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ARITHMETIC PROGRESSIONS: One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories
Examples:
The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term.
Ans: a4= 0
⇒ a + 3d = 0
T.P a25= 3 (a11)
⇒ a + 24d = 3 (a + 10d)
⇒ a + 24d = 3a + 30d
RHS sub a = - 3d
- 3d + 24d = 21d
LHS 3a + 30d
- 9d + 30d = 21d
LHS = RHS Hence proved
Evaluate the volume and surface area of a rectangular solid: Calculate the volume & surface area of a rectangular solid along with a = 3", b = 4", & c = 5". Solution:
Estimation of difference among two means We know that the standard error of a sample is given by the value of the standard deviation (σ) divided by the square root of the numbe
howto know whether a region is bounded or not
NULL/ VOID/ EMPTY SET A set which has no element is known as the null set or empty set and is indicated by f (phi). The number of elements of a set A is indicated as n (A) and
3^2=8
joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the
A firm buys a product using the price schedule given in the table: The company estimate holding costs at 10% of the purchase price per year and ordering costs at $40 per order .
Find out if the following sets of functions are linearly dependent or independent. (a) f ( x ) = 9 cos ( 2 x ) g ( x ) = 2 cos2 ( x ) - 2 sin 2 ( x ) (b) f
how do you solve quadratic equations by factoring?
Explain the Absorbing States of a markov chain.
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