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…
Question Number 145019 by mathdanisur last updated on 01/Jul/21 $${Solve}\:{the}\:{equation}: \\ $$$${y}+\mathrm{1}={x}^{\mathrm{6}} −\mathrm{9}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{2}} \:\:;\:\:{x};{y}\in{P} \\ $$ Answered by Rasheed.Sindhi last updated on 01/Jul/21 $${y}={x}^{\mathrm{6}}…
Question Number 13929 by ajfour last updated on 25/May/17 $${prove}\:{for}\:{real}\:\boldsymbol{{x}},\boldsymbol{{y}}\:{and}\:\boldsymbol{{a}}\:{that} \\ $$$$\sqrt{\left(\boldsymbol{{x}}+\boldsymbol{{a}}\right)^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} }+\sqrt{\left(\boldsymbol{{x}}−\boldsymbol{{a}}\right)^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} }\geqslant\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:. \\ $$$$ \\ $$ Answered by mrW1…
Question Number 145003 by mathdanisur last updated on 01/Jul/21 $${Solve}\:{the}\:{equation}: \\ $$$$\mathrm{2}^{\boldsymbol{{a}}} \mathrm{3}^{\boldsymbol{{b}}} \mathrm{7}^{\boldsymbol{{c}}} \:=\:\overline {\boldsymbol{{c}}^{\mathrm{2}} \boldsymbol{{cbb}}^{\mathrm{6}} \:}\:\:;\:\:\boldsymbol{{a}};\boldsymbol{{b}};\boldsymbol{{c}}\in\boldsymbol{{P}} \\ $$ Terms of Service Privacy Policy…