Question Number 142765 by mr W last updated on 05/Jun/21 $${A}\:{class}\:{has}\:\mathrm{13}\:{children}.\:{To}\:{play}\:{a} \\ $$$${game}\:{one}\:{child}\:{is}\:{the}\:{referee}\:{and}\:{the} \\ $$$${other}\:{children}\:{are}\:{divided}\:{in}\:{three}\: \\ $$$${teams}\:{with}\:{four}\:{children}\:{in}\:{each}\:{team}. \\ $$$${In}\:{how}\:{many}\:{ways}\:{can}\:{the}\:{class}\:{play} \\ $$$${the}\:{game}? \\ $$ Commented by…
Question Number 77230 by Umar last updated on 04/Jan/20 $$\mathrm{An}\:\mathrm{astromer}\:\mathrm{finds}\:\mathrm{a}\:\mathrm{new}\:\mathrm{absorption}\: \\ $$$$\mathrm{line}\:\mathrm{with}\:\lambda=\mathrm{164}.\mathrm{1nm}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ultraviolet} \\ $$$$\mathrm{region}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sun}'\mathrm{s}\:\mathrm{continuous}\:\mathrm{spectrum}. \\ $$$$\mathrm{He}\:\mathrm{attributes}\:\mathrm{the}\:\mathrm{line}\:\mathrm{to}\:\mathrm{hydrogen}'\mathrm{s}\: \\ $$$$\mathrm{Layman}\:\mathrm{series}.\:\mathrm{Is}\:\mathrm{he}\:\mathrm{right}?\:\mathrm{Justify} \\ $$$$\mathrm{your}\:\mathrm{answer}. \\ $$$$ \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{help}}. \\…
Question Number 11695 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Mar/17 Commented by mrW1 last updated on 30/Mar/17 $${there}\:{is}\:{no}\:{max}.\:{or}\:{min}.\:{there}\:{is}\:{only} \\ $$$${a}\:{local}\:{max}. \\ $$ Commented by mrW1 last…
Question Number 77229 by Maclaurin Stickker last updated on 04/Jan/20 Commented by Maclaurin Stickker last updated on 04/Jan/20 $${ABC}\:{is}\:{a}\:{triangle}.\:{Radius}\:{circumferences} \\ $$$${shown}\:{in}\:{the}\:{figure}\:{are}\:{drawn} \\ $$$${internally}\:{to}\:{the}\:{triangle}\:{tanging} \\ $$$${two}\:{of}\:{its}\:{sides}\:{and}\:{the}\:{incircle}.…
Question Number 142763 by lapache last updated on 05/Jun/21 Commented by Ar Brandon last updated on 05/Jun/21 $$\mathcal{I}=\int\sqrt{\mathrm{tanx}}\mathrm{dx}\:,\:\mathrm{t}^{\mathrm{2}} =\mathrm{tanx}\:\Rightarrow\mathrm{2tdt}=\left(\mathrm{1}+\mathrm{t}^{\mathrm{4}} \right)\mathrm{dx} \\ $$$$\:\:\:=\int\frac{\mathrm{2t}^{\mathrm{2}} \mathrm{dt}}{\mathrm{1}+\mathrm{t}^{\mathrm{4}} }=\int\frac{\left(\mathrm{t}^{\mathrm{2}} +\mathrm{1}\right)+\left(\mathrm{t}^{\mathrm{2}}…
Question Number 77221 by john santu last updated on 04/Jan/20 $$\int\:\frac{\sqrt{\mathrm{2}+{x}}\:{dx}}{\:\sqrt{{x}^{\mathrm{5}} }}\:=\:? \\ $$ Answered by jagoll last updated on 04/Jan/20 $$\int\:\frac{\sqrt{\mathrm{2}+\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}}}\mathrm{dx}\:=\:\int\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\sqrt{\frac{\mathrm{2}}{\mathrm{x}}+\mathrm{1}}\:\mathrm{dx} \\…
Question Number 77218 by john santu last updated on 04/Jan/20 $${what}\:{is}\:{solution}\:{in}\:\mathbb{R}\: \\ $$$$\frac{\mathrm{sin}\:\left({x}\right)−\mid{x}+\mathrm{2}\mid}{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}}\geqslant\mathrm{0}\:?\: \\ $$ Answered by MJS last updated on 04/Jan/20 $$\mathrm{sin}\:{x}\:−\mid{x}+\mathrm{2}\mid\geqslant\mathrm{0}\wedge\left({x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}\right)>\mathrm{0}…
Question Number 77219 by john santu last updated on 04/Jan/20 $${if}\:\mathrm{log}_{\mathrm{9}} \left({a}\right)=\mathrm{log}_{\mathrm{4}} \left({a}+{b}\right)=\mathrm{log}_{\mathrm{6}} \left({b}\right)\: \\ $$$${what}\:{is}\:\frac{{a}}{{b}}\:? \\ $$ Answered by jagoll last updated on 04/Jan/20…
Question Number 142755 by ERA last updated on 05/Jun/21 $$\mathrm{log}_{\mathrm{3}} \mathrm{x}^{\mathrm{3}} +\mathrm{log}_{\mathrm{2}} \mathrm{x}^{\mathrm{2}} =\frac{\mathrm{2lg6}}{\mathrm{lg2}}+\mathrm{1}\:\:\mathrm{find}\:\:\mathrm{x} \\ $$ Commented by iloveisrael last updated on 05/Jun/21 $${what}\:{different}\:\mathrm{log}\:\:{and}\:\mathrm{lg}\:? \\…
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