anonymous
  • anonymous
please helpppppppp...... medals and fan question in comments
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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anonymous
  • anonymous
@Michele_Laino help me once again
anonymous
  • anonymous
British curriculum?

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anonymous
  • anonymous
what ?
Michele_Laino
  • Michele_Laino
please wait, I'm working on your question...
anonymous
  • anonymous
okay...
Michele_Laino
  • Michele_Laino
here is my reasoning: |dw:1434709278703:dw| we have: \[\Large L = 2r\sin x\]
anonymous
  • anonymous
thank you...
Michele_Laino
  • Michele_Laino
now, using the theorem of Pitagora, we can write: \[\begin{gathered} \sqrt {4{r^2} - A{B^2}} = 2r\sin x \hfill \\ \sqrt {4{r^2} - A{B^2}} = 2r\sqrt {1 - {{\left( {\cos x} \right)}^2}} \hfill \\ 2r\sqrt {1 - {{\left( {\frac{{AB}}{{2r}}} \right)}^2}} = 2r\sqrt {1 - {{\left( {\cos x} \right)}^2}} \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
\[\Large \begin{gathered} \sqrt {4{r^2} - A{B^2}} = 2r\sin x \hfill \\ \sqrt {4{r^2} - A{B^2}} = 2r\sqrt {1 - {{\left( {\cos x} \right)}^2}} \hfill \\ 2r\sqrt {1 - {{\left( {\frac{{AB}}{{2r}}} \right)}^2}} = 2r\sqrt {1 - {{\left( {\cos x} \right)}^2}} \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
so, by comparison, we can write: \[\large \cos x = \frac{{AB}}{{2r}}\]
Michele_Laino
  • Michele_Laino
now, using the condition of your problem, we can write: \[\large \begin{gathered} AB + AC + arc(BC) = \pi r \hfill \\ 2AB + 2xAB = \pi r \hfill \\ 2AB\left( {1 + x} \right) = \pi r \hfill \\ AB = \frac{{\pi r}}{{2\left( {1 + x} \right)}} \hfill \\ \end{gathered} \] since, by definition of radians we can write: \[\large arc(BC) = 2xAB\]
Michele_Laino
  • Michele_Laino
now substitute the value of AB, into the expression for cos x, what do you get?
alekos
  • alekos
brilliant!
Michele_Laino
  • Michele_Laino
thanks!! :) @alekos
anonymous
  • anonymous
thanks @Michele_Laino
Michele_Laino
  • Michele_Laino
:) @yajna
alekos
  • alekos
it all follows through quite nicely. how the hell you came up with that so quickly astounds me
anonymous
  • anonymous
@Michele_Laino is a genius @alekos
anonymous
  • anonymous
btw @yajna this is the hardest question of this type you can hope to find in p3. So don't stress yourself too much if you find it hard the first time.
Miracrown
  • Miracrown
A true genius she is! @Michele_Laino :)
anonymous
  • anonymous
yes...
Michele_Laino
  • Michele_Laino
thanks! @Miracrown
alekos
  • alekos
@michele what do you do for a living?
Michele_Laino
  • Michele_Laino
at the moment I have no job!
alekos
  • alekos
you've got to be kidding! what sort of job are you looking for?
Michele_Laino
  • Michele_Laino
for example teacher, draftsman or translator from English to Italian. my last job was to translate texts of patents
Michele_Laino
  • Michele_Laino
from English to Italian
Michele_Laino
  • Michele_Laino
and my preceding job was nautical draughtsman
alekos
  • alekos
have you been out of work for long?
Michele_Laino
  • Michele_Laino
at the moment I am without job from at least 10 months!
alekos
  • alekos
i am sure you will find another job soon. keep looking and it will happen. you're a smart lady and you deserve it.
Michele_Laino
  • Michele_Laino
Thanks for your encouragement!! :) nevertheless, please keep in mind that I'm a male, Lol!!

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