Question Number 195571 by York12 last updated on 05/Aug/23 $${let}\:{f}\left({x}+{y}\right)+{f}\left({x}−{y}\right)=\mathrm{2}{f}\left({x}\right){f}\left({y}\right)\wedge{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=−\mathrm{1} \\ $$$${compute}\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\left[\frac{\mathrm{1}}{\mathrm{sin}\:\left({k}\right)\mathrm{sin}\:\left({k}+{f}\left({k}\right)\right)}\right] \\ $$ Answered by mahdipoor last updated on 05/Aug/23 $${x}=\mathrm{1}/\mathrm{2}\:\:\:{y}=\mathrm{0}\:\Rightarrow\:\mathrm{2}{f}\left(\mathrm{1}/\mathrm{2}\right)=\mathrm{2}{f}\left(\mathrm{1}/\mathrm{2}\right){f}\left(\mathrm{0}\right)\:\Rightarrow{f}\left(\mathrm{0}\right)=\mathrm{1} \\…
Question Number 195592 by mathlove last updated on 06/Aug/23 $${f}\left({x}\right)=\frac{\mathrm{1376}}{\left({x}−\mathrm{1}\right)^{{ln}\left(\frac{\mathrm{2}}{\mathrm{4689}}\right)} } \\ $$$${dom}\:{f}\left({x}\right)=? \\ $$$${answer}\:{this} \\ $$ Commented by bbbbbbbb last updated on 06/Aug/23 $$\boldsymbol{\mathrm{D}}\mathrm{omainf}\left(\mathrm{x}\right)=\mathrm{R}\backslash\left\{\mathrm{1}\right\}…
Question Number 195511 by Calculusboy last updated on 04/Aug/23 Answered by mr W last updated on 04/Aug/23 $${there}\:{are}\:{infinite}\:{values}\:{for}\:{k}+\mathrm{1}. \\ $$$$ \\ $$$${curve}\:{x}^{{y}} +{y}^{{x}} =\mathrm{8}\:{is}\:{symmetric}\:{about}\: \\…
Question Number 195454 by universe last updated on 02/Aug/23 Commented by mr W last updated on 03/Aug/23 $${see}\:{also}\:{Q}\mathrm{157749} \\ $$ Answered by Frix last updated…
Question Number 195419 by CrispyXYZ last updated on 02/Aug/23 $${x}\neq\mathrm{0}.\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{ix}^{{i}−\mathrm{1}} =? \\ $$ Answered by MathedUp last updated on 02/Aug/23 $${x}\neq\mathrm{0}.\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{ix}^{{i}−\mathrm{1}}…
Question Number 195413 by Calculusboy last updated on 02/Aug/23 Commented by Rasheed.Sindhi last updated on 02/Aug/23 $${x}^{{y}} +{y}^{{x}} =\mathrm{8}\Rightarrow{x}={y}=\mathrm{2} \\ $$$${x}+{y}={k}^{\mathrm{2}} \Rightarrow{k}^{\mathrm{2}} =\mathrm{2}+\mathrm{2}=\mathrm{4}\Rightarrow{k}=\pm\mathrm{2} \\ $$$${k}+\mathrm{1}=\pm\mathrm{2}+\mathrm{1}=\mathrm{3},−\mathrm{1}…
Question Number 195435 by universe last updated on 02/Aug/23 $$\sqrt{\mathrm{5}+\mathrm{1}\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{7}+\mathrm{3}\sqrt{\mathrm{8}+\mathrm{4}\sqrt{…}}}}}\:\:=\:\:\:? \\ $$ Answered by mr W last updated on 02/Aug/23 $$\mathrm{3}=\sqrt{\mathrm{9}}=\sqrt{\mathrm{5}+\mathrm{4}} \\ $$$$\mathrm{4}=\mathrm{1}×\mathrm{4}=\mathrm{1}×\sqrt{\mathrm{16}}=\mathrm{1}×\sqrt{\mathrm{6}+\mathrm{10}} \\ $$$$\mathrm{10}=\mathrm{2}×\mathrm{5}=\mathrm{2}×\sqrt{\mathrm{25}}=\mathrm{2}×\sqrt{\mathrm{7}+\mathrm{18}}…
Question Number 195428 by mathlove last updated on 02/Aug/23 $$\mathrm{3}^{{a}} =\mathrm{7}^{{b}} =\mathrm{441} \\ $$$$\frac{{ab}}{{a}+{b}}=? \\ $$ Answered by Frix last updated on 02/Aug/23 $$\mathrm{441}=\mathrm{3}^{\mathrm{2}} \mathrm{7}^{\mathrm{2}}…
Question Number 195404 by universe last updated on 01/Aug/23 Answered by AST last updated on 01/Aug/23 $$\left(\frac{\mathrm{127}^{\mathrm{2}} }{{xy}}+\frac{{x}}{{y}}+\frac{{y}}{{x}}\right)\left(\mathrm{127}+{x}+{y}\right) \\ $$$$=\frac{\mathrm{127}^{\mathrm{3}} }{{xy}}+\frac{\mathrm{127}^{\mathrm{2}} }{{y}}+\frac{\mathrm{127}^{\mathrm{2}} }{{x}}+\frac{\mathrm{127}{x}}{{y}}+\frac{{x}^{\mathrm{2}} }{{y}}+{x}+\frac{\mathrm{127}{y}}{{x}}+{y}+\frac{{y}^{\mathrm{2}} }{{x}}…
Question Number 195407 by mustafazaheen last updated on 01/Aug/23 $$\mathrm{f}'\left(\mathrm{2}\right)=\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{g}\left(\mathrm{2}\right)=\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\left(\mathrm{fog}\right)'\left(\mathrm{2}\right)=? \\ $$ Answered by gatocomcirrose last updated on 01/Aug/23 $$\left(\mathrm{fog}\right)'\left(\mathrm{2}\right)=\mathrm{f}'\left(\mathrm{g}\left(\mathrm{2}\right)\right)\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{2f}'\left(\mathrm{2}\right)=\mathrm{4} \\ $$ Answered…