Tag: maths

To change a $pm$ time to $24$ hours time , you have to add $12 \ \ pm$ to the hours unless it is $12\ \ pm$ then the time remain unchanged .

Volume of wire (cyl)= Vol of sphere 
$\displaystyle \Rightarrow \pi \times \left ( 0.2 \right )^{2}\times h=\dfrac{4}{3}\times \pi \times 3^{3}$
$\displaystyle\Rightarrow h=900 cm = 9 m $

Volume of wire (cyl)=Volume of sphere 
$\displaystyle \Rightarrow \pi r^{2}\times 72=\dfrac{4}{3}\pi \times 3^{3}$
$\displaystyle \Rightarrow r=\dfrac{1}{\sqrt{2}}cm$
Thus diameter$\displaystyle \dfrac{2}{\sqrt{2}}cm=\sqrt{2}cm=1.4cm$

Volume of cylinder = Volume of sphere
$\displaystyle \Rightarrow \pi \left ( \dfrac{d}{2} \right )^{2}h=\dfrac{4}{3}\pi \left ( \dfrac{d}{2} \right )^{3}$
$\displaystyle \Rightarrow h=\dfrac{2}{3}d\Rightarrow \dfrac{h}{2}=\dfrac{d}{3}$

Any terminating decimal between 2.357 and 3.121 will be a rational number like, ${3}$

Any non-terminating and non-recurring decimal between  2.357 and 3.121 will be an irrational number like $3.101101110...$

$4>3.623623$ and $4.90900900...>3.623623$

We know that, $ \sqrt {3} = 1.732 $ and $ \sqrt {5} = 2.236 $





Hence three rational numbers between $ 1.732 $ and $ 2.236 $  can be $

1.8( = \frac {18}{10}) ; 2 $ and $ 2.2 (= \frac {22}{10}) $

The average of the two numbers will be in between the two numbers.
$ \cfrac { \left( \dfrac { 1 }{ 3 }  \right) +\left( \dfrac { 1 }{ 2 }  \right)  }{ 2 } $