Question Number 193377 by Humble last updated on 12/Jun/23 $${Evaluate} \\ $$$${I}=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$ Commented by Frix last updated…
Question Number 193375 by Humble last updated on 12/Jun/23 $${Quantitative}\:{Reasoning} \\ $$$${Example}:\:\:{P}_{\mathrm{4}} +{M}_{\mathrm{3}} =\mathrm{16} \\ $$$${M}_{\mathrm{4}} −{P}_{\mathrm{3}} =\mathrm{18},\:{P}_{\mathrm{5}} +{M}_{\mathrm{3}} =\mathrm{2} \\ $$$${Find}: \\ $$$${P}_{\mathrm{6}} +{M}_{\mathrm{4}}…
Question Number 193368 by MATHEMATICSAM last updated on 11/Jun/23 $$\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 $$\mathrm{log}_{\mathrm{8}} \mathrm{a}=\mathrm{x}+\mathrm{1}\:\Rightarrow\:\mathrm{ln}\left(\mathrm{a}\right)=\mathrm{3}\left(\mathrm{x}+\mathrm{1}\right)\mathrm{ln}\left(\mathrm{2}\right)\:\Rightarrow\:\mathrm{ln}\left(\mathrm{a}\right)=\mathrm{3ln}\left(\mathrm{2}^{\mathrm{x}+\mathrm{1}}…
Question Number 193371 by gloriousman last updated on 11/Jun/23 $$\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…
Question Number 193366 by aipman last updated on 11/Jun/23 $$\mathrm{2sin}\:^{\mathrm{2}} \mathrm{2}{x}>\mathrm{3cos}\:{x}+\mathrm{3} \\ $$ Answered by Frix last updated on 11/Jun/23 $$\mathrm{2sin}^{\mathrm{2}} \:\mathrm{2}{x}\:−\mathrm{3}\left(\mathrm{1}+\mathrm{cos}\:{x}\right)>\mathrm{0} \\ $$$${c}=\mathrm{cos}\:{x} \\…
Question Number 193360 by MATHEMATICSAM last updated on 11/Jun/23 $$\mathrm{If}\:{x}\:=\:\mathrm{2}^{{p}} \:\mathrm{and}\:{y}\:=\:\mathrm{4}^{{q}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{log}_{\mathrm{2}} \left({x}^{\mathrm{3}} {y}\right)\:=\:\mathrm{3}{p}\:+\:\mathrm{2}{q} \\ $$ Answered by AST last updated on 11/Jun/23…
Question Number 193363 by MATHEMATICSAM last updated on 11/Jun/23 $${y}\:=\:\mathrm{4}\:×\:\mathrm{10}^{\mathrm{2}{x}} \\ $$$$\mathrm{Express}\:{x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{y},\:\mathrm{giving}\:\mathrm{an}\:\mathrm{exact} \\ $$$$\mathrm{simplified}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{log}\:\mathrm{base}\:\mathrm{10}. \\ $$ Answered by aba last updated on 11/Jun/23 $$\mathrm{y}=\mathrm{4}×\mathrm{10}^{\mathrm{2x}} \:\Rightarrow\:\mathrm{10}^{\mathrm{2x}}…
Question Number 193356 by leandrosriv02 last updated on 11/Jun/23 Answered by AST last updated on 11/Jun/23 $${m}=\mathrm{4} \\ $$$$\frac{{d}}{{dm}}\mathrm{3}^{{m}} =\mathrm{3}^{{m}} {In}\left(\mathrm{3}\right)>\:\frac{{d}}{{dm}}\left(\mathrm{2}^{{m}} +\mathrm{65}\right)=\mathrm{2}^{{m}} {In}\left(\mathrm{2}\right)\:\left({when}\:{m}>\mathrm{0}\right) \\ $$$${So},{there}\:{exists}\:{no}\:{other}\:{solution}\:{after}\:{their}\:…
Question Number 193351 by Mingma last updated on 11/Jun/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 193349 by Mingma last updated on 11/Jun/23 Answered by som(math1967) last updated on 11/Jun/23 $$\angle{P}=\angle{S} \\ $$$$\angle{Q}=\mathrm{18}\:\therefore\angle{P}=\mathrm{90}−\mathrm{18}=\mathrm{72} \\ $$$$\therefore\angle{S}=\mathrm{72} \\ $$ Commented by…