Question Number 156453 by MathSh last updated on 11/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{9}\:+\:\mathrm{log}_{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{48}}\:=\:\mathrm{2}\:+\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{x}\:-\:\mathrm{1}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156458 by MathSh last updated on 11/Oct/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156452 by MathSh last updated on 11/Oct/21 $$\mathrm{Find}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\begin{cases}{\mathrm{x}-\mathrm{y}-\mathrm{z}\:=\:\mathrm{sin}\boldsymbol{\mathrm{x}}-\mathrm{sin}\boldsymbol{\mathrm{y}}-\mathrm{sin}\boldsymbol{\mathrm{z}}}\\{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} -\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{sin}^{\mathrm{2}} \boldsymbol{\mathrm{x}}-\mathrm{sin}^{\mathrm{2}} \boldsymbol{\mathrm{y}}-\mathrm{sin}^{\mathrm{2}} \boldsymbol{\mathrm{z}}}\\{\mathrm{x}^{\mathrm{3}} -\mathrm{y}^{\mathrm{3}} -\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{sin}^{\mathrm{3}} \boldsymbol{\mathrm{x}}-\mathrm{sin}^{\mathrm{3}} \boldsymbol{\mathrm{y}}-\mathrm{sin}^{\mathrm{3}} \boldsymbol{\mathrm{z}}}\end{cases} \\…
Question Number 90916 by byaw last updated on 26/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 25381 by Tinkutara last updated on 09/Dec/17 $$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{1},\:\mathrm{the} \\ $$$$\mathrm{second}\:\mathrm{is}\:\mathrm{2}\:\mathrm{and}\:\mathrm{every}\:\mathrm{term}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{preceding}\:\mathrm{terms}.\:\mathrm{The}\:{n}^{\mathrm{th}} \:\mathrm{term} \\ $$$$\mathrm{is}. \\ $$ Answered by prakash jain last updated…
Question Number 25378 by Tinkutara last updated on 09/Dec/17 $${If}\:\mathrm{log}\:{x},\:\mathrm{log}\:{y},\:\mathrm{log}\:{z}\:\left({x},{y},{z}\:>\:\mathrm{1}\right)\:{are}\:{in} \\ $$$${GP}\:{then}\:\mathrm{2}{x}+\mathrm{log}\left({bx}\right),\:\mathrm{3}{x}+\mathrm{log}\left({by}\right), \\ $$$$\mathrm{4}{x}+\mathrm{log}\left({bz}\right)\:{are}\:{in}\:{A}.{P}. \\ $$$$\boldsymbol{{True}}/\boldsymbol{{False}}? \\ $$ Answered by Rasheed.Sindhi last updated on 09/Dec/17…
Question Number 156448 by MathSh last updated on 11/Oct/21 $$\mathrm{If}\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}<\pi\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{sin}\sqrt{\mathrm{ab}}}{\mathrm{sin}\left(\frac{\mathrm{a}+\mathrm{b}}{\mathrm{2}}\right)}\:\geqslant\:\frac{\mathrm{32a}^{\mathrm{2}} \mathrm{b}^{\mathrm{2}} \sqrt{\mathrm{ab}}}{\left(\mathrm{a}+\mathrm{b}\right)^{\mathrm{5}} } \\ $$ Answered by ghimisi last updated on 11/Oct/21 $${f}\left({t}\right)=\frac{{sint}}{{t}^{\mathrm{5}}…
Question Number 156447 by MathSh last updated on 11/Oct/21 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{functions}\:\:\mathrm{f}\::\:\mathbb{Z}\:\rightarrow\:\mathbb{R}\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{f}\left(\mathrm{n}+\mathrm{m}\right)=\mathrm{nf}\left(\mathrm{n}\right)+\mathrm{mf}\left(\mathrm{m}\right)+\mathrm{nm}-\mathrm{n}-\mathrm{m} \\ $$$$\forall\mathrm{n};\mathrm{m}\in\mathbb{Z} \\ $$ Answered by ghimisi last updated on 11/Oct/21 $${m}=\mathrm{1};{n}=\mathrm{0}\Rightarrow{f}\left(\mathrm{1}\right)={f}\left(\mathrm{1}\right)−\mathrm{1}\Rightarrow\mathrm{0}=−\mathrm{1} \\…
Question Number 156423 by cortano last updated on 11/Oct/21 Commented by john_santu last updated on 11/Oct/21 $${answer}\:=\:\frac{\mathrm{81}\left(\sqrt{\mathrm{4}\sqrt{\mathrm{3}}−\mathrm{3}}−\mathrm{1}\right)}{\mathrm{2}}\:{sq}\:{units} \\ $$ Commented by cortano last updated on…
Question Number 156404 by ajfour last updated on 10/Oct/21 $$\:\:\mathrm{x}^{\mathrm{4}} +\mathrm{bx}^{\mathrm{2}} +\mathrm{cx}+\mathrm{d}=\mathrm{0} \\ $$$$\mathrm{let}\:\:\mathrm{cx}=\mathrm{m}+\mathrm{px}^{\mathrm{2}} +\mathrm{x}^{\mathrm{4}} \\ $$$$\Rightarrow\:\:\mathrm{2x}^{\mathrm{4}} +\left(\mathrm{b}+\mathrm{p}\right)\mathrm{x}^{\mathrm{2}} +\mathrm{m}+\mathrm{d}=\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}} =−\left(\frac{\mathrm{b}+\mathrm{p}}{\mathrm{4}}\right)\pm\sqrt{\left(\frac{\mathrm{b}+\mathrm{p}}{\mathrm{4}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{m}+\mathrm{d}}{\mathrm{2}}\right)} \\ $$$$\left(\mathrm{p}−\mathrm{b}\right)\mathrm{x}^{\mathrm{2}}…