Question Number 10762 by 2525 last updated on 24/Feb/17 $$\mathrm{in}\:\mathrm{eac}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{problems}\:\mathrm{you}\:{are} \\ $$$$\mathrm{given}\:\mathrm{a}\:\mathrm{function}\:\mathrm{on}\:\mathrm{the}\:\mathrm{interval}\:\:−\pi<{x}<\pi. \\ $$$$\mathrm{Sketch}\:\mathrm{several}\:\mathrm{periods}\:\mathrm{of}\:\mathrm{the}\:\mathrm{corresponding} \\ $$$$\mathrm{periodic}\:\mathrm{function}\:\mathrm{of}\:\mathrm{period}\:\mathrm{2}\pi.\:\mathrm{Expand}\:\mathrm{the} \\ $$$$\mathrm{periodic}\:\mathrm{function}\:\mathrm{in}\:\mathrm{a}\:\mathrm{sine}−\mathrm{consine}\:\mathrm{Fourier} \\ $$$$\mathrm{series}.\:\: \\ $$$$ \\ $$$${F}\left({x}\right)\:=\:\left\{\overset{{x}+\pi} {\:}_{\mathrm{0}}…
Question Number 10742 by okhema last updated on 24/Feb/17 $${let}\:{the}\:{roots}\:{of}\:{the}\:{equation}\mathrm{2}{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{6}=\mathrm{0} \\ $$$${be}\:\alpha,\beta\:{and}\:\gamma. \\ $$$$\left.{i}\right){state}\:{the}\:{values}\:{of}\:\alpha+\beta+\gamma,\:\alpha\beta+\alpha\gamma+\beta\gamma\:{and}\:\alpha\beta\gamma. \\ $$$$\left.{ii}\right){hence}\:{or}\:{otherwise}\:{determine}\:{an}\:{equation}\:{with}\:{integer}\:{coefficients}\:{which}\:{as}\:{roots}\:\frac{\mathrm{1}}{\alpha^{\mathrm{2}\:} },\:\frac{\mathrm{1}}{\beta^{\mathrm{2}} }\:,\:{and}\:\frac{\mathrm{1}}{\gamma^{\mathrm{2}} } \\ $$$$ \\ $$…
Question Number 10736 by Saham last updated on 23/Feb/17 $$\mathrm{A}\:\mathrm{tennis}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{vertically}\:\mathrm{upward}\:\mathrm{with}\:\mathrm{an}\:\mathrm{initial}\:\mathrm{velocity}\:\mathrm{of} \\ $$$$\mathrm{50m}/\mathrm{s},\:\mathrm{when}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{return}\:\mathrm{to}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{projection}\:\mathrm{it}\:\mathrm{renounce}\: \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{velocity}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{heigth}\:\mathrm{after}\:\mathrm{renounce}. \\ $$ Answered by mrW1 last updated on 24/Feb/17 $$\frac{\mathrm{1}}{\mathrm{2}}{mV}_{\mathrm{2}} ^{\mathrm{2}}…
Question Number 10728 by Saham last updated on 23/Feb/17 $$\mathrm{A}\:\mathrm{pipe}\:\mathrm{closed}\:\mathrm{at}\:\mathrm{one}\:\mathrm{end}\:\mathrm{emits}\:\mathrm{sound}\:\mathrm{wave}\:\mathrm{of}\:\mathrm{frequency}\:\mathrm{440}\:\mathrm{Hz}.\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{air}\:\mathrm{column} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Frequencies}\:\mathrm{of}\:\mathrm{the}\:\mathrm{second}\:\mathrm{harmonic}\:\mathrm{and}\:\mathrm{the}\:\mathrm{third}\:\mathrm{harmonic} \\ $$$$\mathrm{Velocity}\:\mathrm{of}\:\mathrm{sound}\:\mathrm{is}\:\mathrm{330m}/\mathrm{s} \\ $$$$\mathrm{Refractive}\:\mathrm{index}\:\mathrm{of}\:\mathrm{glass}\:\mathrm{is}\:\mathrm{1}.\mathrm{50},\:\mathrm{that}\:\mathrm{of}\:\:\mathrm{air}\:\mathrm{is}\:\mathrm{1}.\mathrm{00},\: \\ $$$$\mathrm{and}\:\mathrm{that}\:\mathrm{of}\:\mathrm{water}\:\mathrm{is}\:\mathrm{1}.\mathrm{33} \\ $$ Answered by sandy_suhendra…
Question Number 141791 by Chhing last updated on 23/May/21 $$\mathrm{Calculate} \\ $$$$\:\underset{\mathrm{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\:\frac{\mathrm{n}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{n}} } \\ $$ Answered by mr W last updated on…
Question Number 10713 by Saham last updated on 23/Feb/17 $$\mathrm{y}\:=\:\mathrm{5sin}\left(\mathrm{2000}\pi\mathrm{t}\:−\:\mathrm{0}.\mathrm{4x}\right),\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{wavelength} \\ $$ Answered by ridwan balatif last updated on 23/Feb/17 $$\mathrm{y}=\mathrm{5sin}\left(\mathrm{2000}\pi\mathrm{t}−\mathrm{0}.\mathrm{4x}\right) \\ $$$$\mathrm{base}\:\mathrm{formula}'\mathrm{s}\:\mathrm{y}=\mathrm{Asin}\left(\omega\mathrm{t}−\mathrm{kx}\right) \\ $$$$\mathrm{A}=\mathrm{5}…
Question Number 10712 by Saham last updated on 23/Feb/17 $$\mathrm{If}\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{x}} ,\:\:\mathrm{find}\:\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$ Answered by mrW1 last updated on 23/Feb/17 $${y}={x}^{{x}} \\ $$$$\mathrm{ln}\:{y}={x}\mathrm{ln}\:{x} \\ $$$$\frac{\mathrm{1}}{{y}}×\frac{{dy}}{{dx}}=\mathrm{ln}\:{x}+\mathrm{1}…
Question Number 10704 by Saham last updated on 23/Feb/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{bulk}\:\mathrm{modulus}\:\mathrm{for}\:\mathrm{water}\:\mathrm{is}\:\mathrm{2}.\mathrm{28}\:×\:\mathrm{10}^{\mathrm{9}} \mathrm{Nm}^{−\mathrm{2}} \:,\:\mathrm{determine}\:\mathrm{the}\: \\ $$$$\mathrm{time}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{for}\:\mathrm{a}\:\mathrm{sound}\:\mathrm{to}\:\mathrm{travel}\:\mathrm{a}\:\mathrm{distant}\:\mathrm{of}\:\mathrm{110m}\:\mathrm{in}\:\mathrm{water}\:\mathrm{of}\: \\ $$$$\mathrm{density}\:\mathrm{1000kgm}^{−\mathrm{3}} . \\ $$ Answered by ridwan balatif last updated…
Question Number 10705 by Saham last updated on 23/Feb/17 $$\mathrm{A}\:\mathrm{pipe}\:\mathrm{closed}\:\mathrm{at}\:\mathrm{one}\:\mathrm{end}\:\mathrm{emits}\:\mathrm{sound}\:\mathrm{waves}\:\mathrm{of}\:\mathrm{frequency}\:\mathrm{440Hz}.\: \\ $$$$\mathrm{Determine}\:\left(\mathrm{i}\right)\:\mathrm{The}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{air}\:\mathrm{column}\:\: \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{frequencies}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{overtones}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76232 by Rio Michael last updated on 25/Dec/19 $${how}\:{do}\:{we}\:{find} \\ $$$$\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:{sinh}^{−\mathrm{1}} {x}\:{dx}\:{and}\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mathrm{cosh}\:^{−\mathrm{1}} {xdx} \\ $$ Commented by mr W…