Question Number 201134 by mnjuly1970 last updated on 30/Nov/23 $$\: \\ $$$$\:\:\:\:\:\:{S}\::\:\:{Area}\:\:{of}\:\:\:{A}\overset{\Delta} {{B}C} \\ $$$$\:\:\:\:\:{in}\:\:\:\:{A}\overset{\Delta} {{B}C}\:\::\:\:\:\frac{{a}^{\:\mathrm{2}} }{\mathrm{4}{S}}\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({cot}\left({B}\right)+{cot}\left({C}\right)\right) \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\:\mathrm{2}} }{\mathrm{4}{S}}\:=\:\frac{\:{a}^{\:\mathrm{2}} }{\mathrm{4}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:{bc}\:{sin}\left({A}\right)\right)}=\frac{\mathrm{4}{R}^{\mathrm{2}} {sin}^{\:\mathrm{2}}…
Question Number 201135 by 281981 last updated on 30/Nov/23 Answered by MM42 last updated on 30/Nov/23 $${SX}+{SM}=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}{SM}=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\left({SP}+{PQ}+{QM}\right)=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\left(\frac{\mathrm{4}{a}−{b}}{\mathrm{2}}\right)=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\Rightarrow{m}+{n}=\frac{\mathrm{9}}{\mathrm{10}}\:\:\checkmark\:\:\left(\mathrm{1}\right)…
Question Number 201112 by cherokeesay last updated on 29/Nov/23 Answered by Frix last updated on 29/Nov/23 $$\mathrm{Approximation}\:\mathrm{only} \\ $$$${x}\approx−.\mathrm{581935060421} \\ $$$${x}\approx\mathrm{8}.\mathrm{44603068951} \\ $$ Terms of…
Question Number 201081 by Calculusboy last updated on 29/Nov/23 Answered by Rasheed.Sindhi last updated on 29/Nov/23 $$\mathrm{AnOther}\:\mathrm{Way} \\ $$$$\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} −\mathrm{22}{x}−\mathrm{24}=\mathrm{0} \\ $$$${let}\:{the}\:{two}\:{roots}\:{are}\:\mathrm{3}{a}\:\&\:\mathrm{4}{a}\:{where}\:{a}\neq\mathrm{0} \\ $$$$\bullet\mathrm{2}\left(\mathrm{3}{a}\right)^{\mathrm{3}}…
Question Number 201108 by SLVR last updated on 29/Nov/23 Commented by SLVR last updated on 29/Nov/23 $${Now}\:{ok}\:{sir} \\ $$ Commented by mr W last updated…
Question Number 201110 by emilagazade last updated on 29/Nov/23 $$\int\frac{\mathrm{1}}{\:\sqrt{\left({x}−{a}\right)^{\mathrm{3}} }+\sqrt{\left({x}+{a}\right)^{\mathrm{3}} }}{dx} \\ $$ Answered by Frix last updated on 29/Nov/23 $$\sqrt{{p}}+\sqrt{{q}}=\sqrt{{p}+\mathrm{2}\sqrt{{pq}}+{q}} \\ $$$$\int\frac{{dx}}{\:\left({x}−{a}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} +\left({x}+{a}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 201106 by mnjuly1970 last updated on 29/Nov/23 $$ \\ $$$$\:\:\:\:\:{calculate}\:… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\left(\mathrm{2}{n}\:\right)}{\mathrm{2}^{\:{n}} .{n}}\:=\:? \\ $$$$ \\ $$ Answered by…
Question Number 201107 by behi834171 last updated on 29/Nov/23 $${two}\:{weels},\:{those}\:{have}\:{the}\:{same}\:{materials}, \\ $$$${with}\:{radii}:\boldsymbol{{r}}_{\mathrm{1}} =\mathrm{4}\:{and}\:\boldsymbol{{r}}_{\mathrm{2}} =\mathrm{14} \\ $$$${are}\:{starting}\:{to}\:{move}\:{on}\:{a}\:{surface},{with} \\ $$$${the}\:{same}\:{velocity},{from}:\boldsymbol{{x}}=\mathrm{0}\:{to}\:\boldsymbol{{x}}=\mathrm{20}. \\ $$$${the}\:{surface}\:{has}\:{no}\:{friction}. \\ $$$${wich}\:{one}\:{arrives}\:{faster}? \\ $$$${any}\:{informations}\:{needed}? \\…
Question Number 201070 by Rodier97 last updated on 29/Nov/23 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Un}\:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}} \\ $$$$ \\ $$$${show}\:\:{that}\:{the}\:{sequence}\:{converges}\:{and} \\ $$$${determine}\:{the}\:{limit}\: \\ $$$$ \\…
Question Number 201089 by SLVR last updated on 29/Nov/23 Commented by SLVR last updated on 29/Nov/23 $${kindly}\:{help}\:{me} \\ $$ Commented by SLVR last updated on…