Question Number 149323 by naka3546 last updated on 04/Aug/21 $${How}\:\:{many}\:\:{ordered}\:\:{pairs}\:\left({a},{b}\right)\:{with}\:\:{b}\:<\:{a}\:<\:\mathrm{100}\:\:,\:\:{a},{b}\:\in\:\mathbb{N}\:\:{such}\:\:{that}\:\:\frac{{a}}{{b}}\:\:{both}\:\:\:\frac{{a}+\mathrm{1}}{{b}+\mathrm{1}}\:\:{are}\:\:{integers}\:\:.\: \\ $$ Answered by Olaf_Thorendsen last updated on 05/Aug/21 $$\mathrm{N}\:=\:\underset{{b}=\mathrm{1}} {\overset{\mathrm{98}} {\sum}}\underset{{a}={b}+\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\lfloor\frac{\lfloor\frac{{a}}{{b}}\rfloor}{\frac{{a}}{{b}}}×\frac{\lfloor\frac{{a}+\mathrm{1}}{{b}+\mathrm{1}}\rfloor}{\frac{{a}+\mathrm{1}}{{b}+\mathrm{1}}}\rfloor \\…
Question Number 149322 by mathdanisur last updated on 04/Aug/21 $$\frac{\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\sqrt{\mathrm{10}\:+\:\sqrt{\boldsymbol{{n}}}}\right)}{\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\sqrt{\mathrm{10}\:-\:\sqrt{\boldsymbol{{n}}}}\right)}\:=\:? \\ $$ Commented by amin96 last updated on 04/Aug/21 $$? \\…
Question Number 149317 by tabata last updated on 04/Aug/21 $${lim}_{{x}\rightarrow\infty} \sqrt{{x}^{\mathrm{6}} +\mathrm{5}{x}^{\mathrm{3}} }−{x} \\ $$ Answered by EDWIN88 last updated on 04/Aug/21 $$\left.\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{{x}^{\mathrm{6}} \left(\mathrm{1}+\mathrm{5}{x}^{−\mathrm{3}}…
Question Number 83782 by jagoll last updated on 06/Mar/20 $$\mathrm{f}^{\left(\mathrm{5}\right)} \:\left(\mathrm{x}\right)\:=\:\mathrm{4}^{−\mathrm{sin}\:\mathrm{x}} \\ $$$$\mathrm{f}^{\left(\mathrm{7}\right)} \left(\mathrm{x}\right)\:=?\: \\ $$ Commented by john santu last updated on 06/Mar/20 $$\mathrm{f}^{\left(\mathrm{n}\right)}…
Question Number 18247 by mjaat7088@gmail.com last updated on 17/Jul/17 $$\frac{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 83781 by john santu last updated on 06/Mar/20 $$\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{5cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$ Commented by niroj last updated on 06/Mar/20 $$\:\:\int_{\mathrm{0}}…
Question Number 18243 by ajfour last updated on 17/Jul/17 Commented by ajfour last updated on 17/Jul/17 $$\mathrm{If}\:\:\:\:\mathrm{z}=\mid\mathrm{z}\mid\left(\mathrm{e}^{\mathrm{i}\boldsymbol{\phi}} \mathrm{cos}\:\theta+\mathrm{jsin}\:\theta\right) \\ $$$$\mathrm{z}_{\boldsymbol{\phi}+\bigtriangleup\boldsymbol{\phi}} =\mid\mathrm{z}\mid\left(\mathrm{e}^{\mathrm{i}\boldsymbol{\phi}+\mathrm{i}\bigtriangleup\boldsymbol{\phi}} \mathrm{cos}\:\theta+\mathrm{jsin}\:\theta\right) \\ $$$$\mathrm{z}^{\theta+\bigtriangleup\theta} \:=\mid\mathrm{z}\mid\left[\mathrm{e}^{\mathrm{i}\boldsymbol{\phi}}…
Question Number 149309 by ArielVyny last updated on 04/Aug/21 $${if}\:\:\:\:{t}={tanx}\:{what}\:{is}\:{the}\:{value}\:{of} \\ $$$${sinx}\:{and}\:{cosx}\:? \\ $$ Answered by nimnim last updated on 04/Aug/21 $${sinx}=\frac{{t}}{\:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }},\:\:{cosx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }} \\…
Question Number 83774 by jagoll last updated on 06/Mar/20 $$\mathrm{Given}\:\mathrm{2}\sqrt{\mathrm{log}_{\mathrm{3}} \:{x}−\mathrm{1}}\:−\:\mathrm{log}_{\mathrm{3}} \:{x}^{\mathrm{3}} \:+\mathrm{8}\:>\:\mathrm{0} \\ $$$${have}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{a}\:\leqslant\:{x}\:<\:{b}.\: \\ $$$${what}\:{is}\:{b}\:?\: \\ $$ Answered by john santu last updated…
Question Number 18236 by Joel577 last updated on 17/Jul/17 $$\int\:\frac{{dx}}{\mathrm{1}\:−\:\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com