Question Number 139668 by aupo14 last updated on 30/Apr/21 Commented by mr W last updated on 30/Apr/21 $${x}^{\mathrm{2}} \:{can}\:{only}\:{be}\:{formed}\:{from}\:{two}\:{times}\: \\ $$$$\left(\mathrm{1}+{x}+{x}^{\mathrm{3}} \right).\:{therefore}\:{the}\:{coefficient} \\ $$$${of}\:{x}^{\mathrm{2}} \:{is}\:{C}_{\mathrm{2}}…
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Question Number 74130 by mathocean1 last updated on 19/Nov/19 $$\left.\mathrm{h}\left.\mathrm{e}\left.\mathrm{l}\left.\mathrm{l}\left.\mathrm{o}\right]\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\right]−\Pi;\Pi\right]×\right]−\Pi;\Pi\right]\:\mathrm{please} \\ $$$$\begin{cases}{\mathrm{x}−\mathrm{y}=\frac{\Pi}{\mathrm{6}}}\\{\mathrm{cosx}−\sqrt{\mathrm{3}}\mathrm{cosy}=−\frac{\mathrm{1}}{\mathrm{2}}}\end{cases} \\ $$ Answered by Tanmay chaudhury last updated on 19/Nov/19 $${cos}\left(\frac{\pi}{\mathrm{6}}+{y}\right)−\sqrt{\mathrm{3}}\:{cosy}=\frac{−\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{cosy}−\frac{\mathrm{1}}{\mathrm{2}}{siny}−\sqrt{\mathrm{3}}\:{cosy}=\frac{−\mathrm{1}}{\mathrm{2}}…
Question Number 8595 by diofanto last updated on 17/Oct/16 $${Let}\:{N}\:\in\:\mathbb{Z}.\:{Show}\:{that} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{N}−\mathrm{1}} {\sum}}\frac{{N}−{k}}{{sin}\left({k}\pi/{N}\right)}\:>\:\mathrm{2}{N}−\mathrm{2}+\underset{{k}=\mathrm{2}} {\overset{{N}−\mathrm{1}} {\sum}}\frac{{N}−{k}}{{sin}\left(\left({k}−\mathrm{1}\right)\pi/\left({N}−\mathrm{1}\right)\right)} \\ $$$${if},\:{and}\:{only}\:{if},\:{N}\:\geqslant\:\mathrm{12} \\ $$ Commented by prakash jain last…
Question Number 74131 by Learner-123 last updated on 19/Nov/19 $${Can}\:{anyone}\:{share}\:{the}\:{solutions}\:\left({pdf}\right) \\ $$$${of}\:{the}\:{book}\:{Advanced}\:{engineering} \\ $$$${Mathematics}\:{by}\:{Erwin}\:{kreyzig}\:\mathrm{8}{th} \\ $$$${edition}\:? \\ $$$$ \\ $$ Commented by ajfour last updated…
Question Number 74129 by malwaan last updated on 19/Nov/19 $$\mathrm{2}\boldsymbol{{C}}_{\mathrm{4}} ^{\boldsymbol{{n}}} \:=\:\mathrm{35}\boldsymbol{{C}}_{\mathrm{3}} ^{\frac{\boldsymbol{{n}}}{\mathrm{2}}} \: \\ $$$$\Rightarrow\:\boldsymbol{{n}}\:=\:? \\ $$ Answered by MJS last updated on 20/Nov/19…
Question Number 139656 by mohammad17 last updated on 30/Apr/21 $${if}\:\:^{\mathrm{4}} \mathrm{2}=\mathrm{2}^{{x}} \:\:{find}\:{x} \\ $$ Commented by mr W last updated on 30/Apr/21 $${what}\:{is}\:^{\mathrm{4}} \mathrm{2}? \\…
Question Number 74123 by liki last updated on 19/Nov/19 Commented by liki last updated on 19/Nov/19 $$…{i}\:{need}\:{help}\:{roman}\:\left({iii}\right)\:{plz}.. \\ $$ Commented by liki last updated on…
Question Number 8585 by tawakalitu last updated on 17/Oct/16 Commented by ridwan balatif last updated on 17/Oct/16 $$\mathrm{we}\:\mathrm{must}\:\mathrm{count}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}? \\ $$ Commented by ridwan balatif last…
Question Number 74121 by Raxreedoroid last updated on 19/Nov/19 $$\mathrm{Factor}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\left(\frac{{c}}{\mathrm{2}}\right){x}^{\mathrm{2}} +\left({b}−\frac{\mathrm{3}{c}}{\mathrm{2}}\right){x}+\left({c}−{b}+{a}\right) \\ $$ Commented by MJS last updated on 19/Nov/19 $$\left({x}+\frac{{b}}{{c}}−\frac{\mathrm{3}}{\mathrm{2}}+\frac{\sqrt{\left(\mathrm{2}{b}−{c}\right)^{\mathrm{2}} −\mathrm{8}{ac}}}{\mathrm{2}{c}}\right)\left({x}+\frac{{b}}{{c}}−\frac{\mathrm{3}}{\mathrm{2}}−\frac{\sqrt{\left(\mathrm{2}{b}−{c}\right)^{\mathrm{2}} −\mathrm{8}{ac}}}{\mathrm{2}{c}}\right)…