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Category: Algebra

Express-tan-3-in-surd-form-

Question Number 209768 by OmoloyeMichael last updated on 20/Jul/24 $$\boldsymbol{{Express}}\:\boldsymbol{{tan}}\left(\mathrm{3}\right)\:\boldsymbol{{in}}\:\boldsymbol{{surd}}\:\boldsymbol{{form}} \\ $$ Answered by Frix last updated on 22/Jul/24 $$\mathrm{tan}\:\left(\alpha−\beta\right)\:=\frac{\mathrm{tan}\:\alpha\:−\mathrm{tan}\:\beta}{\mathrm{1}+\mathrm{tan}\:\alpha\:\mathrm{tan}\:\beta} \\ $$$$\mathrm{Use}\:\alpha=\mathrm{18}°\:\mathrm{and}\:\beta=\mathrm{15}°.\:\mathrm{The}\:\mathrm{only}\:\mathrm{problem}\:\mathrm{is} \\ $$$$\mathrm{to}\:\mathrm{factorize}\:\mathrm{it}… \\…

tan-3x-tan-5x-2-Find-x-

Question Number 209735 by hardmath last updated on 19/Jul/24 $$\mathrm{tan}\left(\mathrm{3x}\right)\:\:+\:\:\mathrm{tan}\left(\mathrm{5x}\right)\:\:=\:\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by a.lgnaoui last updated on 20/Jul/24 $$\mathrm{voir}\:\mathrm{reponse}\:\mathrm{en}\:\mathrm{bas} \\ $$$$\:\left(\mathrm{a}\:\mathrm{l}\:\mathrm{exeption}\:\:\mathrm{d}\:'\mathrm{ereur}\:\mathrm{de}\:\mathrm{calcul}\right) \\…

If-a-b-2-7-a-b-4-Find-2a-b-

Question Number 209695 by hardmath last updated on 18/Jul/24 $$\mathrm{If}: \\ $$$$\left(\mathrm{a}\:+\:\mathrm{b}\right)\centerdot\sqrt{\mathrm{2}}\:=\:\mathrm{7}\centerdot\left(\mathrm{a}−\mathrm{b}−\mathrm{4}\right) \\ $$$$\mathrm{Find}: \\ $$$$\left(\mathrm{2a}\:+\:\mathrm{b}\right)\:=\:? \\ $$ Answered by mr W last updated on…

Question-209633

Question Number 209633 by Abdullahrussell last updated on 17/Jul/24 Answered by som(math1967) last updated on 17/Jul/24 $$\left({x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)\left(\mathrm{6}{x}+\mathrm{5}\right)^{\mathrm{2}} =\mathrm{6} \\ $$$$\Rightarrow\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}\right)\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{60}{x}+\mathrm{25}\right)=\mathrm{6} \\ $$$$\Rightarrow\left({a}+\mathrm{2}\right)\left(\mathrm{12}{a}+\mathrm{25}\right)=\mathrm{6} \\…

If-a-n-gt-0-and-lim-n-a-n-0-Find-lim-n-1-n-k-1-n-ln-k-n-a-n-

Question Number 209580 by hardmath last updated on 15/Jul/24 $$\mathrm{If}\:\:\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} >\mathrm{0}\:\:\:\mathrm{and}\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:=\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{ln}\:\left(\frac{\mathrm{k}}{\mathrm{n}}\:+\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} \right)\:=\:? \\ $$ Answered by mr W…