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11111nata11111 [884]
3 years ago
13

Sketch f(x) = 5x2 - 20 labelling any intercepts.​

Computers and Technology
1 answer:
Norma-Jean [14]3 years ago
8 0

Answer:

  • The graph of the function is attached below.
  • The x-intercepts will be: (2, 0), (-2, 0)
  • The y-intercept will be: (-20, 0)

Explanation:

Given the function

f\left(x\right)\:=\:5x^2-\:20

As we know that the x-intercept(s) can be obtained by setting the value y=0

so

y=\:5x^2-\:20

switching sides

5x^2-20=0

Add 20 to both sides

5x^2-20+20=0+20

5x^2=20

Dividing both sides by 5

\frac{5x^2}{5}=\frac{20}{5}

x^2=4

\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

x=\sqrt{4},\:x=-\sqrt{4}

x=2,\:x=-2

so the x-intercepts will be: (2, 0), (-2, 0)

we also know that the y-intercept(s) can obtained by setting the value x=0

so

y=\:5(0)^2-\:20

y=0-20

y=-20

so the y-intercept will be: (-20, 0)

From the attached figure, all the intercepts are labeled.

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//The Scanner class is imported which allow the program to receive user input

import java.util.Scanner;

//Class Solution is defined to hold problem solution

public class Solution {

   // The main method which signify the begining of program execution

   public static void main(String args[]) {

       // Scanner object 'scan' is defined to receive input from user keyboard

       Scanner scan = new Scanner(System.in);

       // A prompt is display asking the user to enter number of books

       System.out.println("Please enter number of books: ");

       // the user response is assigned to numberOfBook

       int numberOfBook = scan.nextInt();

       // A prompt is displayed asking the user to enter the number of days over due

       System.out.println("Please enter number of days over due: ");

       // the user response is assigned to numberOfDaysOverDue

       int numberOfDaysOverDue = scan.nextInt();

       //displayFine method is called with numberOfBook and numberOfDaysOverDue as arguments

       displayFine(numberOfBook, numberOfDaysOverDue);

   

   }

   

   //displayFine method is declared having two parameters

   public static void displayFine(int bookNumber, int daysOverDue){

       // fine for first seven days is 10cent which is converted to $0.10

       double firstSevenDay = 0.10;

       // fine for more than seven days is 20cent which is converted to $0.20

       double moreThanSevenDay = 0.20;

       // the fine to be paid is declared

       double fine = 0;

       // fine is calculated in the following block

       if(daysOverDue <= 7){

           //the fine if the over due days is less than or equal 7

           fine = bookNumber * daysOverDue * firstSevenDay;

       } else{

           // the extra days on top of the first seven days is calculated and assigned to extraDays

           int extraDays = daysOverDue - 7;

           //fine for first seven days is calculated

           double fineFirstSevenDays = bookNumber * 7 * firstSevenDay;

           // fine for the extradays is calculated

           double fineMoreThanSevenDays = bookNumber * extraDays * moreThanSevenDay;

           // the total fine is calculated by adding fine for first seven days and the extra days

           fine = fineFirstSevenDays + fineMoreThanSevenDays;

       }

       // The total fine is displayed to the user in a nice format.

       System.out.printf("The fine for " + bookNumber + " book(s) for " + daysOverDue + " day(s) is: $%.02f", fine);

   }

}

Explanation:

The program first import Scanner class to allow the program receive user input. Then the class Solution was defined and the main method was declared. In the main method, user is asked for number of books and days over due which are assigned to numberOfBook and numberOfDaysOverDue. The two variable are passed as arguments to the displayFine method.

Next, the displayFine method was defined and the fine for the first seven days is calculated first if the due days is less than or equal seven. Else, the fine is calculated for the first seven days and then the extra days.

The fine is finally displayed to the user.

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