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(Algebra: solve linear equations) Write a method that solves the following 2 × 2 system of linear equations:
The method header is:
public static double[] linearEquation{double[][] a, double[] b)
The method returns null if a00a11 − a01a10 is 0. Write a test program that prompts the user to enter a00, a01, a10, a11, b0 and b1 and displays the result. If a00a11 − a01a10 is 0, report that “The equation has no solution.” A sample run is similar to
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- (Geometry: area of a regular polygon) A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is n x s? Area 4 X tan Here, s is the length of a side. Write a program that prompts the user to enter the number of sides and their length of a regular polygon and displays its area. Here is a sample run:arrow_forward(Demonstrate cancellation errors) A cancellation error occurs when you are manipulating a very large number with a very small number. The large number may cancel out the smaller number. For example, the result of 100000000.0 + 0.000000001 is equal to 100000000.0. To avoid cancellation errors and obtain more accurate results, carefully select the order of computation. For example, in computing the following series, you will obtain more accurate results by comput- ing from right to left rather than from left to right: 1 1 1 1+ + 3 + ... 2 п Write a program that compares the results of the summation of the preceding series, computing from left to right and from right to left with n = 50000.arrow_forward(Geometry: great circle distance) The great circle distance is the distance between two points on the surface of a sphere. Let (x1, y1) and (x2, y2) be the geographi- cal latitude and longitude of two points. The great circle distance between the two points can be computed using the following formula: d = radius * arccos(sin(x1) * sin(x2) + cos(x1) * cos(x2) * cos(y1 - y2)) Write a program that prompts the user to enter the latitude and longitude of two points on the earth in degrees and displays its great circle distance. The average earth radius is 6,378.1 km. The latitude and longitude degrees in the formula are for north and west. Use negative to indicate south and east degrees.arrow_forward
- (Area of a convex polygon) A polygon is convex if it contains any line segment that connects two points of the polygon. Write a program that prompts the user to enter the number of points in a convex polygon, then enter the points clockwise, and display the area of the polygon. Sample Run Enter the number of points: 7 Enter the coordinates of the points: -12 0 -8.5 10 0 11.4 5.5 7.8 6 -5.5 0 -7 -3.5 -5.5 The total area is 244.575arrow_forward(Factorials) Factorials are used frequently in probability problems. The factorial of a positive integer n (written n! and pronounced “n factorial”) is equal to the product of the positive integers from 1 to n. Write an application that calculates the factorials of 1 through 20. Use type long . Display the results in tabular format. What difficulty might prevent you from calculating the factorial of 100?arrow_forward(Java in Eclipse) Write code that finds the sum of two matrices. Use the following method header public static int[][] addMatrix(int[][] a, int[][] b) The rules for adding two matrices are:1. both matrices should have the exact same dimensions (i.e. height and width) – you need to check for this rule in your program.2. both matrices should have elements that have compatible types – you don’t have to add extra code to check this rule in your method as it will only accept int arrays included is a test class and a sample runarrow_forward
- (Emirp) An emirp (prime spelled backward) is a nonpalindromic prime number whose reversal is also a prime. For example, 17 is a prime and 71 is a prime, so 17 and 71 are both emirps. Write a Java program that displays the first 100 emirps. Display 10 numbers per line with a spacing of 5; all numbers should be left-aligned.arrow_forward(Random Walk Robot) A robot is initially located at position (0, 0) in a grid [−5, 5] × [−5, 5]. The robot can move randomly in any of the directions: up, down, left, right. The robot can only move one step at a time. For each move, print the direction of the move in and the current position of the robot. Use formatted output to print the direction (Down, Up, Left or Right) in the left. The direction takes 10 characters in total and fill in the field with empty spaces. The statement to print results in such format is given below: cout << setw(10) << left << ‘Down’ << ... ; cout << setw(10) << left << ‘Up’ << ...; If the robot moves back to the original place (0,0), print “Back to the origin!” to the console and stop the program. If it reaches the boundary of the grid, print “Hit the boundary!” to the console and stop the program. A successful run of your code may look like: Due to randomness, your results may have a different trajectory…arrow_forward(Random Walk Robot) A robot is initially located at position (0, 0) in a grid [−5, 5] × [−5, 5]. The robot can move randomly in any of the directions: up, down, left, right. The robot can only move one step at a time. For each move, print the direction of the move in and the current position of the robot. Use formatted output to print the direction (Down, Up, Left or Right) in the left. The direction takes 10 characters in total and fill in the field with empty spaces. The statement to print results in such format is given below: cout << setw(10) << left << ‘Down’ << ... ; cout << setw(10) << left << ‘Up’ << ...; If the robot moves back to the original place (0,0), print “Back to the origin!” to the console and stop the program. If it reaches the boundary of the grid, print “Hit the boundary!” to the console and stop the program. A successful run of your code may look like: Due to randomness, your results may have a different…arrow_forward
- Write a method that computes the binary fraction representation of a positive integer. To find the binary representation, divide the integer by 2 successively and write the remainders left to right until the quotient becomes 0. (C# CONSOLE PROGRAMMİNG)arrow_forward(Geometry: area of a hexagon) The area of a hexagon can be computed using the following formula (s is the length of a side): 6 x s? Area TT 4 X tan 6. Write a program that prompts the user to enter the side of a hexagon and displays its area. Here is a sample run:arrow_forward(Population projection) The U.S. Census Bureau projects population based on thefollowing assumptions:■■ One birth every 7 seconds■■ One death every 13 seconds■■ One new immigrant every 45 secondsWrite a program to display the population for each of the next five years. Assume thatthe current population is 312,032,486, and one year has 365 days. Hint: In Java, iftwo integers perform division, the result is an integer. The fractional part is truncated.For example, 5 / 4 is 1 (not 1.25) and 10 / 4 is 2 (not 2.5). To get an accurate resultwith the fractional part, one of the values involved in the division must be a numberwith a decimal point. For example, 5.0 / 4 is 1.25 and 10 / 4.0 is 2.5.arrow_forward
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