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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
Evaluate following. (a) 625 3/4 Solution (a) 625 3/4 Again, let's employ both forms to calculate this one. 625 3/4 =( 625 1/4 ) 3 =(5) 3 = 12
how can a curve be divided in three equal part?
Assume that (X, d) is a metric space and let (x1, : : : , x n ) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , x n ) obtain
which ne is greater -4 4/25 or -4.12?
107*98
There's a nice way to show why the expresion for the area of a circle of radius R is: Pi * R 2 . It has an comman relationship with the experation for the circumference of a
Find out the next number in the subsequent pattern. 320, 160, 80, 40, . . . Each number is divided by 2 to find out the next number; 40 ÷ 2 = 20. Twenty is the next number.
how to solve temperature converting
Temperature: On one day in Fairfield, Montana the temperature dropped 80 degree fahrenheit from noon to midnight. If the temperature at midnight was -21 degree fahrenheit, write an
A garden shop wishes to prepare a supply of special fertilizer at a minimal cost by mixing two fertilizers, A and B. The mixture is to contain at least 45 units of phosphate at lea
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