Question Number 206489 by Simurdiera last updated on 16/Apr/24 $${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{sin}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$ Answered by Frix last updated on 16/Apr/24 $${t}=\mathrm{tan}\:{x} \\…
Question Number 206490 by Simurdiera last updated on 16/Apr/24 $${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{cos}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$ Answered by Frix last updated on 16/Apr/24 $${t}=\mathrm{tan}\:{x} \\…
Question Number 206491 by cortano21 last updated on 16/Apr/24 Commented by cortano21 last updated on 16/Apr/24 $$\:\:\underbrace{\:} \\ $$ Answered by mr W last updated…
Question Number 206500 by MATHEMATICSAM last updated on 16/Apr/24 $$\mathrm{If}\:{a}\mathrm{sin}^{\mathrm{2}} \theta\:+\:{b}\mathrm{cos}^{\mathrm{2}} \theta\:=\:{c},\:{b}\mathrm{sin}^{\mathrm{2}} \phi\:+\:{a}\mathrm{cos}^{\mathrm{2}} \phi\:=\:{d} \\ $$$$\mathrm{and}\:{a}\mathrm{tan}\theta\:=\:{b}\mathrm{tan}\phi\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:=\:\frac{\mathrm{1}}{{c}}\:+\:\frac{\mathrm{1}}{{d}}\:. \\ $$ Answered by Berbere last updated…
Question Number 206484 by sonukgindia last updated on 16/Apr/24 Answered by mr W last updated on 16/Apr/24 Commented by mr W last updated on 16/Apr/24…
Question Number 206501 by hardmath last updated on 16/Apr/24 $$\mathrm{If} \\ $$$$\mathrm{x}^{\boldsymbol{\mathrm{log}}_{\mathrm{3}} \:\boldsymbol{\mathrm{x}}\:−\:\mathrm{1}} \:\:=\:\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}\:+\:\mathrm{3} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}_{\mathrm{2}} \:=\:? \\ $$ Commented by…
Question Number 206477 by hardmath last updated on 15/Apr/24 $$\mathrm{If}\:\:\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{4a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4ab} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{a}\:−\:\mathrm{b}}{\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$ Answered by MATHEMATICSAM last updated on 16/Apr/24 $$\mathrm{4}{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}}…
Question Number 206473 by hardmath last updated on 15/Apr/24 $$\mathrm{If}\:\:\:\mathrm{4}^{\boldsymbol{\mathrm{p}}} \:=\:\mathrm{5} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{2}^{\mathrm{3}\boldsymbol{\mathrm{p}}} \:=\:? \\ $$ Answered by A5T last updated on 15/Apr/24 $$\mathrm{2}^{\mathrm{2}{p}} =\mathrm{5}\Rightarrow\mathrm{2}^{\mathrm{3}{p}}…
Question Number 206458 by mathlove last updated on 15/Apr/24 $${if}\:{f}\left({x}\right)=\sqrt{{x}−{x}^{\mathrm{2}} }\:\:\:\:\:{then}\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$ Answered by Skabetix last updated on 15/Apr/24 $${f}^{−\mathrm{1}} \left({x}\right)=\frac{\mathrm{1}\pm\sqrt{−\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}}{\mathrm{2}} \\…
Question Number 206475 by hardmath last updated on 15/Apr/24 $$\mathrm{If}\:\:\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{12}}\:−\:\mathrm{5b}^{\mathrm{3}} \:=\:−\mathrm{30} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{2}}{\mathrm{45}}\:\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{8}}{\mathrm{3}}\:\mathrm{b}^{\mathrm{3}} \:=\:? \\ $$ Answered by A5T last updated on 15/Apr/24…