2, 3 and 1+2+3=6arrow_forward
- A group of people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After x number of passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. For example: number of passes = 1 and number of players = 5, the order of elimination is 2, 4, 1, 5. Write a program for general values of X and N. Ask a user for the number of people and number of passes To speed up the input and debugging, you may wish to store the names of the people in a file. Make sure no two names start the same letter ( Alex and Ana are not OK). Alternatively, you can number the players. Output number and/or the name of a person being eliminated Output number and the name of the winner Do not expect a user to do the right thing, error check the user input; among other things, what do you think a reasonable…arrow_forwardA group of people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After x number of passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. For example: number of passes = 1 and number of players = 5, the order of elimination is 2, 4, 1, 5. Write a program for general values of X and N. Ask a user for the number of people and number of passes To speed up the input and debugging, you may wish to store the names of the people in a file. Make sure no two names start the same letter ( Alex and Ana are not OK). Alternatively, you can number the players. Output number and/or the name of a person being eliminated Output number and the name of the winner Do not expect a user to do the right thing, error check the user input; among other things, what do you think a reasonable…arrow_forwardWhen you borrow money to buy a house, a car, or for some other purpose, you repay the loan by making periodic payments over a certain period of time. Of course, the lending company will charge interest on the loan. Every periodic payment consists of the interest on the loan and the payment toward the principal amount. To be specific, suppose that you borrow $1,000 at an interest rate of 7.2% per year and the payments are monthly. Suppose that your monthly payment is $25. Now, the interest is 7.2% per year and the payments are monthly, so the interest rate per month is 7.2/12 = 0.6%. The first months interest on $1,000 is 1000 0.006 = 6. Because the payment is $25 and the interest for the first month is $6, the payment toward the principal amount is 25 6 = 19. This means after making the first payment, the loan amount is 1,000 19 = 981. For the second payment, the interest is calculated on $981. So the interest for the second month is 981 0.006 = 5.886, that is, approximately $5.89. This implies that the payment toward the principal is 25 5.89 = 19.11 and the remaining balance after the second payment is 981 19.11 = 961.89. This process is repeated until the loan is paid. Write a program that accepts as input the loan amount, the interest rate per year, and the monthly payment. (Enter the interest rate as a percentage. For example, if the interest rate is 7.2% per year, then enter 7.2.) The program then outputs the number of months it would take to repay the loan. (Note that if the monthly payment is less than the first months interest, then after each payment, the loan amount will increase. In this case, the program must warn the borrower that the monthly payment is too low, and with this monthly payment, the loan amount could not be repaid.)arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage LearningC++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr