Question Number 207885 by hardmath last updated on 29/May/24 $$\mathrm{Find}: \\ $$$$\boldsymbol{\mathrm{i}}^{\mathrm{4}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{8}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{12}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{16}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{20}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{24}} \:+…+\:\boldsymbol{\mathrm{i}}^{\mathrm{100}} \:=\:? \\ $$ Commented by mr W…
Question Number 207897 by hardmath last updated on 29/May/24 $$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{12}\:\:\centerdot\:\:\mathrm{13}\:\:\centerdot\:\:\mathrm{14}\:\:\centerdot\:\:\mathrm{15}\:\:+\:\:\mathrm{1}}\:\:=\:\:? \\ $$ Answered by Frix last updated on 29/May/24 $$\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)+\mathrm{1}}= \\ $$$$=\sqrt{{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{3}}…
Question Number 207876 by hardmath last updated on 29/May/24 $$\mathrm{Find}:\:\:\:\mathrm{ln}\:\left(\frac{\mathrm{2}\:\mathrm{tg}\:\mathrm{22},\mathrm{30}°}{\mathrm{1}\:−\:\mathrm{tg}^{\mathrm{2}} \:\mathrm{22},\mathrm{30}°}\right)\:=\:? \\ $$ Commented by mr W last updated on 29/May/24 $${use}\:{your}\:{calculator}! \\ $$ Answered…
Question Number 207866 by efronzo1 last updated on 29/May/24 $$\:\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{system}\:\begin{cases}{\mathrm{y}=−\mathrm{mx}^{\mathrm{2}} −\mathrm{2}}\\{\mathrm{4x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\mathrm{4}}\end{cases} \\ $$$$\:\:\mathrm{have}\:\mathrm{only}\:\mathrm{one}\:\mathrm{solution}\: \\ $$$$\:\:\mathrm{them}\:\mathrm{m}\:=\: \\ $$$$\:\:\left(\mathrm{A}\right)\:\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\left(\mathrm{B}\right)\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\:\left(\mathrm{C}\right)\:\mathrm{1}\:\:\:\:\left(\mathrm{D}\right)\:\sqrt{\mathrm{2}}\:\:\:\left(\mathrm{E}\right)\:\sqrt{\mathrm{3}} \\ $$$$\:\: \\ $$ Answered by…
Question Number 207852 by hardmath last updated on 28/May/24 Answered by MM42 last updated on 28/May/24 $${y}\left({y}+{x}+\mathrm{2}\right)={x}^{\mathrm{2}} \\ $$$${y}^{\mathrm{2}} +{xy}+\mathrm{2}{y}−{x}^{\mathrm{2}} =\mathrm{0}={f}\left({x},{y}\right) \\ $$$${x}=\mathrm{4}\Rightarrow{y}^{\mathrm{2}} +\mathrm{6}{y}−\mathrm{16}=\mathrm{0}\Rightarrow{y}=\mathrm{2} \\…
Question Number 207845 by hardmath last updated on 28/May/24 $$\mathrm{Find}: \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+…+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{40}} \\ $$ Answered by Frix last updated on 28/May/24 $$\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\underset{{k}=\mathrm{1}} {\overset{{j}}…
Question Number 207846 by kgmxdd last updated on 28/May/24 Answered by Frix last updated on 30/May/24 $${x}=\frac{\mathrm{2}}{\mathrm{3}−{x}} \\ $$$${x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}=\mathrm{0} \\ $$$${x}=\mathrm{1}\vee{x}=\mathrm{2} \\ $$ Commented…
Question Number 207779 by Tawa11 last updated on 26/May/24 Answered by mr W last updated on 26/May/24 Commented by Tawa11 last updated on 26/May/24 $$\mathrm{Thanks}\:\mathrm{sir}.…
Question Number 207771 by hardmath last updated on 25/May/24 $$\mathrm{Simplify}:\:\:\:\:\:\frac{\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}\:\:\sqrt{\boldsymbol{\mathrm{b}}}}{\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}}\:\:=\:\:? \\ $$ Answered by Rasheed.Sindhi last updated on 26/May/24 $$\frac{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{2}} −{c}^{\mathrm{1}/\mathrm{4}} {b}^{\mathrm{1}/\mathrm{2}} }{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{2}}…
Question Number 207747 by MASANJAJJ last updated on 25/May/24 $${find}\:{the}\:{value}\:{of}\:{y}\:{given}\:{that}\:{y}^{{y}\:} =\mathrm{3}^{{y}+\mathrm{9}} \\ $$ Commented by A5T last updated on 25/May/24 $$\mathrm{3}^{\mathrm{9}+\mathrm{9}} =\mathrm{3}^{\mathrm{18}} =\left(\mathrm{3}^{\mathrm{2}} \right)^{\mathrm{3}^{\mathrm{2}} }…