Answered Essay: Plz answer all the questions on both pictures

ooo cricket 1:58 AM isidore.udayton.edu 17_FA CPS 150 N1 HW Assigns >Homework Assignment 1: Intro to Java Programming > CPS 150 Homewor R2.21 You are cutting off a piece of pie like this, where c is the length of the straight part (called the chord length) and h is the height of the piece. There is an approximate formula for the area: A ch 2c However, h is not so easy to measure, whereas the diameter d of a pie is usually well-known. Calculate the area where the diameter of the pie is 12 inches and the chord length of the segment is 10 inches. Generalize to an algorithm that yields the area for any diameter and chord length. R2.25 For each of the following computations in Java, determine whether the result is exact, an overflow, or a roundoff error. . a. 2.01.1 b. 1.0E61.0E6 C. 6553665536 d. 1 000 000L1 000 00OL R2.26 Write a program that prints the values . 3100010001000 3.0 * 1000 * 1000 * 1000 Explain the results. R2.27 This chapter contains a number of recommendations regarding variables and constants that make programs easier to read and maintain. Briefly summarize these .
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Plz answer all the questions on both pictures

ooo cricket 1:58 AM isidore.udayton.edu 17_FA CPS 150 N1 HW Assigns >Homework Assignment 1: Intro to Java Programming > CPS 150 Homewor R2.21 You are cutting off a piece of pie like this, where c is the length of the straight part (called the chord length) and h is the height of the piece. There is an approximate formula for the area: A ch 2c However, h is not so easy to measure, whereas the diameter d of a pie is usually well-known. Calculate the area where the diameter of the pie is 12 inches and the chord length of the segment is 10 inches. Generalize to an algorithm that yields the area for any diameter and chord length. R2.25 For each of the following computations in Java, determine whether the result is exact, an overflow, or a roundoff error. . a. 2.01.1 b. 1.0E61.0E6 C. 6553665536 d. 1 000 000L1 000 00OL R2.26 Write a program that prints the values . 3100010001000 3.0 * 1000 * 1000 * 1000 Explain the results. R2.27 This chapter contains a number of recommendations regarding variables and constants that make programs easier to read and maintain. Briefly summarize these .

Expert Answer

 

2.21 Calculation of h:

We know that h is the altitude, therefore the angle made by the line segment h on chord c is 90 degree. We know if radius is perpendicular to a chord then it bisects the chord. So by pythagoras theorem we can calculate the length of h as:

r2 = (c/2)2 + (r-h)2

(r-h)2 = r2 – (c/2)2

r-h = sqrt{}(r2-(c/2)2)

h = r – sqrt{}(r2-(c/2)2)

//Program to calculate the area given the diameter and chord_length

import java.io.*;

public class CalArea {

// function to calculate value of h and then calculate the area

double calculateArea(int diameter,int chord_length)

{

double radius = (double)diameter/2; // calculating the radius

double h = 0;

double l = Math.pow(radius,2)-Math.pow((chord_length/2),2);

l = Math.sqrt(l);

h = radius – l;

double area = ((2*chord_length*h)/3) + (Math.pow(h, 3)/(2*chord_length));

return area;

// end of calculateArea

public static void main(String[] args) {

CalArea a = new CalArea();

double area =a.calculateArea(12,10);// 12 is the diameter and 10 is the chord length

System.out.println(“Area =”+area); //print the resultant area

// end of main

// end of class

Output:

R2.25 (a) 2.0-1.1 = 0.8999999999999999

We get that the result contins round-off error, as 2.0-1.1 = 0.9 but we obtain the result as 0.8999999999999999, which contains round-off error.

(b) 1.0E6 * 1.0E6 = 1.0E12

We get that the result is exact since 1.0E6 * 1.0E6 = 1.0E(6+6) = 1.0E12

(c) 65536 * 65536 = 0

We get that the result is an overflow since the max int result java can represent is 231 -1 . Since the result is greater than 231-1, so it goes back to the minimum value and continues from there.

(d) 1_000_000L * 1_000_000L = 1000000000000

We get that the result is an exact as it is multiplication of long values (specified by L), and not int multiplication and so overflow doesn’t occur.

R2.26  3*1000*1000*1000 = -1294967296 —–1

3.0*1000*1000*1000 = 3.0E9 —–2

  • In 1, we see that we get negative result, it is because the result overflows as it is int multiplication and the result is greater than 231-1. So it goes back to the minimum value i.e -2147483648 and continues from there.
  • In 2 , we get an exact result because it involves multiplication of double values.Hence the result doesn;t overflow since maximum number that can be represented by double is 263-1. and the result is less than the maximum number so it returns the exact result.

R2.27 Recommendations regarding variables and constants that make programs easier to read and maintain are:

  • Variables declared in the programs must be initialized as this can cause errors.
  • Variable declaration must have the below structure:

<type><variable_name> = <value according to the type of the variable>

  • There are several types of numbers : short,int,long,float,double. Do not use comma as a decimal separator
  • Do not use fractions , use decimal notation
  • When a variable anme is selected, it should be picked in such a way that it explains its purpose
  • Variable names should start with a letter or underscore character and remaining characters must be letters, numbers or underscores
  • Spaces are not permitted in variable names
  • Variable names are case-sensitive
  • Reserved keywords cannot be used for variable names
  • In java, variable names should start with a lowercase and class name should start with uppercase letter
  • Comments should be added in the program for explanation as this helps anyone who reads your program to understand it
  • Variable should be declared before it is used, else it causes error
  • When variables are declared as final, it becomes constants. Constants are usually written in capital letters to distinguish it from variables.
  • Use named constants to explain the meaning of numeric constants in programs

 

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