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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
A mortgage lender seeks to maximize the expected value of its portfolio. The portfolio, of course, is the sum of all of the mortgages in it, so no generality is lost by examining t
Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin
in one point of the circle only one tangent can be drawn. prove
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
definiton
Joey participated within a dance-a-thon. His team begin dancing at on Friday 10 A.M. and stopped at 6 P.M. on Saturday. How many hours did Joey's team dance? From 10 A.M. Frida
at what price a 6.25%rs 100 share be quoted when the money is worth 5%
long ago, people decided to divide the day into units called hours. they choose 24 as the number of hours in one day. why is 24 a more convenient choice than 23 or 25?
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
2/4t=1/2
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