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…
Question Number 145002 by mathdanisur last updated on 01/Jul/21 $${Find}\:{the}\:{last}\:{digit}\:{of}\:{the}\:{number}: \\ $$$$\mathrm{1}^{\mathrm{1989}} +\mathrm{2}^{\mathrm{1989}} +\mathrm{3}^{\mathrm{1989}} +…+\mathrm{1989}^{\mathrm{1989}} \\ $$ Commented by mr W last updated on 01/Jul/21…
Question Number 144989 by mathdanisur last updated on 01/Jul/21 $${lcm}\left(\mathrm{2}{a};\mathrm{3}{a}\right)={lcm}\left(\mathrm{45};\mathrm{100}\right)\Rightarrow{a}=? \\ $$ Answered by Rasheed.Sindhi last updated on 01/Jul/21 $${lcm}\left(\mathrm{2}{a};\mathrm{3}{a}\right)={lcm}\left(\mathrm{45};\mathrm{100}\right)\Rightarrow{a}=? \\ $$$${lcm}\left(\mathrm{2}{a};\mathrm{3}{a}\right)=\mathrm{6}{a}={lcm}\left(\mathrm{45};\mathrm{100}\right)=\mathrm{900} \\ $$$${a}=\mathrm{900}/\mathrm{6}=\mathrm{150} \\…
Question Number 144981 by mathdanisur last updated on 01/Jul/21 $$\underset{{k}=\mathrm{1}} {\overset{\mathrm{35}} {\sum}}\:\frac{\sqrt{{k}}}{{k}\:+\:\sqrt{{k}^{\mathrm{2}} \:+\:{k}}}\:=\:? \\ $$ Answered by liberty last updated on 01/Jul/21 $$\:\frac{\sqrt{\mathrm{k}}}{\mathrm{k}+\sqrt{\mathrm{k}^{\mathrm{2}} +\mathrm{k}}}\:=\:\frac{\sqrt{\mathrm{k}}\:\left(\mathrm{k}−\sqrt{\mathrm{k}^{\mathrm{2}} +\mathrm{k}}\right)}{−\mathrm{k}}…
Question Number 144961 by mathdanisur last updated on 30/Jun/21 $${x}\in\mathbb{Z}^{+} \\ $$$$\mathrm{15}^{\mathrm{48}\boldsymbol{{a}}+\mathrm{1}} \:\equiv\:{x}\:\left({mod}\:\mathrm{17}\right)\:\:{find}\:\:{x}=?\: \\ $$ Answered by Rasheed.Sindhi last updated on 01/Jul/21 $$\mathrm{15}^{\mathrm{8}} \equiv{x}\left({mod}\mathrm{17}\right) \\…
Question Number 79424 by peter frank last updated on 25/Jan/20 $${Derive}\:{the}\:{width}\:{of}\:{the} \\ $$$${diffraction}\:{pattern}\:{for} \\ $$$${the}\:{case}\:{of} \\ $$$$\left({i}\right){single}\:{slits} \\ $$$$\left({ii}\right){double}\:{slits} \\ $$ Terms of Service Privacy…
Question Number 144959 by mathdanisur last updated on 30/Jun/21 Answered by Ar Brandon last updated on 01/Jul/21 $$\mathrm{sin72}°=\mathrm{cos18}°=\frac{\sqrt{\mathrm{10}+\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}} \\ $$ Commented by Ar Brandon last…