Question Number 99227 by Algoritm last updated on 19/Jun/20 Commented by Algoritm last updated on 19/Jun/20 $$\mathrm{thank}\:\mathrm{you} \\ $$ Commented by MJS last updated on…
Question Number 33690 by mondodotto@gmail.com last updated on 22/Apr/18 $$\int\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}}+\sqrt{\boldsymbol{\mathrm{x}}}} \\ $$ Answered by math1967 last updated on 22/Apr/18 $${let}\:{x}={z}^{\mathrm{6}} \:\:\therefore{dx}=\mathrm{6}{z}^{\mathrm{5}} {dz} \\ $$$$\mathrm{6}\int\frac{{z}^{\mathrm{5}} {dz}}{{z}^{\mathrm{2}}…
Question Number 33688 by mondodotto@gmail.com last updated on 22/Apr/18 $$\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{10}^{\boldsymbol{{x}}} +\mathrm{10}^{−\boldsymbol{{x}}} \right)\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{y}}\right)=\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)+\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 22/Apr/18…
Question Number 164753 by akolade last updated on 21/Jan/22 Answered by som(math1967) last updated on 21/Jan/22 $${Xlog}_{\mathrm{5}} \mathrm{5}×\mathrm{12} \\ $$$$={X}\left({log}_{\mathrm{5}} \mathrm{5}+{log}_{\mathrm{5}} \mathrm{12}\right) \\ $$$$={log}_{\mathrm{12}} \mathrm{5}\left(\mathrm{1}+{log}_{\mathrm{5}}…
Question Number 33681 by naka3546 last updated on 22/Apr/18 $${Let}\:\:{a},\:{b},\:{c}\:\:\:{are}\:\:{positive}\:{real}\:\:{numbers}\:\:{such}\:\:{that}\:\:\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:\:=\:\:\mathrm{3}\:. \\ $$$${Prove}\:{that}\::\:\:\:{a}\:+\:{b}\:+\:{c}\:\:+\:\:\frac{\mathrm{4}}{\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\left({abc}\right)^{\mathrm{2}} }}\:\:\:\geqslant\:\:\mathrm{5} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33660 by mondodotto@gmail.com last updated on 21/Apr/18 $$\:\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{sinh}{u}}=\boldsymbol{\mathrm{tan}\vartheta} \\ $$$$\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{tanh}}\frac{\boldsymbol{\mathrm{u}}}{\mathrm{2}}=\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\vartheta}}{\mathrm{2}} \\ $$$$\:\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{cosh}{u}}=\boldsymbol{\mathrm{sec}\vartheta} \\ $$$$\:\left(\boldsymbol{\mathrm{iii}}\right)\boldsymbol{\mathrm{u}}=\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{sec}\vartheta}+\boldsymbol{\mathrm{tan}\vartheta}\right) \\ $$$$\:\left(\boldsymbol{\mathrm{iv}}\right)\boldsymbol{\mathrm{tanh}{u}}=\boldsymbol{\mathrm{sin}\vartheta} \\ $$ Answered by tanmay.chaudhury50@gmail.com…
Question Number 33663 by mondodotto@gmail.com last updated on 21/Apr/18 $$\:\boldsymbol{\mathrm{Qn}}:\left(\boldsymbol{\mathrm{a}}\right) \\ $$$$\:\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{B}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{disjoint}}\:\boldsymbol{\mathrm{sets}} \\ $$$$\:\boldsymbol{\mathrm{shade}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{venn}}\:\boldsymbol{\mathrm{diagram}} \\ $$$$\:\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{B}}\cap\boldsymbol{\mathrm{C}}\:\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{A}}−\left(\boldsymbol{\mathrm{B}}\cup\boldsymbol{\mathrm{C}}\right)\:\left(\boldsymbol{\mathrm{iii}}\right)\left(\boldsymbol{\mathrm{B}}\cup\boldsymbol{\mathrm{C}}\right)−\boldsymbol{\mathrm{A}} \\ $$$$\:\boldsymbol{\mathrm{Qn}}:\left(\boldsymbol{\mathrm{b}}\right) \\ $$$$\:\boldsymbol{\mathrm{G}}\mathrm{i}\boldsymbol{\mathrm{ven}}\:\boldsymbol{\mathrm{that}}\:\mid\boldsymbol{\mathrm{A}}\mid=\mathrm{19}\:\mid\boldsymbol{\mathrm{B}}\mid=\mathrm{23}\:\mid\boldsymbol{\mathrm{C}}\mid=\mathrm{24} \\ $$$$\:\mid\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\mid=\mathrm{30}\:\mid\left(\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\right)−\boldsymbol{\mathrm{C}}\mid=\mathrm{5}\:\mid\left(\boldsymbol{\mathrm{B}}\cap\boldsymbol{\mathrm{C}}\right)\mid=\mathrm{10} \\ $$$$\:\mid\left(\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\right)^{'} \mid=\mathrm{20}\:\boldsymbol{\mathrm{and}}\:\mid\boldsymbol{\mathrm{C}}−\left(\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\right)\mid=\mathrm{10}…
Question Number 33659 by mondodotto@gmail.com last updated on 21/Apr/18 $$\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}} \\ $$$$\:\boldsymbol{\mathrm{cosh}{y}}−\mathrm{7}\boldsymbol{\mathrm{sinh}{x}}=\mathrm{3}\:\boldsymbol{\mathrm{and}} \\ $$$$\:\boldsymbol{\mathrm{cosh}{y}}−\mathrm{3}\boldsymbol{\mathrm{sinh}}^{\mathrm{2}} \boldsymbol{{x}}=\mathrm{2} \\ $$ Answered by MJS last updated on 21/Apr/18 $${I}−{II}…
Question Number 33644 by mondodotto@gmail.com last updated on 21/Apr/18 $$\:\int\left(\boldsymbol{\mathrm{sec}}^{\mathrm{2}} \boldsymbol{{x}}\right)\boldsymbol{{e}}^{\boldsymbol{\mathrm{tan}{x}}} \boldsymbol{{dx}} \\ $$ Answered by Joel578 last updated on 21/Apr/18 $${I}\:=\:\int\:\left(\mathrm{sec}^{\mathrm{2}} \:{x}\right)\:{e}^{\mathrm{tan}\:{x}} \:{dx} \\…
Question Number 33643 by mondodotto@gmail.com last updated on 21/Apr/18 $$\:\int\frac{\mathrm{2}\boldsymbol{{x}}+\mathrm{3}}{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{4}}\boldsymbol{{dx}} \\ $$ Answered by Joel578 last updated on 21/Apr/18 $${I}\:=\:\int\:\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} \:+\:\mathrm{4}}\:{dx}\:+\:\:\mathrm{3}\int\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} \:+\:\mathrm{4}}\:{dx} \\ $$$${u}\:=\:{x}^{\mathrm{2}}…