Question Number 124797 by oustmuchiya@gmail.com last updated on 06/Dec/20 Answered by benjo_mathlover last updated on 06/Dec/20 $$\left.{Q}\mathrm{2}\right)\:\mathrm{2}{p}^{\mathrm{2}} +{p}−\mathrm{10}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\left(\mathrm{2}{p}+\mathrm{5}\right)\left({p}−\mathrm{2}\right)=\mathrm{0}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{p}=\mathrm{2}\:\Rightarrow\mathrm{3}^{{x}} \:=\:\mathrm{2}\:=\:\mathrm{3}^{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}\right)} \\…
Question Number 190325 by Shrinava last updated on 31/Mar/23 Answered by mehdee42 last updated on 31/Mar/23 $${I}=\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{\mathrm{2}{tan}\frac{\beta}{\mathrm{2}}{x}}{\alpha{tan}^{\mathrm{2}} \frac{\beta}{\mathrm{2}}{x}+\mathrm{2}{tan}\frac{\beta}{\mathrm{2}}{x}+\alpha}{dx} \\ $$$${if}\:\:{tan}\frac{\beta}{\mathrm{2}}{x}={u}\Rightarrow{I}=\int_{\mathrm{0}} ^{{tan}\frac{\beta}{\mathrm{4}}} \:\frac{\mathrm{4}{du}}{\alpha{u}^{\mathrm{2}} +\mathrm{2}{u}+\alpha}…
Question Number 190324 by Shrinava last updated on 31/Mar/23 Commented by senestro last updated on 01/Apr/23 $${how}\:{can}\:{we}\:{solve}\:{it}? \\ $$ Answered by witcher3 last updated on…
Question Number 190321 by a.lgnaoui last updated on 31/Mar/23 $${What}\:{is}\:{the}\:{length}\:\:\boldsymbol{{x}}\:\:{of}\:{triangle} \\ $$$${equilateral}\:{A}^{'} {B}'{C}',{such}\:{that} \\ $$$${Area}\left({triangle}\:{ABC}\right)={Area}\left({triangle}\:{A}'{B}^{'} {C}'\right) \\ $$$$ \\ $$ Commented by a.lgnaoui last updated…
Question Number 124791 by ajfour last updated on 06/Dec/20 Commented by ajfour last updated on 06/Dec/20 $${If}\:{p},\:{q},\:{r}\:{are}\:{roots}\:{of}\:{equation} \\ $$$${x}^{\mathrm{3}} −{x}−{c}\:=\:\mathrm{0}\:\:\:,\:\:{find}\:{k}. \\ $$ Answered by ajfour…
Question Number 190303 by mnjuly1970 last updated on 31/Mar/23 $$ \\ $$$$\:\:\:\:\:\mathrm{I}{f},\:\:{f}\left({x}\right)=\:\frac{\lfloor−{x}\:\rfloor}{{x}}\:+\mathrm{1}\:\:\Rightarrow\:\:{critical}\:{points}\:\:=\:? \\ $$$$ \\ $$ Answered by mehdee42 last updated on 31/Mar/23 $$\mathbb{Z}\cup\left(−\mathrm{1},\mathrm{0}\right) \\…
Question Number 190297 by Shrinava last updated on 31/Mar/23 Answered by Frix last updated on 31/Mar/23 $$\mathrm{Let}\:{u}=\mathrm{cos}\:{x}\:\wedge{v}=\mathrm{sin}\:{x} \\ $$$$\mathrm{Transforming}\:\mathrm{leads}\:\mathrm{to} \\ $$$${u}^{\mathrm{6}} +\mathrm{2}{u}^{\mathrm{3}} {v}^{\mathrm{3}} +\mathrm{2}{u}^{\mathrm{2}} {v}^{\mathrm{2}}…
Question Number 190284 by cortano12 last updated on 31/Mar/23 $$\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{if}\:\mathrm{4}^{\mathrm{2023}} \: \\ $$$$\mathrm{divides}\:\mathrm{by}\:\mathrm{7} \\ $$ Answered by alcohol last updated on 31/Mar/23 $$\mathrm{4}^{\mathrm{3}} \:\equiv\:\mathrm{1}\left({mod}\:\mathrm{7}\right) \\…
Question Number 124740 by ajfour last updated on 05/Dec/20 Commented by ajfour last updated on 05/Dec/20 $${Find}\:{eq}.\:{of}\:{circle}\:{passing}\:{through} \\ $$$${intersection}\:{points}\:{of}\:\:{curves} \\ $$$${y}={x}^{\mathrm{2}} −\mathrm{1}\:\:{and}\:\:{y}=\frac{{c}}{{x}}\:;\:\:\:\left({c}\:<\:\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\right) \\ $$ Answered…
Question Number 190275 by aye786naing last updated on 30/Mar/23 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{i}^{\mathrm{n}} \:\mathrm{for}\:\mathrm{every}\:\mathrm{positive} \\ $$$$\:\mathrm{integer}\:\mathrm{n},\:\mathrm{where}\:\mathrm{i}^{\mathrm{2}} \:=\:−\mathrm{1},\:\mathrm{i}^{\mathrm{3}} =\:\mathrm{i}^{\mathrm{2}} \mathrm{i},\:\mathrm{i}^{\mathrm{4}} \:=\:\mathrm{i}^{\mathrm{2}} \mathrm{i}^{\mathrm{2}} \:,\:{etc}. \\ $$ Answered by Frix last…