Question and Answers Forum

All Questions      Topic List

Coordinate Geometry Questions

Previous in All Question      Next in All Question      

Previous in Coordinate Geometry      Next in Coordinate Geometry      

Question Number 153912 by cherokeesay last updated on 12/Sep/21

Answered by mr W last updated on 12/Sep/21

Commented by mr W last updated on 12/Sep/21

$$R=3$$$$\tan \alpha =\frac{R}{2R}=\frac{1}{2}$$$$\theta =\pi -2\alpha =\pi -{2\tan }^{-1}\frac{1}{2}$$$$\sin \theta =\sin \left(2\alpha \right)=2\times \frac{1}{\sqrt{5}}\times \frac{2}{\sqrt{5}}=\frac{4}{5}$$$$areaofshadedsegmentA$$$$A=\frac{R^2}{2}(\theta -\sin \theta )=\frac{3^2}{2}(\pi -{2\tan }^{-1}\frac{1}{2}-\frac{4}{5})$$$$\approx 6.364$$

Commented by Tawa11 last updated on 12/Sep/21

$$\mathrm{Weldone}\mathrm{sir}$$

Commented by cherokeesay last updated on 12/Sep/21

$${it}^{\prime }sverybeautiful!$$$$thankyoumrW!$$

Commented by talminator2856791 last updated on 12/Sep/21

$$\mathrm{this}\mathrm{is}\mathrm{wrong}\theta \ne \alpha$$

Commented by mr W last updated on 12/Sep/21

$$whosaid\theta =\alpha ?{didn}^{\prime }tyousee$$$$\theta =\pi -2\alpha ?$$

Answered by talminator2856791 last updated on 12/Sep/21

$$$$$$u={\tan }^{-1}\left(\frac{1}{2}\right)$$$$$$$$\mathrm{shaded}\mathrm{region}$$$$=9\pi \left(\frac{\pi -2u}{2\pi }\right)-(3\cdot \sin \left(u\right))(3\cdot \cos \left(u\right))$$$$=\frac{9}{2}(\pi -u)-\frac{18}{5}$$$$\approx 8.45$$$$$$

Commented by cherokeesay last updated on 12/Sep/21

$$numerically:$$$${\mathcal{A}}_{A.S.P}=\frac{\pi .9[180°-(2\times 26,565°)]}{360°}-3,6=$$$$=9,96-3,6=6,36{cm}^2$$

Commented by cherokeesay last updated on 12/Sep/21

$$thankyousir!$$

Commented by mr W last updated on 12/Sep/21

$$checktheansweragain,{it}^{\prime }swrong!$$$$itshouldbe$$$$=\frac{9}{2}(\pi -2u)-\frac{18}{5}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com