Question Number 198050 by akolade last updated on 09/Oct/23 Answered by mr W last updated on 10/Oct/23 $$\mathrm{2}^{{x}} =\mathrm{3}^{{y}} ={k},\:{say} \\ $$$$\Rightarrow{x}=\frac{\mathrm{log}\:{k}}{\mathrm{log}\:\mathrm{2}},\:{y}=\frac{\mathrm{log}\:{k}}{\mathrm{log}\:\mathrm{3}} \\ $$$$\frac{\mathrm{2}×\mathrm{log}\:\mathrm{2}+\mathrm{3}×\mathrm{log}\:\mathrm{3}}{\mathrm{log}\:{k}}=\mathrm{1} \\…
Question Number 198040 by akolade last updated on 08/Oct/23 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198039 by universe last updated on 08/Oct/23 Answered by MathematicalUser2357 last updated on 09/Oct/23 $${f}\left({n}\right)=\mathrm{GreatestInteger}\left(\sqrt{{n}}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\mathrm{According}\:\mathrm{to}\:\mathrm{my}\:\mathrm{function}\:\mathrm{graph},\:\mathrm{term}\rightarrow\mathrm{3} \\ $$ Terms of Service Privacy…
Question Number 198029 by hardmath last updated on 08/Oct/23 Commented by TheHoneyCat last updated on 08/Oct/23 Sorry but could you give some context? Is there an index in the sum? (can't be lambda, it's also on the other side of the inequality, same for x) also, are you sure you are not going to use y and z? Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198030 by hardmath last updated on 08/Oct/23 Answered by Mathspace last updated on 09/Oct/23 $${let}\:\sqrt{{arcsinx}}={t}\:\Rightarrow{x}={sin}\left({t}^{\mathrm{2}} \right) \\ $$$${and}\:{I}=\int_{\sqrt{{arcsint}}} ^{\sqrt{{arcsin}\left({t}^{\mathrm{2}} \right)}} \:\:\:\frac{{t}}{{sin}\left({t}^{\mathrm{2}} \right)\left({sin}\left({t}^{\mathrm{2}} \right)−\mathrm{1}\right)}\mathrm{2}{tcos}\left({t}^{\mathrm{2}}…
Question Number 198031 by cortano12 last updated on 08/Oct/23 Answered by AST last updated on 08/Oct/23 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{20}{ab}\Rightarrow\left({a}−{b}\right)^{\mathrm{2}} =\mathrm{18}{ab}…\left({i}\right) \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} =\mathrm{19}{ab}\Rightarrow\left({a}+{b}\right)\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 197980 by mr W last updated on 07/Oct/23 Commented by mr W last updated on 07/Oct/23 $${please}\:{exact}\:{solution}! \\ $$ Commented by Blackpanther last…
Question Number 198014 by hardmath last updated on 07/Oct/23 Answered by mahdipoor last updated on 07/Oct/23 $$=\underset{{x}=−\mathrm{1}} {\overset{−\infty} {\sum}}\left(\underset{{y}={x}−\mathrm{1}} {\overset{−\infty} {\sum}}\mathrm{2}^{{x}+\mathrm{1}} ×\mathrm{3}^{{y}} ×\mathrm{5}\right)=\mathrm{5}\left(\underset{{x}=−\mathrm{1}} {\overset{−\infty} {\sum}}\mathrm{2}^{{x}+\mathrm{1}}…
Question Number 197982 by hardmath last updated on 07/Oct/23 Answered by witcher3 last updated on 11/Oct/23 $$\mathrm{sin}\left(\frac{\mathrm{12}\pi}{\mathrm{180}}\right)\mathrm{sin}\left(\frac{\mathrm{15}\pi}{\mathrm{180}}\right)\mathrm{sin}\left(\frac{\mathrm{51}\pi}{\mathrm{180}}\right)\mathrm{sin}\left(\frac{\mathrm{57}\pi}{\mathrm{180}}\right)\mathrm{sin}\left(\frac{\mathrm{63}\pi}{\mathrm{180}}\right) \\ $$$$\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{60}}\right)\mathrm{sin}\left(\frac{\mathrm{5}\pi}{\mathrm{60}}\right)\mathrm{sin}\left(\frac{\mathrm{17}\pi}{\mathrm{60}}\right)\mathrm{sin}\left(\frac{\mathrm{19}\pi}{\mathrm{60}}\right)\mathrm{sin}\left(\frac{\mathrm{21}\pi}{\mathrm{60}}\right) \\ $$$$\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{60}}\right)=\mathrm{sin}\left(\frac{\pi}{\mathrm{30}}\right)=\mathrm{sin}\left(\frac{\pi}{\mathrm{5}}−\frac{\pi}{\mathrm{6}}\right) \\ $$$$\mathrm{sin}\left(\frac{\mathrm{5}\pi}{\mathrm{60}}\right)=\mathrm{sin}\left(\frac{\pi}{\mathrm{12}}\right)=\mathrm{sin}\left(\frac{\pi}{\mathrm{3}}−\frac{\pi}{\mathrm{4}}\right) \\ $$$$\mathrm{sin}\left(\frac{\mathrm{17}\pi}{\mathrm{60}}\right)=\mathrm{sin}\left(\frac{\pi}{\mathrm{5}}+\frac{\pi}{\mathrm{12}}\right)…
Question Number 197960 by a.lgnaoui last updated on 06/Oct/23 $$\mathrm{determiner}\:\mathrm{le}\:\mathrm{total}\:\mathrm{de}\:\mathrm{nombres}\:\mathrm{de}\: \\ $$$$\mathrm{5}\:\mathrm{chiffres}\:\mathrm{comprises}\:\mathrm{entre}\:\mathrm{10000}\:\mathrm{et}\: \\ $$$$\mathrm{50000}\:\:\mathrm{divisibles}\:\mathrm{simultanement}\:\mathrm{par} \\ $$$$\mathrm{5}\:\mathrm{et}\:\mathrm{9}\:\:\: \\ $$$$\left(\mathrm{sans}\:\mathrm{utiliser}\:\mathrm{les}\:\mathrm{formules}\:\mathrm{d}\:\mathrm{arrangement}\right. \\ $$$$\left.\mathrm{et}\:\mathrm{de}\:\mathrm{combinaison}\right) \\ $$$$ \\ $$ Answered…