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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
Who discovered unitary method? ?
The ratio of boys to girls at the dance was 3:4. There were 60 girls at the dance. How many boys were at the dance? Use a proportion comparing boys to girls at the dance. Boys/
3.6 in a fraction
Expected opportunity loss or EOL method EOL method is aimed at minimizing the expected opportunity loss or OEL. The decision maker chooses the strategy along with the minimum e
show that a*0=a
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Determine whether R is an equivalence relation or a p
Interpretations of the Derivative : Before moving on to the section where we study how to calculate derivatives by ignoring the limits we were evaluating in the earlier secti
Find the equation for each of the two planes that just touch the sphere (x - 1) 2 + (y - 4) 2 + (z - 2)2 = 36 and are parallel to the yz-plane. And give the points on the sphere
What is a Function, Anyway? Domain? Range? Next time you're at a fast-food restaurant, take a look at the price list. It may look something like this: • Hamburger.............
Three mixtures were prepared with very narrow molar mass distribution polyisoprene samples with molar masses of 8000, 25,000, and 100,000 as indicated below. (a) Equal numbers o
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