2. Create a program that approximates the three roots of the equation f(x) = 5.3221 x3 - 4.2842 x2 - 2.1351 x + 1.1819 using any of the following methods (choose 1): %3D • Bisection Method • False Position and Secant Methods • Newton-Raphson Method
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- Create a program that approximates the three roots of the equation f(x) = 5.3221 x3 - 4.2842 x2 - 2.1351 x + 1.1819 using any of the following methods (choose 1): Bisection Method False Position and Secant Methods Newton-Raphson MethodThe German mathematician Gottfried Leibniz developed the following method to approximate the value of Pi Pi/4 = 1 - 1/3 + 1/5 - 1/7+… Write a program that allows the user to specify the number of iterations used in this approximation and that displays the resulting value. An example of the program input and output is shown below: Enter the number of iterations: 5 The approximation of pi is 3.3396825396825403Write a program to calculate the surface area and volume of a square pyramid. A square pyramid has a base that is square and all triangle faces are congruent isosceles triangles. (An isosceles triangle is a triangle in which two of the sides are equal. Length of the base: a Height of the pyramid: h Volume = a2h/3 Slant height, s = sqrt(h2 + (a/2)2) This is the Pythagorean Theorem part. Area of one pyramid side = s*a/2 For this program you are to determine two things about a square pyramid. 1) the surface area of the four sides. 2) the volume. Do not include surface area of the base. Test case 1: Height: 5.0' Base: 2.5' Test case 2: Height 2.5 Base: 4.3' The program asks the user to enter the pyramid height (in feet) and length of the base (in feet). Your program will need to determine surface area, and volume by using pythagorean theorem. Your output should neatly show the height, base, total surface area, and volume of the pyramid using 33 decimal place of…
- For the three poiats 4 (Xa, Ya), B (Xb, ¥5) and C (Xe, ¥e) the cquation of the line L parallel to the segment AB and passing by the point C is given by: ¥ = mX + k where: va m is the slope and computed as = m = [ ke is the intercept and computed as : k = Ye — m. Xc Write & java program that calculate and display the slope, the intercept and the equation of the Line parallel to AB and passing by C for the given values: A (1.5,2), B (2.5, -4)and C (-1.5, 105) ‘Your program should output exactly the following: Sample Run The slope is -6.0 “The interceptis 1.5 “The equation of the parallel is ¥ =-6.0 X+ 1.5Write a program that calculates the potential energy of 3 charges q1 = 1, q2 = 2, q3 = 3located at points (1, 2, 3), (3, −4, −5), and (−4, 2, −6) respectively. The units are coulombs forcharge and meters for coordinates. The energy is given by the expressionThe German mathematician Gottfried Leibniz developed the following method to approximate the value of π: π/4 = 1 - 1/3 + 1/5 - 1/7 + . . . Write a program that allows the user to specify the number of iterations used in this approximation and that displays the resulting value. An example of the program input and output is shown below: PYTHON!!!! Enter the number of iterations: 5 The approximation of pi is 3.3396825396825403 Results you should get: 4 3.3396825396825403 3.0418396189294032 3.142593654340044
- Write a program that displays the area and perimeter of a circle that has a radius of 6.5 using the following formula: p = 3.14159 perimeter = 2 × radius × p area = radius × radius × pWrite a program that finds the day of the week for any given date using Zeller’s congruence. Zeller found the following formula to calculate the day of the week using the day of the month, the month, and the year. weekday = (day + 26 * (month + 1) / 10 + year + year / 4 − year /100 + year /400 ) % 7; The formula is based on the following: There are seven days in the week so the calculation must be done modulo 7. The first term, day, shows that each day of the month moves the weekday forward by 1. The second term, 26 * (month + 1) / 10, is the Zeller congruence. Instead of worrying about the number of days in each month, Zeller devised this solution. Zeller’s formula works for a solar system when the year starts from March, not January. Therefore, we must consider the months January and February as months13 and 14 of the previous year. In other words, January of 2017 must be considered as month 13 of year 2016. The next term, year, moves the week day one day for each year because…Write a program to calculate the surface area and volume of a square pyramid. A square pyramid has a base that is square and all triangle faces are congruent isosceles triangles. (An isosceles triangle is a triangle in which two of the sides are equal. Length of the base: a Height of the pyramid: h Volume = a2h/3 Slant height, s = sqrt(h2 + (a/2)2) This is the Pythagorean Theorem part. Area of one pyramid side = s*a/2 Test Case #1 Height(h): 5.0’ Base(a): 2.5’
- Write a program that calculates the sum of all positive integers less than or equal to a given number N.In the example below, the sum of the fourth powers of each digit that forms the 4-digit numbers gives the number itself: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 And sum of these numbers is 1634 + 8208 + 9474 = 19316. Find the sum of all numbers that can be written as the sum of the fifth forces of their numbers. (P.s.: You have to done it by C++)Write a program that generates 1,000 lowercase letters randomly, counts the occurrence of each letter, and displays a histogram for the occurrences, as shown in Figure 10.16a.
