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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
Given that f(x,y) = 3xy - x 2 y - xy 2 . Find all the points on the surface z = f(x, y)where local maxima, local minima, or saddles occur
Drawing Escher style tessellation
If tanA+sinA=m and m2-n2 = 4vmn, show that tanA-sinA=n
the ratio of boys to girls in the sixth grade is 2:3 if there are 24 boys, how many are girls?
10 puzzles
what is the simplest form of 6:9?
Why x and y are Simplifying Expressions? You're doing algebra now, and you know you're going to see x's and y's. But before we work with x's and y's, we'll explore why we use t
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
Download the data on Gas Mileage. This is a sample of 81 passenger cars with information about gas consumption and other technical details. a. Estimate the following
What is Markov Chains or Processes?
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