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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
Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w → (cu → ) * v → =
Easy Rider taxi service charges a pick-up fee of $2 and $1.25 for each mile. Luxury Limo taxi service charges a pick-up fee of $3.25 and $1 per mile. How many miles required to be
What is input - output analysis?
Find the value of x if 2x + 1, x 2 + x +1, 3 x 2 - 3 x +3 are consecutive terms of an AP. Ans: a 2 -a 1 = a 3 -a 2 ⇒ x 2 + x + 1-2 x - 1 = 3x 2 - 3x + 3- x
Problem. You are given an undirected graph G = (V,E) in which the edge weights are highly restricted. In particular, each edge has a positive integer weight of either {1, 2, . .
The area of a rectangle is 24 square inches. The length of the rectangle is 2 inches more than the width. How many inches is the width? Let x = the number of inches in the widt
Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
Examples on Log rules: Example: Calculate (1/3)log 10 2. Solution: log b n√A = log b A 1/n = (1/n)log b A (1/3)log 10 2 = log 10 3 √2 = log 10 1.
1.A=the set of whole numbers less tan 4 ? 2.B=the set of prime numbers less than 19 ? 3.C=the set of first three days of week?
Find out Least Common Multiple? The smallest number that is a common multiple of two numbers (that is, both numbers share the same multiple) is called the least common multiple
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