SCIENCE AND MATHEMATICS

Factorials

Newton’s Law of Motion Sir Isaac Newton was an English mathematician, astronomer and physicist who gave three laws which proved to be fundamental laws for describing the motion of a body. These are generally known as Newton’s laws of motion. We will discuss each law of motion one by one in detail. Newton’s First Law of Motion: Newton’s first law of motion  states that “A body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it”. Suppose a block is kept on the floor, it will remain at rest until we apply some external force to it. Also, we know that it takes us more effort or force to move a heavy mass. This is directly related to a property known as Inertia. This law is also known as the law of inertia. Newton’s Second Law of Motion The first law has already given us a qualitative definition of force. Now we are interested in finding out its magnitude. According to  Newton’s second law of mot...

Linear Equations Definitions Linear Equation - An equation involving variables of the first degree only (i.e., no quadratic (x 2 ) or cubic (x 3 ) terms). For example, 10x + 2 = 5x + 12 is a linear equation while x 2  + 4 = x - 5 is not a linear equation but is rather a quadratic equation. Solution - A number that, when substituted for the unknown, will make the equation true. For example, in the equation x + 3 = 4, the number 1 is the solution since 1 + 3 = 4 Examples of Linear and Non Linear Equations Linear Equations The following is a linear equation, even though it has two different variables. 5x + 7y = 14 The following is a system of linear equations, even though it has two different equations with two different variables in each equation. 10x + 15y = 72 22x + 3y = 102 Non Linear Equations The following are not linear equations since they have an  exponent  with a power that is not 1. x 2  - 2x + 1 = 0 x -5  + y -5  + 15...

Quadratic Equations: It is defined as the two degree equation Equations having two values for variables which may be real and imaginary. These values known as roots of equation. Consider the general quadratic equation  ax 2  + bx + c = 0 Example:    x 2  + 3x – 4 = 0 Quadratic formula : Methods of Solving Quadratic Equations There are three main methods for solving quadratic equations: Factorization method Completing the square method Quadratic Equation Formula Factorization Example 1:  Solve the equation: x 2  + 3x – 4 = 0 Solution: This method is also known as splitting the middle term method. Here, a = 1, b = 3, c = -4. Let us multiply a and c = 1 * (-4) = -4. Next, the middle term is split into two terms. We do it such that the product of the new coefficients equals the product of a and c. We have to get 3 here. Consider (+4) and (-1) as the factors, whose multiplication is -4 and sum is 3. Hence, we w...