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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
Simultaneous equations by substitution: Solve the subsequent simultaneous equations by substitution. 3x + 4y = 6 5x + 3y = -1 Solution: Solve for x: 3x = 6
approximate the following problem as a mixed integer program. maximize z=e-x1+x1+(x2+1)2 subject to x12+x2 =0
AREAS RELATED TO CIRCLES The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. In t
Evaluate the following integral. ∫ (x+2 / 3√(x-3)) (dx) Solution Occasionally while faced with an integral that consists of a root we can make use of the following subs
A Pythagorean triple is a set of positive integers (a,b,c) like a2 + b2 = c2. Write a function "ispythag" that will receive 3 positive integers (a, b, c in that order) and will r
Write 3.5 × 104 in decimal notation? Move the decimal point 4 places to the right to get 35,000.
10 statements must be shown to be logically equivalent to the Statement the nxn matrix is invertible.
A firm is manufacturing 45,000 units of nuts. The probability of having a defective nut is 0.15 Compute the given i. The expected no. of defective nuts ii. The standard an
Dividing a quantity in a given ratio
Descrbe about Arithmetic and Geometric Sequences? When numbers are listed according to a particular pattern, we call the list a sequence. In a sequence, the numbers are separat
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