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HCF  and LCM > Important Formulas( HCF ) Highest Common Factor( HCF ) Highest Common Factor( HCF ) of two or more numbers is the greatest number which divides each of them exactly. Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer  HCF . If you want to buy a book of HCF click here - CLICK Highest Common Factor(HCF) Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly. Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF. Example : HCF of 60 and 75 = 15 because 15 is the highest number which divides both 60 and 75 exactly. We can find out HCF using prime factorization method or by dividing the numbers or division method. Example 1:  Find out HCF of 60 and 75 Step 1 : Express each number as a product of prime factors. 60 = 2 2  × 3 × 5 75 = 3 × 5 2 Example 2:  Find out HCF of 36, 24 and 12 Step 1: Expres

Molality, also called molal concentration, is a measure of the concentration of a solute in a solution in terms of amount of substance in a specified amount of mass of the solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. The properties and behavior of many solutions depend not only on the nature of the solute and solvent but also on the concentration of the solute in the solution. Chemists use many different units when expressing concentration; however, one of the most common units is molarity. Molarity (M) is the concentration of a solution expressed as the number of moles of solute per liter of solution. Mole fraction is another way of expressing the concentration of a solution or mixture. It is equal to the moles of one component divided by the total moles in the solution or mixture. a = the component that is being identified for mole fraction Mole fraction is used in a variety of calculations, b

The  Biot - Savart Law  is an equation that describes the magnetic field created by a current-carrying wire, and allows you to calculate its strength at various points. ... If you point your thumb in the direction of the current in a wire, your fingers will curl around that wire in the direction of the magnetic field. Electric fields and magnetic fields might seem different, but they're actually part of one larger force called the electromagnetic force. Charges that aren't moving produce electric fields. But when those charges do move, they instead create magnetic fields. For example, a magnet is only a magnet because of moving charges inside it. And charges moving in an electric wire also produce magnetic fields. If you move a compass near to an electric wire, you'll find that the compass needle changes direction. The  Biot-Savart Law  is an equation that describes the magnetic field created by a current-carrying wire, and allows you to calculate its strength at vari

Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called electrostatic force or Coulomb force. The interaction between charged objects is a non-contact force that acts over some distance of separation. Charge, charge and distance. Every electrical interaction involves a force that highlights the importance of these three variables. Whether it is a plastic golf tube attracting paper bits, two like-charged balloons repelling or a charged Styrofoam plate interacting with electrons in a piece of aluminum, there is always two charges and a distance between them as the three critical variables that influence the strength of the interaction. In this section of Lesson 3, we will explore the importance of these three variables.                           Coulomb's Law equation The quantitative expre

Kirchhoff's law Kirchhoff's laws  are two equalities that deal with the current and potential difference(commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called  Kirchhoff's rules  or simply  Kirchhoff's laws . These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the Circuits. Kirchhoffs First Law – The Current Law, (KCL) Kirchhoffs Current Law  or KCL, states that the “ total current or charge entering a junction or node

Integration In mathematics, an  integral  assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimaldata. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function  f  of a  real   variable   x  and an interval  [ a ,  b ]  of the real line, the  definite integral {\displaystyle \int _{a}^{b}f(x)\,dx} is defined informally as the signed area of the region in the  xy -plane that is bounded by the graph of  f , the  x -axis and the vertical lines  x  =  a  and  x  =  b . The area above the  x -axis adds to the total and that below the  x -axis subtracts from the total. The operation of integration, up to an additive constant, is the inverse of the operation of differentiation. For this reason, the term  integral  may also refer to the related notion of the antiderivative, a function  F  whose derivative is the given fun

Inverse Trigonometric function In  mathematics , the  inverse trigonometric functions  (occasionally also called  arcus functions ,   antitrigonometric functions  or  cyclometric functions ) are the  inverse functions  of the  trigonometric functions  (with suitably restricted  domains ). Specifically, they are the inverses of the  sine ,  cosine ,  tangent ,  cotangent ,  secant , and  cosecant  functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in  engineering ,  navigation ,  physics , and  geometry . There are several notations used for the inverse trigonometric functions. The most common convention is to name inverse trigonometric functions using an arc- prefix:  arcsin( x ) ,  arccos( x ) ,  arctan( x ) , etc. (This convention is used throughout this article.) This notation arises from the following geometric relationships:  When  measuring in radians, an angle of  θ radians will

Matrix In  mathematics , a  matrix  (plural:  matrices ) is a  rectangular   array  of  numbers ,  symbols , or  expressions , arranged in  rows  and  columns . For example, the dimensions of the matrix below are 2 × 3 (read "two by three"), because there are two rows and three columns: {\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.} Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be  added  or subtracted element by element (see  Conformable matrix ). The rule for  matrix multiplication , however, is that  two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second  (i.e., the inner dimensions are the same,  n  for an ( m × n )-matrix times an ( n × p )-matrix, resulting in an ( m × p )-matrix. There is no product the other way round, a first hint that matrix multiplication is not  commutat