Question Number 208466 by Tawa11 last updated on 16/Jun/24 Answered by A5T last updated on 17/Jun/24 Commented by A5T last updated on 17/Jun/24 $$\mathrm{4}{x}+\mathrm{3}{x}+\mathrm{2}{x}=\mathrm{180}\Rightarrow{x}=\mathrm{20}° \\…
Question Number 208467 by Tawa11 last updated on 16/Jun/24 Answered by A5T last updated on 17/Jun/24 Commented by A5T last updated on 17/Jun/24 $${sin}\theta=\frac{\mathrm{3}\sqrt{\mathrm{10}}}{\:\mathrm{10}}\Rightarrow{cos}\theta=\frac{\sqrt{\mathrm{10}}}{\mathrm{10}} \\…
Question Number 208463 by hardmath last updated on 16/Jun/24 $$\mathrm{Compare}\:\mathrm{it}: \\ $$$$\mathrm{a}\:=\:\mathrm{log}_{\mathrm{3}} \:\mathrm{4} \\ $$$$\mathrm{b}\:=\:\mathrm{log}_{\mathrm{5}} \:\mathrm{6} \\ $$$$\mathrm{c}\:=\:\mathrm{log}_{\mathrm{6}} \:\mathrm{2} \\ $$ Answered by Frix last…
Question Number 208453 by hardmath last updated on 16/Jun/24 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\left(\mathrm{2a}\:+\:\mathrm{1}\right)\centerdot\mathrm{x}\:+\:\mathrm{1}}{\mathrm{x}\:−\:\mathrm{a}}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{3}\:=\:? \\ $$ Answered by efronzo1 last updated on 16/Jun/24 $$\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=\frac{\mathrm{ax}+\mathrm{1}}{\mathrm{x}−\left(\mathrm{2a}+\mathrm{1}\right)}\:=\:\frac{\left(\mathrm{2a}+\mathrm{1}\right)\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{a}}…
Question Number 208455 by efronzo1 last updated on 16/Jun/24 Commented by mr W last updated on 16/Jun/24 $${the}\:{green}\:{one}\:{even}\:{doesn}'{t}\:{need}\:{to}\:{be}\: \\ $$$${a}\:{semicircle}. \\ $$ Commented by mr…
Question Number 208412 by efronzo1 last updated on 15/Jun/24 Answered by A5T last updated on 15/Jun/24 $$\mathrm{8}=\mathrm{24}^{\frac{\mathrm{1}}{{a}}} ,\mathrm{27}=\mathrm{24}^{\frac{\mathrm{1}}{{b}}} ,\mathrm{64}=\mathrm{24}^{\frac{\mathrm{1}}{{c}}} \\ $$$$\Rightarrow\mathrm{24}^{\mathrm{3}} =\mathrm{8}×\mathrm{27}×\mathrm{64}=\mathrm{24}^{\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=\frac{{ab}+{bc}+{ca}}{{abc}}\right)} \\ $$$$\Rightarrow\frac{{ab}+{bc}+{ca}}{{abc}}=\mathrm{3}\Rightarrow\frac{\mathrm{2022}{abc}}{{ab}+{bc}+{ca}}=\mathrm{2022}×\frac{\mathrm{1}}{\mathrm{3}}=\mathrm{674} \\…
Question Number 208431 by alcohol last updated on 15/Jun/24 $${h}_{{a}} \left({x}\right)\:=\:{e}^{−{x}} \:+\:{ax}^{\mathrm{2}} \\ $$$${show}\:{that}\:{h}_{{a}} \:{admits}\:{a}\:{minimum}\:{in}\:\mathbb{R} \\ $$ Answered by mathzup last updated on 15/Jun/24 $${cas}\:\mathrm{1}\:\:\:\:\:\:{a}>\mathrm{0}…
Question Number 208409 by hardmath last updated on 15/Jun/24 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\mid\mathrm{1}\:−\:\mathrm{x}\mid\:\mathrm{dx}\:=\:? \\ $$ Answered by mr W last updated on 15/Jun/24 $$=\mathrm{2}\int_{\mathrm{1}} ^{\mathrm{2}} \left({x}−\mathrm{1}\right){dx}…
Question Number 208420 by lepuissantcedricjunior last updated on 15/Jun/24 $$\boldsymbol{{resoudre}}\:\boldsymbol{{dans}}\:\mathbb{R}^{\mathrm{3}} \\ $$$$\begin{cases}{\boldsymbol{{x}}+\boldsymbol{{y}}=\mathrm{3}}\\{\boldsymbol{{y}}+\boldsymbol{{z}}=\mathrm{5}}\end{cases}\boldsymbol{{x}}+\boldsymbol{{z}}=\mathrm{4} \\ $$ Commented by A5T last updated on 15/Jun/24 $${You}\:{should}\:{learn}\:{to}\:{signify}\:{that}\:{you}\:{changed} \\ $$$${a}\:{question}. \\…
Question Number 208421 by lepuissantcedricjunior last updated on 15/Jun/24 Commented by Frix last updated on 15/Jun/24 $$\Psi=\mathrm{2}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{tan}\:\mathrm{2}{x}}}\:\overset{{t}=\sqrt{\mathrm{tan}\:\mathrm{2}{x}}} {=}\:\mathrm{2}\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dt}}{{t}^{\mathrm{4}} +\mathrm{1}}=\frac{\sqrt{\mathrm{2}}\pi}{\mathrm{2}} \\ $$…