Question Number 54206 by ajfour last updated on 31/Jan/19 Commented by ajfour last updated on 31/Jan/19 $${Find}\:{the}\:{area}\:{of}\:{trapezium}\:{ABCD} \\ $$$${in}\:{terms}\:{of}\:\boldsymbol{{a}}.\:\left({the}\:{red}\:{circles}\:{are}\:{each}\right. \\ $$$${within}\:{a}\:{half}\:{quarter}\:{circle}\:{and}\:{the} \\ $$$$\left.{outer}\:{boundary}\:{is}\:{a}\:{square}\:{of}\:{side}\:\boldsymbol{{a}}\right). \\ $$…
Question Number 185268 by Rupesh123 last updated on 19/Jan/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 185271 by Mingma last updated on 19/Jan/23 Answered by HeferH last updated on 19/Jan/23 Commented by HeferH last updated on 19/Jan/23 $$\frac{\mathrm{4}\:+{x}\sqrt{\mathrm{3}}}{\mathrm{2}}\:+\:\mathrm{9}\:=\:\mathrm{4}\:+\:\mathrm{10}\:−\:{x}\sqrt{\mathrm{3}} \\…
Question Number 54194 by ajfour last updated on 30/Jan/19 Commented by ajfour last updated on 31/Jan/19 $${If}\:{the}\:{small}\:{circles}\:{have}\:{the}\:{same} \\ $$$${radii},\:{find}\:\theta.\:\:\:\:\:\left({source}:\:{ajfour}\right) \\ $$ Answered by ajfour last…
Question Number 185178 by Rupesh123 last updated on 18/Jan/23 Commented by Rupesh123 last updated on 18/Jan/23 All are squares sitting on a horizontal base with areas given. Find Green Areas Answered by HeferH last updated on 18/Jan/23 Commented…
Question Number 54045 by ajfour last updated on 28/Jan/19 Commented by ajfour last updated on 28/Jan/19 $${ABCD}\:{is}\:{a}\:{square},\:{and}\:{its}\:{diagonal} \\ $$$${as}\:{a}\:{side}\:{of}\:{the}\:{rectangle}.\:{Find}\:{R}/{r}. \\ $$ Answered by ajfour last…
Question Number 54022 by ajfour last updated on 28/Jan/19 Commented by ajfour last updated on 28/Jan/19 $${Given}\:{a}\:{and}\:{b},\:{find}\:\theta\:{and}\:{R}\:{in}\:{terms} \\ $$$${of}\:{a}\:{and}\:{b}.\:\:\:\: \\ $$ Commented by tanmay.chaudhury50@gmail.com last…
Question Number 185077 by emmanuelson123 last updated on 16/Jan/23 Answered by mahdipoor last updated on 16/Jan/23 $${get}\:{side}\:{of}\:{rectangle}\:{are}\:{A}\:,\:{B}\: \\ $$$$\Delta\mathrm{1}\equiv\Delta\mathrm{2}\equiv\Delta\mathrm{3}\:\:\:\:\Rightarrow \\ $$$${side}\:{of}\:\Delta\mathrm{1}:{A}\:,\:{B}\:,\:\sqrt{{A}^{\mathrm{2}} +{B}^{\mathrm{2}} } \\ $$$${and}\:{r}_{\mathrm{1}}…
Question Number 185073 by emmanuelson123 last updated on 16/Jan/23 Answered by Frix last updated on 16/Jan/23 $$\mathrm{16}°\mathrm{52}'\mathrm{30}''\:=\:\frac{\mathrm{3}\pi}{\mathrm{32}} \\ $$$$\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{8}}\:=\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\frac{{x}}{\mathrm{2}}\:=\sqrt{\frac{\mathrm{1}−\sqrt{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{x}}}{\mathrm{2}}} \\ $$$$\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{16}}\:=\frac{\sqrt{\mathrm{2}−\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}}}{\mathrm{2}} \\…
Question Number 185052 by emmanuelson123 last updated on 16/Jan/23 Commented by Frix last updated on 16/Jan/23 $$\forall{x}\in\left[\sqrt{\mathrm{2}},\:+\infty\right):\:−\mathrm{1}\leqslant\frac{\mathrm{1}}{\mathrm{1}−\lfloor{x}^{\mathrm{2}} \rfloor}<\mathrm{0}\:\Rightarrow \\ $$$$\forall{x}\in\left[\sqrt{\mathrm{2}},\:+\infty\right):\:\lfloor\frac{\mathrm{1}}{\mathrm{1}−\lfloor{x}^{\mathrm{2}} \rfloor}\rfloor=−\mathrm{1}\:\Rightarrow \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{1};\:\sqrt{\mathrm{2}}\leqslant{x}<+\infty \\…