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This document contains 10 mathematical identities relating to polynomials, as well as formulas for speed, velocity, acceleration, position, time, and motion. The identities include the difference of two squares, the sum and difference of two cubes, and factoring polynomial expressions. Formulas defined include the relationships between speed, velocity, displacement, time, and the kinematic equations for velocity as a function of time, position as a function of time and velocity, and the connection between position, velocity and acceleration.
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India has enacted several laws and acts to protect children and promote their healthy development, as children represent the future of the country but are also vulnerable. The laws aim to guarantee children justice, liberty, equality, and fraternity as citizens, and protect their right against exploitation by banning employment of children under 14 in hazardous jobs or industries. Violating child labor laws by employing children in homes, restaurants or tea shops is a punishable offense carrying a prison sentence of up to three years or a fine of Rs. 10,000-20,000.
mensuration
1. The document provides a winter break assignment for Class 8 math students. It contains two parts - designing a 3D model using different shapes and their surface areas and volumes, and solving 15 mensuration problems.
2. The mensuration problems involve calculating volumes and surface areas of cubes, cylinders, boxes, rooms, and more using formulas like volume of a cube, surface area of a cylinder, volume of water flowing in a river, etc.
3. Students are asked to find dimensions of objects, amounts of materials required, heights, radii, and other measurements by applying concepts of length, breadth, height, diameter, perimeter, and rates.
Water by aman goel
The document discusses ways to conserve water, including using structures called baolis to store rainwater and treating sewage and factory waste before disposal to prevent polluting water sources. Baolis are structures used to collect and store rainwater during monsoon months, which can then be used in non-monsoon months and help recharge groundwater. The document also provides images of baolis.
RELIGIOUS BELIEFS & SCIENCE
The document discusses different views on how Christianity reconciles belief and science. It examines methods of arriving at understanding like revelation through scripture, tradition, experience and design. It also analyzes the scientific method. Some views presented are that revelation requires faith while science relies on testing, but they don't have to contradict. Another view is that Genesis could be taken literally or symbolically to allow compatibility with science. Thomas Aquinas' cosmological argument for a first cause of God as creator is also examined.
Laugh out loud by aman goel
The document is titled "Laugh out loud" and is authored by Aman Goel and Sahil Goel. It does not contain any other text or information beyond the title and authors.
Federalism
This document outlines the powers and functions of different levels of government in India. The central government deals with matters of national importance and has authority over state governments. State governments enjoy independence in governing matters within their states but must follow the central government on issues that impact the nation as a whole. The document was created by a group led by Aditya to explain the division of powers between federal, state, and central governments in India.
science
This document contains 30 multiple choice and short answer questions related to crop production and management. The questions cover topics like essential conditions for growing maize, propagation of ginger, effects of organic manure and fertilizers, agricultural tools and implements, crop rotation, irrigation methods, and more. Sample answer keys are also provided for some questions.
Sst
This document outlines the curriculum plan for social science classes in semester 1 and 2 for 8th grade students. It details the topics that will be covered in geography, history, and civics for each month and the formative and summative assessments that will evaluate student learning. Key topics include natural resources, colonization of India, the constitution, agriculture, industries, and independence. Learning will be tested through unit tests, homework assignments, classroom activities, and projects focused on the material for each semester.
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Formula
- 1. IDENTITY–1 (𝑎 + 𝑏)2 = 𝑎2 + 2𝑎𝑏 + 𝑏2 IDENTITY-2 (𝑎 − 𝑏)2 = 𝑎2 − 2𝑎𝑏+ 𝑏2 IDENTITY-3 𝑎2 − 𝑏2 = ( 𝑎 + 𝑏)(𝑎 − 𝑏) IDENTITY-4 ( 𝑥 + 𝑎)( 𝑥 + 𝑏) = 𝑥2 + ( 𝑎 + 𝑏) 𝑥 + 𝑎𝑏 IDENTITY-5 (𝑥 + 𝑦 + 𝑥)2 = 𝑥2 + 𝑦2 + 𝑧2 + 2𝑥𝑦 + 2𝑦𝑧+ 2𝑧𝑥 IDENTITY-6 (𝑥 + 𝑦)3 = 𝑥3 + 𝑦3 + 3𝑥2 𝑦 + 3𝑥𝑦2 IDENTITY-7 (𝑥 − 𝑦)3 = 𝑥3 − 3𝑥2 𝑦 + 3𝑥𝑦2 − 𝑦3 IDENTITY-8 𝑥3 + 𝑦3 + 𝑧3 − 3𝑥𝑦𝑧 = ( 𝑥 + 𝑦 + 𝑧)(𝑥2 + 𝑦2 + 𝑧2 − 𝑥𝑦 − 𝑦𝑧 − 𝑧𝑥 IDENTITY-9 𝑎3 + 𝑏3 = ( 𝑎 + 𝑏)(𝑎2 − 𝑎𝑏 + 𝑏2 ) IDENTITY-10 𝑎3 − 𝑏3 = ( 𝑎 − 𝑏)(𝑎2 + 𝑎𝑏 + 𝑏2 ) Speed= 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑖𝑚𝑒 velocity= 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒 Averagespeed= 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑒𝑑 𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 Averagevelocity= 𝑣+𝑢 2 Acceleration 𝑎 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑡𝑖𝑚𝑒 = 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦−𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑡𝑖𝑚𝑒 = 𝑣−𝑢 𝑡 VELOCITYTIMEEQUATION Slope = 𝑦2−𝑦1 𝑥2−𝑥1 𝑎 = 𝑣 − 𝑢 𝑡 𝑣 = 𝑢 + 𝑎𝑡 POSITIONTIMEEQUATION 𝑠 = 𝑢𝑡 + 1 2 (𝑣 − 𝑢)𝑡 𝑠 = 𝑢𝑡 + 1 2 𝑎𝑡2 POSITION VELOCITY EQUATION 𝑠 = 1 2 ( 𝑣 + 𝑢) 𝑡 𝑠 = ( 𝑣 − 𝑢)(𝑣 + 𝑢) 2𝑎 𝑣2 = 𝑢2 + 2𝑎𝑠 2𝑎𝑠 = 𝑣2 − 𝑢2