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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 the expression and write the result in the form a + bi. I^37
Suppose m be a positive integer, then the two integer a and b called congurent modulo m ' if a - b is divisible by m i.e. a - b = m where is an positive integer. The congru
A ladder sets against a wall at an angle α to the horizontal. If the foot is pulled away from the wall through a distance of 'a', so that is slides a distance 'b' down the wall ma
The boundary of the shaded portion in the adjoining figure consists of our half-circles and two quarter-circles. Find the length of the boundary and the area of the shaded portion
how the parametric equations of parabola are derived?and what is the condition for the parabola whose equation is in the form of general equation of the two intersecting lines?
Explain Graphing Equations with a Negative Slope? If the slope is a negative fraction, place the negative sign on either the numerator or the denominator. Example graph y = -2/
how do you graph y+3=-x+3x on a TI-83 graphing calculator?
Determine the linear approximation for f(x)= sin delta at delta =0
Prove that a simple graph is connected if and only if it has a spanning tree. Ans: First assume that a simple graph G has a spanning tree T. T consists of every node of G.
steps to draw direction or slope fields
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