Notes, summaries, assignments, exams, and problems for Primary education

Calculating the Future Value of an Annuity Due

Step 1: Determine the Variables

The problem provides the following details:

• Annual payment: Rs. 200. Therefore, the half-yearly payment (Pmt) is:
  
  Rs. 200 / 2 = Rs. 100
  Rs. 200 / 2 = Rs. 100
• Annual interest rate (r): 4% or 0.04. Since the interest is compounded half-yearly, the interest rate per period (i) is:
  
  0.04 / 2 = 0.02
  0.04 / 2 = 0.02
• Term: 20 years. Payments are made half-yearly, so the total number of periods (n) is:
  
  20 × 2 = 40
  20 × 2 = 40
• The annuity type is an annuity due, meaning payments are made at the beginning of each period.

Step 2: Apply the Future Value Formula

The formula for the Future Value (FV) of an annuity due is given by:

FV = Pmt × [((1 + i)^n - 1) / i] × (1 + i)

FV = Pmt × [((1

Matrices (Question 6a)

Verify that A · (\text{adj } A) = (\text{adj } A) · A = |A| · I_3 for
A = \begin{bmatrix} 2 & 3 & 4 \\ 3 & 0 & 1 \\ 2 & 1 & 5 \end{bmatrix}.

Tasks:

• Find the determinant |A|:
• Find the Adjoint (\text{adj } A): This involves finding the cofactor of each element and then transposing the resulting matrix.
• Cofactors: C₁₁ = -1, C₁₂ = -13, C₁₃ = 3, C₂₁ = -11, C₂₂ = 2, C₂₃ = 4, C₃₁ = 3, C₃₂ = 10, C₃₃ = -9
• Multiply A · (\text{adj } A)

4. Financial Arithmetic (Question 2g)

Find the compound interest on Rs. 8,000 for 1 1/2 years at 10% per annum, compounded annually.

• Amount for the first year:
• Interest for the next half year: Use simple interest on the new principal.
• Total Compound Interest:

Answers use standard... Continue reading "Matrix Determinant and Adjoint Verification with AP/GP and CI" »

Building Java GUI Applications with AWT

Creating GUI applications using Abstract Window Toolkit (AWT) involves setting up a top-level container, adding components, arranging them with a Layout Manager, and making the container visible.

Steps to Create an AWT Application

1. Choose a Top-Level Container

The application needs a primary window to hold all components. The most common choice is the Frame class, which provides a title bar, borders, and window controls.

import java.awt.*;

// Class extends Frame to be the application window itself
public class AWTExample extends Frame {
    // Constructor and other methods
}

2. Initialize the Container (The Frame)

Inside the constructor, you set up the basic properties of the window:

• Title: Set the window

Diabetes Mellitus Essentials

• Type 1: Autoimmune, insulin-dependent, early onset.
• Type 2: Insulin resistance, gradual onset, linked to diet/weight.
• Diagnosis: Fasting glucose >126 mg/dL, HbA1c.
• Metformin: Hold before contrast dye; risk of lactic acidosis.

Hypoglycemia vs. Hyperglycemia

• Hypoglycemia (<70 mg/dL): Shaky, sweaty, confused, hungry.
• Hyperglycemia: Headache, nausea, fruity breath.
• Treatment: Juice/glucose if conscious; glucagon or D50 if unconscious.

Insulin Types and Administration

• Rapid-acting (Lispro): Onset 10–15 min, eat immediately after injection.
• Short-acting (Regular): Onset 30–60 min.
• Intermediate-acting (NPH): Peak 4–12 hr (cloudy appearance).
• Long-acting (Glargine): No peak, lasts 24 hr.
• Mixing Insulin: Clear (Regular) before

This document presents two distinct approaches to solving the Traveling Salesperson Problem (TSP) using Prolog: an exact, brute-force method and a heuristic-based Nearest Neighbor algorithm. Both implementations are demonstrated with code and sample queries.

Exact Solver: Brute-Force TSP Algorithm

This section details a Prolog program that finds the optimal (shortest) path for the Traveling Salesperson Problem by generating and evaluating all possible tours. This method guarantees the optimal solution but can be computationally intensive for larger sets of cities.

Defining City Distances in Prolog

The distances between cities are defined using dist/3 facts. The predicate is made symmetric to ensure that dist(X,Y,D) implies dist(Y,X,D).

dist(a,b,

Core Java Programming Concepts Explained

Key Java Definitions

• Exception: An event that disrupts the normal flow of a program's instructions.
• Thread: A lightweight subprocess enabling multitasking within a program.
• Event Handling: Implemented using listeners and event classes that respond to user actions.
• Applet: A small Java program embedded in a web page for interactive content.
• Remote Applets: Used to download and execute applets from a web server over the internet.
• Applet Parameters: Passed to applets using <PARAM> tags in HTML, accessed via the getParameter() method.
• Daemon Thread: Runs in the background for services like garbage collection and ends when main threads finish.
• Thread Synchronization Advantages:
  • Prevents thread interference.
  • Ensures

DC Motor Speed-Torque Characteristics

• Graph Interpretation

  • Y-axis: Speed (N).
  • X-axis: Torque (T).
  • Shape: Linear downward slope (speed decreases as torque increases).

• Speed-Torque Formula

  N=V−IaRaϕN=ϕV−Ia​Ra​​,
  where I_a = armature current, R_a = armature resistance, ϕ = flux.

• Key Performance Points

  • At No Load: High speed, low torque.
  • At Full Load: Low speed, high torque (due to armature reaction).

• Applications

  Used in electric vehicles and cranes for variable speed control.

Working Principle of 3-Phase Induction Motor

• Stator Function

  • A 3-phase AC supply produces a Rotating Magnetic Field (RMF).
  • RMF Speed (Synchronous Speed, N_s): Ns=120fPNs​=P120f​.

• Rotor Operation

  • Conductors (aluminum bars) are cut by the RMF, inducing current (Faraday’s

Respiratory System Basics

Respiratory Key Terms

• Dyspnea: Difficulty breathing
• Orthopnea: Difficulty breathing when lying flat
• Tachypnea: Abnormally fast breathing
• Bradypnea: Abnormally slow breathing
• Hemoptysis: Coughing up blood
• Hypoxia: Tissue oxygen deficiency
• Clubbing: Fingertip rounding due to chronic hypoxia
• Barrel chest: Increased chest diameter often from emphysema
• Cyanosis: Bluish skin or mucous membrane discoloration from low oxygen
• Rales/Crackles: Abnormal lung sounds indicating fluid
• Wheezing: High-pitched whistling from narrowed airways
• Rhonchi: Low-pitched rattling sounds (often due to secretions)
• Productive cough: Cough producing mucus or sputum
• Hypertonia: Increased muscle tone causing stiffness
• Hypotonia: Decreased muscle tone making muscles

1. Create Table Coach

CoachID INT PRIMARY KEY,

CoachName VARCHAR(20) NOT NULL,

Sports VARCHAR(15) NOT NULL,

DOJ DATE NOT NULL,

Gender CHAR(1) NOT NULL,

Salary INT NOT NULL

INSERT INTO Coach (CoachID, CoachName, Sports, DOJ, Gender, Salary)

VALUES

(1001, 'Mulund Gogoi', 'Boxing', '2004-09-01', 'M', 40000),

(1002, 'Arnab Duwara', 'Karate', '1999-10-01', 'M', 60000),

(1003, 'Nayan Bora', 'Arm Wrestling', '2005-02-28', 'M', 50000),

(1004, 'Devesh Hazarika', 'Basketball', '2010-05-05', 'M', 25000),

(1005, 'Chetan Sharma', 'Swimming', '2010-03-31', 'M', 25000),

(1006, 'Lakshmi Devi', 'Boxing', '2012-01-01', 'F', 22000);

3. Queries for Questions:

a) Display the Maximum and Minimum Salary of the Coaches

SELECT MAX(Salary) AS Max_Salary, MIN(Salary) AS Min_Salary

English Connectors and Linkers

1. Reason and Cause

(Razón o causa de algo) →

• Because / as / since (+ sentence)
• Because of / owing to / due to (+ noun)

2. Purpose

(Propósito o finalidad) →

• To / In order to / So as to (+ infinitive)
• In order that / So that (+ sentence with modal verb)

3. Exemplifying

(Aclarar lo que explicamos) →

• For example / for instance
• Such as... / like...

4. Additions

(Para añadir algo) →

• Moreover / Furthermore / Besides (Además)
• In addition to / as well as (+ noun or pronoun)

5. Result or Consequence

(Resultado o consecuencia de una acción) →

• Therefore (Por ello) / Consequently / For this reason / Thus
• As a result of (+ substantive or pronoun)

6. Contrast

→

• However / Nevertheless / On the contrary
• While / Whereas (Sentence with