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Yogita Ingle 6 years, 11 months ago
Let us assume that √3 is a rational number
That is, we can find integers a and b (≠ 0) such that √3 = (a/b)
Suppose a and b have a common factor other than 1, then we can divide by the common factor, and assume that a and b are co-prime.
√3b = a
⇒ 3b2 = a2 (Squaring on both sides) → (1)
Therefore, a2 is divisible by 3
Hence a is also divisible by 3.
So, we can write a = 3c for some integer c.
Equation (1) becomes,
3b2 = (3c)2
⇒ 3b2 = 9c2
∴ b2 = 3c2
This means that b2 is divisible by 3, and so b is also divisible by 3.
Therefore, a and b have at least 3 as a common factor.
But this contradicts the fact that a and b are co-prime.
This contradiction has arisen because of our incorrect assumption that √3 is rational.
So, we conclude that √3 is irrational.
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Yogita Ingle 6 years, 11 months ago
The x - coordinate of a point is its perpendicular distance from the y – axis measured along the x -axis. The x - coordinate is also called the abscissa.
The y - coordinate of a point is its perpendicular distance from the x – axis measured along the y – axis. The y - coordinate is also called the ordinate.
Origin has zero distance from both the axes so that its abscissa and ordinate are both zero. Therefore, the coordinates of the origin are (0, 0).
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Yogita Ingle 6 years, 11 months ago
{tex}\begin{array}{l}\;\frac{\mathrm x}2+\mathrm y+\frac25\;=\;0\\\frac{5\;\mathrm x\;+10\mathrm y+4}{10}\;=\;0\\5\mathrm x\;+\;10\mathrm y\;+\;4\;=\;0\end{array}{/tex}
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Sia ? 6 years, 6 months ago
We have,
Volume of a barrel {tex}= \left( \frac { 22 } { 7 } \times 0.25 \times 0.25 \times 7 \right) \mathrm { cm } ^ { 3 }{/tex}= = 1.375 cm3
Volume of ink in the bottle = {tex}\frac { 1 } { 5 } \text { litre } = \frac { 1000 } { 5 } \mathrm { cm } ^ { 3 } = 200 \mathrm { cm } ^ { 3 }{/tex}
{tex}\therefore{/tex} Total number of barrels that can be filled from the given volume of ink = {tex}\frac { 200 } { 1.375 }{/tex}
So, required number of words ={tex}\frac { 200 } { 1.375 } \times 330 = 48000{/tex}
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