Question Number 204729 by Amidip last updated on 26/Feb/24 Answered by A5T last updated on 26/Feb/24 $$\frac{{sin}\left(\mathrm{2}{x}\right)}{{AD}}=\frac{{sin}\left(\mathrm{140}−\mathrm{2}{x}\right)}{{AB}};\frac{{sin}\left(\mathrm{140}−\mathrm{3}{x}\right)}{{AD}}=\frac{{sin}\left({x}\right)}{{DC}={AB}} \\ $$$$\Rightarrow\frac{{sin}\left(\mathrm{140}−\mathrm{3}{x}\right)}{{sin}\left({x}\right)}=\frac{{sin}\left(\mathrm{2}{x}\right)}{{sin}\left(\mathrm{140}−\mathrm{2}{x}\right)}\Rightarrow{x}=\mathrm{35}° \\ $$ Terms of Service Privacy…
Question Number 204753 by Tawa11 last updated on 26/Feb/24 A wave has an amplitude of 20cm from rest. If the angle of oscillation is 30⁰.…
Question Number 204717 by BaliramKumar last updated on 26/Feb/24 $$\frac{\mathrm{3}^{\mathrm{0}} +\mathrm{3}^{\mathrm{1}} +\mathrm{3}^{\mathrm{2}} \:+………+\:\mathrm{3}^{\mathrm{200}} }{\mathrm{13}}\:\overset{\mathrm{Remainder}} {=}\:? \\ $$ Answered by Rasheed.Sindhi last updated on 26/Feb/24 $$\mathrm{3}^{\mathrm{0}}…
Question Number 204712 by cortano12 last updated on 26/Feb/24 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{real}\:\mathrm{solution}\: \\ $$$$\:\:\:\:\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}}\:+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}}\:=\: \\ $$$$\:\:\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3x}+\mathrm{5}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}\: \\ $$ Commented by Rasheed.Sindhi last updated…
Question Number 204715 by 073 last updated on 26/Feb/24 $${prove}\:{that} \\ $$$$\overset{\mathrm{1}} {\int}_{\mathrm{0}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{{x}}{dx}=\mathrm{2}\zeta\left(\mathrm{3}\right) \\ $$$$ \\ $$ Answered by witcher3 last updated on…
Question Number 204742 by York12 last updated on 26/Feb/24 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:{x} \\ $$ Commented by York12 last updated on 26/Feb/24 Commented by TonyCWX08 last updated on…
Question Number 204739 by hardmath last updated on 26/Feb/24 Answered by mr W last updated on 26/Feb/24 $${x}^{\mathrm{4}} +\mathrm{2}{x}=−\mathrm{4} \\ $$$$\Rightarrow{x}^{\mathrm{3}} +\mathrm{2}=−\frac{\mathrm{4}}{{x}} \\ $$$$\Rightarrow\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{3}}…
Question Number 204701 by Abdullahrussell last updated on 25/Feb/24 Answered by A5T last updated on 25/Feb/24 $${x}^{\mathrm{3}} ={x}−\mathrm{2}\Rightarrow{x}^{\mathrm{4}} ={x}^{\mathrm{2}} −\mathrm{2}{x}\Rightarrow{x}^{\mathrm{5}} ={x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} =−\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{2} \\…
Question Number 204702 by mnjuly1970 last updated on 25/Feb/24 $$ \\ $$$$\:\:\:\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\:\:\:\:\:\:\:\mathrm{cl}\left(\mathbb{Q}×\mathbb{Q}\:\right)\overset{?} {=}\:\mathbb{R}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:{note}:\:\:\:\left({X}\:,{d}\:\right)\:{is}\:{a}\:{metric}\:{space} \\ $$$$\:\:\:\:\:\:\:\:\:\:,\:\:\:{A}\:\subseteq\:{X}\::\:\:\:\:\:{x}\in\:\overset{\:\:−} {{A}}=\mathrm{cl}\left({A}\right)\:\Leftrightarrow\:\forall\:{r}\:>\mathrm{0}\:,\:{B}_{{r}} \:\left({x}\right)\:\cap\:{A}\:\neq\:\phi \\ $$ Answered by…
Question Number 204671 by mr W last updated on 25/Feb/24 $${if}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4},\:{find}\:{f}\left(\mathrm{1}\right)=? \\ $$ Answered by witcher3 last updated on 25/Feb/24 $$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{4} \\ $$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{1}\right)\right)=\mathrm{2}…