Perpendicular Axis Theorem
This is applicable only to a plane lamina. The moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of the moments of inertia of the lamina about any two mutually perpendicular axes, passing in its own plane, intersecting each other at the point..
This is applicable only to a plane lamina. The moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of the moments of inertia of the lamina about any two mutually perpendicular axes, passing in its own plane, intersecting each other at the point..Parallel Axis Theorem
Statement - The moment of inertia of a body about an axis is equal to its moment of inertia about a parallel axis through its centre of gravity plus the product of the mass of the body and the square of the perpendicular distance between the two parallel axe..
Statement - The moment of inertia of a body about an axis is equal to its moment of inertia about a parallel axis through its centre of gravity plus the product of the mass of the body and the square of the perpendicular distance between the two parallel axe..Second Fundamental Theorem of Integral Calculus
Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the va..
Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the va..Second Fundamental Theorem of Integral Calculus
Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(..
Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(..Justify step 2 in the following indirect proof.Given: The sum of the m..
Justify step 2 in the following indirect proof. Given: The sum of the measures of the interior angles of a polygon is 900. Proof: The polygon is not a hexagon. Step 1: Assume the polygon is a hexagon. Step 2: Then the sum of measures of its interior angles is 720. Step 3: But th..
Module Three: Anticipating Patterns
Discrete random variables and their probability distributions, including binomial and geometric Simulation of random behavior and probability distributions Mean (expected value) and standard deviation of a random variable and linear transformation of a random variable Combining independent..
Discrete random variables and their probability distributions, including binomial and geometric Simulation of random behavior and probability distributions Mean (expected value) and standard deviation of a random variable and linear transformation of a random variable Combining independent..central limit theorem sum
Before describing the limits of trigonometric functions, we state few theorems along with Sandwich theorem, which helps in calculating a variety of limits in subsequent chapter..
AP Probability And Statistics
Probability problems with finite sample spaces Conditional probability Discrete/continuous random variables Mean, variance of discrete random variable Standard distributions Mean, standard deviation of normally distributed random variable Central limit theorem Line..
CALCULUS
Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection poin..
Which of the following statements is true?
Which of the following statements is true? => The measure of major arc = 360 - the measure of its minor arc. or The measure of a semicircle is 270. or The sum of measures of the central angles of a circle with no interior points in common is 180. or The measure of major arc = 36..
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