Menu Close

Author: Tinku Tara

Question-193391

Question Number 193391 by DAVONG last updated on 12/Jun/23 Answered by aba last updated on 12/Jun/23 $$\left(\mathrm{1}\right)\:\mathrm{log}_{\mathrm{a}} \left(\mathrm{6}\right)−\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:\mathrm{log}_{\mathrm{a}} \left(\frac{\mathrm{6}}{\mathrm{x}}\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{ln}\left(\frac{\mathrm{6}}{\mathrm{x}}\right)=\mathrm{ln}\left(\sqrt{\mathrm{a}}\right)\:\Rightarrow\:\mathrm{x}=\frac{\mathrm{6}}{\:\sqrt{\mathrm{a}}}\:\checkmark \\ $$ Commented…

Question-193385

Question Number 193385 by AnshKumar last updated on 12/Jun/23 Answered by som(math1967) last updated on 12/Jun/23 $${L}.{H}.{S} \\ $$$$=\frac{{sec}\mathrm{8}{A}−\mathrm{1}}{{sec}\mathrm{4}{A}−\mathrm{1}} \\ $$$$=\frac{\frac{\mathrm{1}}{{cos}\mathrm{8}{A}}−\mathrm{1}}{\frac{\mathrm{1}}{{cos}\mathrm{4}{A}}−\mathrm{1}} \\ $$$$=\frac{{cos}\mathrm{4}{A}\left(\mathrm{1}−{cos}\mathrm{8}{A}\right)}{{cos}\mathrm{8}{A}\left(\mathrm{1}−{cos}\mathrm{4}{A}\right)} \\ $$$$=\frac{{cos}\mathrm{4}{A}×\mathrm{2}{sin}^{\mathrm{2}}…

Question-193387

Question Number 193387 by Mingma last updated on 12/Jun/23 Commented by Frix last updated on 12/Jun/23 $$\mathrm{The}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}: \\ $$$${a}=\mathrm{6} \\ $$$${b}=\mathrm{6}\sqrt{\mathrm{7}} \\ $$$${c}=\mathrm{18} \\ $$$$\Rightarrow…

Question-193381

Question Number 193381 by Mingma last updated on 12/Jun/23 Answered by som(math1967) last updated on 12/Jun/23 $$\:\mathrm{2}{sin}^{\mathrm{2}} \mathrm{4}\theta\:+\mathrm{2}{sin}^{\mathrm{2}} \mathrm{2}\theta−\mathrm{2}{sin}^{\mathrm{2}} \theta=\mathrm{1} \\ $$$$\mathrm{1}−{cos}\mathrm{8}\theta+\mathrm{1}−{cos}\mathrm{4}\theta−\mathrm{1}+{cos}\mathrm{2}\theta=\mathrm{1} \\ $$$${cos}\mathrm{2}\theta−\left({cos}\mathrm{4}\theta+{cos}\mathrm{8}\theta\right)=\mathrm{0} \\…

If-log-a-y-1-3-and-log-8-a-x-1-then-show-that-y-2-x-1-

Question Number 193368 by MATHEMATICSAM last updated on 11/Jun/23 $$\mathrm{If}\:\mathrm{log}_{{a}} {y}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\:\mathrm{log}_{\mathrm{8}} {a}\:=\:{x}\:+\:\mathrm{1}\:\mathrm{then}\:\mathrm{show} \\ $$$$\mathrm{that}\:{y}\:=\:\mathrm{2}^{{x}\:+\:\mathrm{1}} \\ $$ Answered by aba last updated on 11/Jun/23 $$\mathrm{log}_{\mathrm{8}} \mathrm{a}=\mathrm{x}+\mathrm{1}\:\Rightarrow\:\mathrm{ln}\left(\mathrm{a}\right)=\mathrm{3}\left(\mathrm{x}+\mathrm{1}\right)\mathrm{ln}\left(\mathrm{2}\right)\:\Rightarrow\:\mathrm{ln}\left(\mathrm{a}\right)=\mathrm{3ln}\left(\mathrm{2}^{\mathrm{x}+\mathrm{1}}…

Reduce-to-first-order-and-solve-showing-each-step-in-detail-1-y-y-3-siny-0-2-y-1-y-2-

Question Number 193371 by gloriousman last updated on 11/Jun/23 $$\mathrm{Reduce}\:\mathrm{to}\:\mathrm{first}\:\mathrm{order}\:\mathrm{and}\:\mathrm{solve}\:, \\ $$$$\mathrm{showing}\:\mathrm{each}\:\mathrm{step}\:\mathrm{in}\:\mathrm{detail}. \\ $$$$\mathrm{1}.\:\mathrm{y}''\:+\left(\mathrm{y}'\right)^{\mathrm{3}} \mathrm{siny}=\mathrm{0} \\ $$$$\mathrm{2}.\:\mathrm{y}''=\mathrm{1}+\left(\mathrm{y}'\right)^{\mathrm{2}} \\ $$$$ \\ $$ Answered by witcher3 last…