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The numbers used to measure quantities such as length, area, volume, body temperature, GNP, growth rate etc. are called real numbers.
Another definition of real numbers uses a concept called number line (we will learn about it shortly). According to this definition a real number is any number that is the co-ordinate of the point on a real number line.
Sets of real numbers and relations among such sets can often be visualized by the use of a number line or co-ordinate axis. A number line is constructed by fixing a point O called the origin and another point U called the unit point on a horizontal straight line L. It is shown below. Therefore, on a number line we observe that positive numbers are in the increasing order as we move to the right of the origin whereas the negative numbers are in the decreasing order as we move to the left of the origin.
Each point P on the line L is now assigned a "numerical address" or co-ordinate "x" representing its distance from the origin, measured in terms of the given unit. Thus x = +-d, where d is the distance between O and P (shown above). The plus sign or minus sign is used to indicate whether P is to the right of the origin or to the left of the origin. If the resulting number line is drawn to some scale, each point P has a corresponding numerical value and to each real numerical value "x" there will be corresponding unique point P on the number line. This can be observed on the number line. In other words for a point say 3.7, there is only a single point on the number line and for a point Q there will be unique numerical value.
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what is the simplest form of 6:9?
Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans: S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot
all basic knowledge related to geometry
writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
One-to-one Correspondence : Suppose you are given a certain number of cups and saucers, and are asked to find out whether there are enough saucers for all the cups. How would you
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Demerits and merits of the measures of central tendency The arithmetic mean or a.m Merits i. It employs all the observations given ii. This is a very useful
Here we know x can only be 1 or -1. so if it is 1 ans is 2. if x is -1, for n even ans will be 2 if x is -1 and n is odd ans will ne -2. so we can see evenfor negative x also an
Equations of Lines In this part we need to take a view at the equation of a line in R 3 . As we saw in the earlier section the equation y = mx+b does not explain a line in R
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