Question Number 88594 by mr W last updated on 11/Apr/20 $${solve}\:{for}\:{x}\in\mathbb{C} \\ $$$$\mathrm{cos}\:\left({x}\right)={a}+{bi} \\ $$ Commented by abdomathmax last updated on 11/Apr/20 $$\Rightarrow{ch}\left({ix}\right)\:={a}+{bi}\:\Rightarrow\frac{{e}^{{ix}} \:+{e}^{−{ix}} }{\mathrm{2}}={a}+{bi}\:\Rightarrow…
Question Number 154133 by qaz last updated on 14/Sep/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt[{\mathrm{3}}]{\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}+\sqrt[{\mathrm{3}}]{\mathrm{x}−\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }} \\ $$$$\mathrm{Find}\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=? \\ $$ Answered by EDWIN88 last updated on 14/Sep/21 $$\Leftrightarrow{y}−\sqrt[{\mathrm{3}}]{{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 88590 by akash4081 last updated on 11/Apr/20 $${a}^{{a}^{{a}^{{a}^{\mathrm{3}} } } } =\mathrm{5} \\ $$$${find}−{a} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 154099 by EDWIN88 last updated on 14/Sep/21 $$\:\begin{cases}{{x}^{\mathrm{2}} +{y}\sqrt{{xy}}\:=\:\mathrm{72}}\\{{y}^{\mathrm{2}} +{x}\sqrt{{xy}}\:=\:\mathrm{36}}\end{cases} \\ $$ Answered by EDWIN88 last updated on 14/Sep/21 $$\:\begin{cases}{{x}^{\mathrm{2}} +{y}\sqrt{{xy}}\:=\mathrm{72}}\\{\mathrm{2}{y}^{\mathrm{2}} +\mathrm{2}{x}\sqrt{{xy}}\:=\mathrm{72}}\end{cases} \\…
Question Number 23000 by Tinkutara last updated on 24/Oct/17 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{and}\:{p}_{\mathrm{1}} ,\:{p}_{\mathrm{2}} , \\ $$$$…,\:{p}_{{n}} \:\mathrm{be}\:{n}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{all}\:\mathrm{larger} \\ $$$$\mathrm{than}\:\mathrm{5}\:\mathrm{such}\:\mathrm{that}\:\mathrm{6}\:\mathrm{divides}\:{p}_{\mathrm{1}} ^{\mathrm{2}} \:+\:{p}_{\mathrm{2}} ^{\mathrm{2}} \:+\:…\:+ \\ $$$${p}_{{n}} ^{\mathrm{2}} .\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{6}\:\mathrm{divides}\:{n}.…
Question Number 154068 by amin96 last updated on 13/Sep/21 Commented by amin96 last updated on 13/Sep/21 $${easy}\:{question} \\ $$ Commented by MJS_new last updated on…
Question Number 154051 by mathdanisur last updated on 13/Sep/21 $$\mathrm{let}\:\:\mathrm{a}\neq\mathrm{b}\:;\:\mathrm{b}\neq\mathrm{c}\:\mathrm{and}\:\mathrm{c}\neq\mathrm{a} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\boldsymbol{\mathrm{S}}\:=\:\mid\frac{\mathrm{a}}{\mathrm{b}-\mathrm{c}}\mid\:+\:\mid\frac{\mathrm{b}}{\mathrm{c}-\mathrm{a}}\mid\:+\:\mid\frac{\mathrm{c}}{\mathrm{a}-\mathrm{b}}\mid \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 154052 by mathdanisur last updated on 13/Sep/21 $$\mathrm{Prove}\:\mathrm{without}\:\mathrm{any}\:\mathrm{software} \\ $$$$\underset{\:\mathrm{2}−\sqrt{\mathrm{3}}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:<\:\frac{\boldsymbol{\pi}}{\mathrm{6}}\:\:\mathrm{and}\underset{\:\mathrm{1}} {\overset{\:\mathrm{2}+\sqrt{\mathrm{3}}} {\int}}\mathrm{e}^{−\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:<\:\frac{\boldsymbol{\pi}}{\mathrm{6}} \\ $$ Terms of Service…
Question Number 154045 by EDWIN88 last updated on 14/Sep/21 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{{n}}]{\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{k}^{\mathrm{2}} }{\mathrm{2}{k}^{\mathrm{2}} −\mathrm{2}{nk}+{n}^{\mathrm{2}} }\right)\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{k}^{\mathrm{2}} }{\mathrm{3}{k}^{\mathrm{2}} −\mathrm{3}{nk}+{n}^{\mathrm{2}} }\right)}\:=? \\ $$ Commented by…
Question Number 154044 by mathdanisur last updated on 13/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com