Question-197670

Question Number 197670 by mr W last updated on 26/Sep/23

Commented by mr W last updated on 26/Sep/23

You can't use 'macro parameter character #' in math mode

Commented by ajfour last updated on 26/Sep/23

https://youtu.be/Y2LCMHAw3Fw?si=Vt7lXmpu1xLMVuB9

Commented by ajfour last updated on 26/Sep/23

A simple educational video i posted hours back, on dy/dx if y=x and if y= x^2

Commented by mr W last updated on 26/Sep/23

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Answered by mr W last updated on 26/Sep/23

Commented by mr W last updated on 26/Sep/23

s = s i d e l e n g t h o f Δ A B C

\tan α = \frac{s}{3} \times \frac{\sqrt{3}}{2} \times \frac{1}{s - \frac{s}{3} \times \frac{1}{2}} = \frac{\sqrt{3}}{5}

a = \frac{s}{2} \times \tan α = \frac{s}{2} \times \frac{\sqrt{3}}{5} = \frac{s \sqrt{3}}{10}

b = \frac{s}{2}

β = 90 ° - 60 ° = 30 °

c = b - 2 a \cos β = \frac{s}{2} - 2 \times \frac{s \sqrt{3}}{10} \times \frac{\sqrt{3}}{2} = \frac{s}{5}

\frac{b l u e a r e a}{Δ A B C} = {(\frac{c}{s})}^{2} = {(\frac{1}{5})}^{2} = \frac{1}{25} ✓

Commented by mr W last updated on 26/Sep/23

y o u a r e r i g h t s i r!

i t o o k \tan α w r o n g l y a s \sin α .

Commented by ajfour last updated on 26/Sep/23

t r i a n g l e s i d e s 6 s a n d 2 c

\frac{6 s}{2} \times \tan 30 ° = 3 s \tan α + \frac{c}{\cos 30 °} . . (i)

\frac{\sin α}{2 s} = \frac{\sin (α + 60 °)}{6 s}

\Rightarrow 3 \sin α = \frac{1}{2} \sin α + \frac{\sqrt{3}}{2} \cos α

\Rightarrow \tan α = \frac{\sqrt{3}}{5}

n o w f r o m (i)

s \sqrt{3} = \frac{3 \sqrt{3}}{5} s + \frac{2 c}{\sqrt{3}}

\frac{c}{s} = \frac{3}{5} \Rightarrow \frac{2 c}{6 s} = \frac{1}{5}

r_{a r e a} = \frac{1}{25}

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