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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
What is the ratio of the cone''s volume to the cylinder''s volume
Sketch the graph of y = ( x -1) 2 - 4 . Solution Now, it is a parabola .Though, we haven't gotten that far yet and thus we will have to select
Urn A contains 1 white,2 black and 3 red balls;Urn B contains 2 white,1 black and 1 red balls;and Urn C contains 4 white,5 black and 3 red balls.One urn is chosen at random and two
what is the remainder when 75 is divided by 4
no the parallel lines do not meet at infinity because the parallel lines never intersect each other even at infinity.if the intersect then it is called perpendicuar lines
Example Find the values of the given expressions. Also given that a = 2, b = 3, c = 1, and x = 2. 8a + 5bc = 8.2
0.34/100
Consider the following multiplication in decimal notations: (999).(abc)=def132 ,determine the digits a,b,c,d,e,f. solution) a=8 b=6 c=8 d=8 e=6 f=7 In other words, 999 * 877 = 8
Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 . Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co
2x+3y=1, 5x+7y=3.
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