The partial sum of an arithmetic sequence can be found using the formula ##S=n/2(a1+an)## where n= the number of terms, a1= the value of the first term, and an= the value of the last (nth) term.

As an example, if you were to find the partial sum of the sequence 1, 3, 5, 7, 9, …, 49, you would first need to determine that there are 25 terms, a1= 1 and an=49. ##25/2(1+49) = 625##.

Another example might ask you to find the sum of the first 20 terms of the sequence 8, 13, 18, 23, … To find an, you could use the formula ##an=dn+a0## where d= the common difference and a0 = the 0th term, or the term before the first term in the sequence. So ##an=5*20+3 = 103##. Therefore ##S=20/2(8+103) = 1110##.

Here’s a video from my YouTube channel (www.YouTube.com/MrDaveEbert) with another example:

 

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Magnitude = ##|6i-6j|=sqrt(6^2+(-6)^2)=sqrt(72)=6sqrt(2)”##Angle = ##arctan(-6/6)=arctan(-1)=-pi/4=-45°##

If you draw this vector on the plane, the x-y coordinate axis, as (6,-6) because ##i## is the unit vector in the x-direction and ##j## in the y-direction. Then pictorially it might seem easier.

So if you draw the vector (so join the line between the point (6,-6) and the origin), and draw the perpendicular line between the point and the x-axis. Now, you should see a triangle, more specifically a right-angles triangle.

Now that you have you’re right-angles triangle you can use Pythagoras to find the magnitude of the vector (length of the straight line between the origin and the point (6,-6)) and the use SOHCAHTOA to find the angle between the x-axis and the vector (be careful, here if the vector is the on the left-hand side of the plane i.e. the x-coordinate is negative, then you will have to make sure the you take the angle from the positive side of the x-axis, so do ##pi/2(1-theta)##.

Some quick formulae that may be helpful to do quick calculation:magnitude of ##ai+bj=|ai+bj|=sqrt(a^2+b^2)####theta=arctan(b/a)##if ##b<0## then angle of ##ai+bj=pi/2(1-theta)##if ##bge0## then angle of ##ai+bj=theta##

 

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How do I journalize these transactions?Journalizing stockholders equity transactions. Airborne Manufacturing Co. complete the following transactions during 2009Jan 16- Declared a cash dividend on the 4%, $102 par preferred stock (1,050 shares outstanding) Declared a $0.55 per share dividend on the 95,000 shares of common stock outstanding. The date of record is January 31, and the payment due date is February 15.Feb15- Paid the cash dividendsJune 10 Split common stock 2 for 1. Before the split, airborne had 95,000 shares of $10 par common stock outstandingJul 30 Distributed a 25% stock dividend on the common stock. The market value of the common stock was $10 per share

 

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How do I incorporate a selective statement in the code below?

Clarification

1. Demonstrate your understanding of GUI.
2. Use selection and repetition statements in this program.

import java.text.DecimalFormat;

import javax.swing.JOptionPane;

public class module3case {

   public static void main(String[] args) {

      String choice = null;

      do {

         DecimalFormat formatter = new DecimalFormat(“#,##0.00”);

         double propertyTaxRate;

         double actualValue;

         double assessmentValue;

         double tax;

         actualValue = Double.valueOf(JOptionPane.showInputDialog(“What is the value of your property?”));

         propertyTaxRate = Double.valueOf(JOptionPane.showInputDialog(“What is the property tax of the locality?”));

         tax = actualValue * propertyTaxRate/100;

         assessmentValue = actualValue +tax;

         JOptionPane.showMessageDialog(null, “Your assessment value is $”

                + formatter.format(assessmentValue)+”n”

                +”The local real estate property tax rate: “+propertyTaxRate+”n”

                + “Property tax based on the assessment is $”

                + formatter.format(tax) + “.”);

         choice =JOptionPane.showInputDialog(“Press E to terminate the program “);

         }while(!”E”.equalsIgnoreCase(choice));

   }

}

 

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