Question Number 79538 by Pratah last updated on 26/Jan/20 Commented by john santu last updated on 26/Jan/20 $$\left(\sqrt{\mathrm{5}−\mathrm{7}{x}}\right)\left({ln}\left(\frac{\mathrm{9}{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{3}{x}+{a}}\right)\right)=\mathrm{0} \\ $$$$\left(\sqrt{\mathrm{5}−\mathrm{7x}}\right)\left(\mathrm{ln}\left(\frac{\left(\mathrm{3x}+\mathrm{a}\right)\left(\mathrm{3x}−\mathrm{a}\right)}{\left(\mathrm{3x}+\mathrm{a}\right)}\right)\right)=\mathrm{0} \\ $$$$\sqrt{\mathrm{5}−\mathrm{7x}}\:\mathrm{ln}\left(\mathrm{3x}−\mathrm{a}\right)=\mathrm{0}\:,\:\mathrm{a}\neq\:−\mathrm{3x} \\…
Question Number 145073 by gsk2684 last updated on 02/Jul/21 $$\mathrm{let}\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,…,\mathrm{a}_{\mathrm{n}} \:\mathrm{be}\:\mathrm{positive} \\ $$$$\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{a}_{\mathrm{1}} +\mathrm{a}_{\mathrm{2}} +…+\mathrm{a}_{\mathrm{n}} =\mathrm{1}\:\mathrm{then}\:\mathrm{find}\: \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{a}_{\mathrm{1}} ^{\mathrm{a}_{\mathrm{1}}…
Question Number 79536 by Pratah last updated on 26/Jan/20 Commented by Pratah last updated on 26/Jan/20 $$\left.\mathrm{A}\left.\right)\left.\mathrm{0}\left.\:\:\:\:\:\:\:\:\:\mathrm{B}\right)−\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{C}\right)\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{D}\right)−\mathrm{3} \\ $$ Commented by Pratah last updated on…
Question Number 14002 by Joel577 last updated on 26/May/17 $$\mathrm{If}\:\sqrt{−\mathrm{1}}\:=\:{i},\:\mathrm{then}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{{i}}\:? \\ $$ Answered by ajfour last updated on 26/May/17 $${i}={e}^{{i}\left(\frac{\pi}{\mathrm{2}}+\mathrm{2}{n}\pi\right)} \\ $$$$\sqrt{{i}}={e}^{{i}\left(\frac{\pi}{\mathrm{4}}+{n}\pi\right)} \\…
Question Number 13986 by RasheedSindhi last updated on 26/May/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system} \\ $$$$\mathrm{of}\:\mathrm{equations}. \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{x}}}+\frac{\sqrt{\mathrm{y}}}{\mathrm{y}^{\mathrm{2}} }=\frac{\mathrm{1729}}{\mathrm{64}} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{y}^{\mathrm{2}} }{\:\sqrt{\mathrm{x}}}−\frac{\sqrt{\mathrm{y}}}{\mathrm{x}^{\mathrm{2}} }=\frac{\mathrm{6908}}{\mathrm{81}} \\ $$$$ \\ $$ Commented…
Question Number 79512 by M±th+et£s last updated on 25/Jan/20 $${Q}.{solve} \\ $$$${if}\:{t}^{\mathrm{2}} ={n}^{\mathrm{2}} {cos}^{\mathrm{2}} \left({x}\right)+{m}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({x}\right) \\ $$$$ \\ $$$${then}\:{show}\:{that}: \\ $$$${t}+\frac{{d}^{\mathrm{2}} {t}}{{dx}^{\mathrm{2}} }=\frac{\left({nm}\right)^{\mathrm{2}}…
Question Number 79513 by M±th+et£s last updated on 25/Jan/20 $${Q}.{solve} \\ $$$${if}\:{t}^{\mathrm{2}} ={n}^{\mathrm{2}} {cos}^{\mathrm{2}} \left({x}\right)+{m}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({x}\right) \\ $$$$ \\ $$$${then}\:{show}\:{that}: \\ $$$${t}+\frac{{d}^{\mathrm{2}} {t}}{{dx}^{\mathrm{2}} }=\frac{\left({nm}\right)^{\mathrm{2}}…
Question Number 145047 by mathdanisur last updated on 01/Jul/21 Commented by mr W last updated on 01/Jul/21 $${last}\:{digit}\:{is}\:\mathrm{5}. \\ $$ Answered by ArielVyny last updated…
Question Number 145025 by mathdanisur last updated on 01/Jul/21 $$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\sqrt{{n}}+{n}\sqrt{{n}+\mathrm{1}}}\:=\:? \\ $$ Answered by phally last updated on 01/Jul/21 $$=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{n}+\mathrm{1}\right)\sqrt{\mathrm{n}}−\mathrm{n}\sqrt{\mathrm{n}+\mathrm{1}}}{\left[\left(\mathrm{n}+\mathrm{1}\right)\sqrt{\mathrm{n}}\right]^{\mathrm{2}} −\left(\mathrm{n}\sqrt{\mathrm{n}+\mathrm{1}}\right)^{\mathrm{2}}…
Question Number 145023 by mathdanisur last updated on 01/Jul/21 Commented by Rasheed.Sindhi last updated on 02/Jul/21 $$\mathcal{B}{y}\overline {\:\:\boldsymbol{{c}}^{\mathrm{2}} \boldsymbol{{cbb}}^{\mathrm{6}} \:\:}{do}\:{you}\:{mean}\:{digital} \\ $$$${representation}\:{of}\:{a}\:{number}? \\ $$ Commented…