Question Number 28911 by ajfour last updated on 01/Feb/18 Commented by ajfour last updated on 01/Feb/18 $${Find}\:{area}\:{of}\:{coloured}\:{triangle} \\ $$$${and}\:{radius}\:{of}\:{circle}\:{in}\:{terms}\:{of} \\ $$$$\boldsymbol{{a}},\:\boldsymbol{\theta},\:{and}\:\boldsymbol{\phi}\:.\:{Assume}\:\theta\:,\:\phi\:\leqslant\:\frac{\pi}{\mathrm{4}}\:. \\ $$$${Estimate}\:{maximum}\:{value}\:{of} \\ $$$${radius}\:{in}\:{terms}\:{of}\:\boldsymbol{{a}}.…
Question Number 28808 by ajfour last updated on 30/Jan/18 Answered by ajfour last updated on 30/Jan/18 $${taking}\:{A}\:{as}\:{origin}, \\ $$$${and}\:\angle{AED}=\alpha\:=\mathrm{tan}^{−\mathrm{1}} \mathrm{2} \\ $$$${eq}.\:{of}\:{AC}\:\:\:\:\:\:\:\:\:\:\boldsymbol{{y}}=\boldsymbol{{x}} \\ $$$${eq}.\:{of}\:{DE}\:\:\:\:\:\:\:\:\boldsymbol{{y}}=\boldsymbol{{a}}−\mathrm{2}\boldsymbol{{x}} \\…
Question Number 28779 by ajfour last updated on 30/Jan/18 Commented by naka3546 last updated on 30/Jan/18 substitute x and y in a and b. Answered by ajfour last updated on 30/Jan/18 $${Area}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left({a}+{b}\right)^{\mathrm{2}}…
Question Number 28690 by ajfour last updated on 28/Jan/18 Commented by ajfour last updated on 28/Jan/18 $${Find}\:{the}\:{area}\:{in}\:{blue}\:{in}\:{terms}\:{of} \\ $$$$\boldsymbol{{r}}\:{and}\:\boldsymbol{{d}}\:. \\ $$ Commented by beh.i83417@gmail.com last…
Question Number 28574 by ajfour last updated on 27/Jan/18 Commented by ajfour last updated on 27/Jan/18 $${Find}\:{entire}\:{green}\:{area}\:{in}\:{terms} \\ $$$${of}\:\boldsymbol{{r}},\:\boldsymbol{\theta}\:.\:{The}\:{two}\:{frames}\:{are} \\ $$$${square}\:{frames}\:{with}\:{common} \\ $$$${centre}.\:{Find}\:{also}\:{the}\:{maximum} \\ $$$${of}\:{the}\:{area}\:{for}\:{constant}\:\boldsymbol{{r}}.…
Question Number 28547 by tawa tawa last updated on 26/Jan/18 Answered by mrW2 last updated on 26/Jan/18 $${Area}\:{of}\:\Delta{PQR}=\frac{\mathrm{1}}{\mathrm{2}}×{QR}×{PM}=\frac{\mathrm{1}}{\mathrm{2}}×{PR}×{QT} \\ $$$$\Rightarrow{QR}×{PM}={PR}×{QT} \\ $$$$\Rightarrow\mathrm{8}×{PM}=\mathrm{7}×\mathrm{4} \\ $$$$\Rightarrow{PM}=\frac{\mathrm{7}×\mathrm{4}}{\mathrm{8}}=\frac{\mathrm{7}}{\mathrm{2}}=\mathrm{3}.\mathrm{5}\:{cm} \\…
Question Number 28508 by ajfour last updated on 26/Jan/18 Commented by ajfour last updated on 26/Jan/18 $${Q}.\mathrm{28479}\:\left({solution}\right) \\ $$ Answered by ajfour last updated on…
Question Number 94020 by i jagooll last updated on 16/May/20 Commented by i jagooll last updated on 16/May/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{area} \\ $$ Commented by i jagooll…
Question Number 93991 by i jagooll last updated on 16/May/20 Commented by i jagooll last updated on 16/May/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{area} \\ $$$$ \\ $$ Commented by…
Question Number 28399 by ajfour last updated on 25/Jan/18 Answered by ajfour last updated on 25/Jan/18 $${eq}.\:{of}\:{circle}: \\ $$$${x}={r}+{r}\mathrm{cos}\:\theta\:\:,\:{y}={r}+{r}\mathrm{sin}\:\theta \\ $$$${eq}.\:{of}\:{line}: \\ $$$$\frac{{x}}{{a}}+\frac{{y}}{{b}}=\mathrm{1} \\ $$$$\:{intersection}\:{points}:\:\:\theta_{\mathrm{1}}…