Question Number 11805 by tawa last updated on 01/Apr/17 $$\mathrm{x}^{\mathrm{y}} \:=\:\mathrm{y}^{\mathrm{x}} \:\:\:\: \\ $$$$\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{y}^{\mathrm{3}} \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$ Answered by mrW1 last updated on…
Question Number 77340 by BK last updated on 05/Jan/20 Answered by mind is power last updated on 05/Jan/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{t}\right)=\mathrm{t}^{\mathrm{3}} +\mathrm{t}^{\mathrm{2}} +\mathrm{16t}+\mathrm{60} \\ $$$$\mathrm{z}=\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{y}=\mathrm{fof}\left(\mathrm{x}\right)…
Question Number 142865 by EnterUsername last updated on 06/Jun/21 $$\mathrm{Let}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:…\:\mathrm{be}\:\mathrm{an}\:\mathrm{arithmethic}\:\mathrm{progression}\:\mathrm{of} \\ $$$$\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers}.\:\mathrm{Then} \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{1}}{\:\sqrt{{a}_{\mathrm{1}} }+\sqrt{{a}_{\mathrm{2}} }}+\frac{\mathrm{1}}{\:\sqrt{{a}_{\mathrm{2}} }+\sqrt{{a}_{\mathrm{3}} }}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\:\sqrt{{a}_{{n}−\mathrm{1}} }+\sqrt{{a}_{{n}} }}= \\ $$$$\left(\mathrm{A}\right)\:\frac{{n}+\mathrm{1}}{\:\sqrt{{a}_{\mathrm{1}}…
Question Number 142863 by mathsuji last updated on 06/Jun/21 Answered by mnjuly1970 last updated on 06/Jun/21 $$\:\:\:\:\:\frac{\mathrm{2}\left({R}+{r}\right)}{{F}\rightarrow!!!??} \\ $$ Commented by mathsuji last updated on…
Question Number 77313 by David Danile last updated on 05/Jan/20 $$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{2} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{3} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{x}^{\mathrm{8}}…
Question Number 11768 by Nayon last updated on 31/Mar/17 $${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0}\:{solve}\:{it}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 11764 by Peter last updated on 31/Mar/17 $$\mathrm{if}\:\mathrm{x}\:\mathrm{y}\:\mathrm{and}\:\mathrm{z}\:\mathrm{are}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\frac{\mathrm{x}\:+\:\mathrm{xy}}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{1}}\:=\:\mathrm{2} \\ $$$$\frac{\mathrm{2x}\:+\:\mathrm{xz}}{\mathrm{x}\:+\:\mathrm{z}\:+\mathrm{2}}\:=\:\mathrm{3} \\ $$$$\frac{\mathrm{2}\:+\:\mathrm{2y}+\:\mathrm{z}\:+\:\mathrm{yz}}{\mathrm{y}\:+\:\mathrm{z}\:+\mathrm{3}}\:=\:\mathrm{4} \\ $$$$\mathrm{so},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{z}\:+\:\mathrm{2}\:}\:=\:….? \\ $$$$ \\ $$ Answered…
Question Number 11766 by uni last updated on 31/Mar/17 $$\int\frac{\mathrm{1}}{\mathrm{sin2x}}\mathrm{dx}=? \\ $$ Answered by ajfour last updated on 31/Mar/17 $$\int\:\frac{{dx}}{\mathrm{2sin}\:{x}\mathrm{cos}\:{x}}=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} {x}}{\mathrm{tan}\:{x}}\:{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{tan}\:{x}\mid+{C} \\ $$…
Question Number 142829 by liberty last updated on 06/Jun/21 $$\:{Find}\:{the}\:{simplest}\:{form}\:{for}\: \\ $$$$\:\:{T}\:=\:\sqrt{\mathrm{1}+\sqrt{−\mathrm{3}}}\:+\sqrt{\mathrm{1}−\sqrt{−\mathrm{3}}}\: \\ $$ Answered by EDWIN88 last updated on 06/Jun/21 $$\mathrm{Let}\:\sqrt{\mathrm{a}}\:+\sqrt{−\mathrm{b}}\:=\:\sqrt{\mathrm{1}+\sqrt{−\mathrm{3}}}\:\mathrm{with}\:\mathrm{a}>\mathrm{0}\:,\mathrm{b}>\mathrm{0} \\ $$$$\Rightarrow\mathrm{a}−\mathrm{b}+\mathrm{2}{i}\sqrt{\mathrm{ab}}\:=\:\mathrm{1}+{i}\sqrt{\mathrm{3}}\:\mathrm{we}\:\mathrm{get}\:\begin{cases}{\mathrm{a}−\mathrm{b}=\mathrm{1}}\\{\mathrm{2}\sqrt{\mathrm{ab}}\:=\sqrt{\mathrm{3}}}\end{cases} \\…
Question Number 11754 by Joel576 last updated on 31/Mar/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{between}\:\mathrm{1}\:−\:\mathrm{2017} \\ $$$$\mathrm{that}\:\mathrm{aren}'\mathrm{t}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5},\:\mathrm{6},\:\mathrm{7},\:\mathrm{8}\:? \\ $$ Answered by mrW1 last updated on 31/Mar/17 $${let}\:{a}={count}\:{of}\:{numbers}\:{which}\:{are}\:{multiple}\:{of}\:\mathrm{5} \\ $$$${let}\:{b}={count}\:{of}\:{numbers}\:{which}\:{are}\:{multiple}\:{of}\:\mathrm{6} \\…