Question Number 142362 by mnjuly1970 last updated on 30/May/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} {ln}\left(\frac{\mathrm{1}}{{x}}\right).{j}_{\mathrm{0}} \left({x}\right){dx}:=\:\gamma+{ln}\left(\mathrm{2}\right)\: \\ $$$$\:\:\:\:\:{Hint}:\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:{j}_{\mathrm{0}} \left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}}…
Question Number 11288 by agni5 last updated on 19/Mar/17 $$\mathrm{Sketch}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\:\mathrm{is}\:\mathrm{defined} \\ $$$$\mathrm{by}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{4}} +\mathrm{8x}^{\mathrm{3}} ,\:\mathrm{clearly}\:\mathrm{giving}\:\mathrm{all}\:\mathrm{the}\: \\ $$$$\mathrm{properties}\:\mathrm{used}\:\mathrm{in}\:\mathrm{it}. \\ $$ Answered by ajfour last updated on 19/Mar/17…
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Question Number 11285 by uni last updated on 19/Mar/17 $$\frac{{sin}\mathrm{20}}{{cos}\mathrm{80}−{tan}\mathrm{30}×{sin}\mathrm{80}}=? \\ $$ Answered by mrW1 last updated on 19/Mar/17 $$=\frac{{sin}\mathrm{20}}{{cos}\mathrm{80}−\frac{\mathrm{sin}\:\mathrm{30}}{\mathrm{cos}\:\mathrm{30}}×{sin}\mathrm{80}} \\ $$$$=\frac{{sin}\mathrm{20}×\mathrm{cos}\:\mathrm{30}}{\mathrm{cos}\:\mathrm{30}×{cos}\mathrm{80}−\mathrm{sin}\:\mathrm{30}×{sin}\mathrm{80}} \\ $$$$=\frac{{sin}\mathrm{20}×\mathrm{cos}\:\mathrm{30}}{\mathrm{cos}\:\mathrm{110}} \\…
Question Number 142358 by rs4089 last updated on 30/May/21 $$\int_{\mathrm{0}} ^{\infty} {x}^{{n}−\mathrm{1}} {log}_{{e}} \left(\mathrm{1}−{x}\right){dx} \\ $$ Answered by mathmax by abdo last updated on 30/May/21…
Question Number 11284 by suci last updated on 19/Mar/17 $${a}+\mathrm{2}{b}+\mathrm{3}{c}….\left(\mathrm{1}\right) \\ $$$$−\mathrm{3}{a}−\mathrm{4}{b}+\mathrm{2}{c}….\left(\mathrm{2}\right) \\ $$$$\mathrm{2}{a}−{b}−{c}….\left(\mathrm{3}\right) \\ $$$${a}=…?? \\ $$$${b}=…?? \\ $$$${c}=…?? \\ $$ Terms of Service…
Question Number 11283 by suci last updated on 19/Mar/17 $$\mathrm{2}{a}+{b}+\mathrm{4}{c}….\left(\mathrm{1}\right) \\ $$$${a}+\mathrm{3}{c}….\left(\mathrm{2}\right) \\ $$$$−\mathrm{3}{a}−\mathrm{4}{b}−{c}….\left(\mathrm{4}\right) \\ $$$${a}=..?? \\ $$$${b}=..?? \\ $$$${c}=..?? \\ $$ Terms of Service…
Question Number 76819 by Rio Michael last updated on 30/Dec/19 $$\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{foci}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ellipse} \\ $$$$\:\:\:\:\:\frac{{x}^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{{y}^{\mathrm{2}} }{\mathrm{4}}\:=\:\mathrm{1}\:\mathrm{is} \\ $$$$\mathrm{A}.\:\left(\mathrm{4},\mathrm{0}\right) \\ $$$$\mathrm{B}.\:\left(\mathrm{9},\mathrm{0}\right) \\ $$$$\mathrm{C}.\:\left(\mathrm{5},\mathrm{0}\right) \\ $$$$\mathrm{D}.\:\left(\sqrt{\mathrm{5}}\:,\:\mathrm{0}\right) \\ $$…
Question Number 76817 by Rio Michael last updated on 30/Dec/19 $$\mathrm{A}\:\mathrm{compound}\:\mathrm{pendulum}\:\mathrm{ocsillates} \\ $$$$\mathrm{through}\:\mathrm{angles}\:\theta\:\mathrm{about}\:\mathrm{its}\:\mathrm{equilibrium} \\ $$$$\mathrm{position}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{8}{a}\theta^{\mathrm{2}} \:=\:\mathrm{9}{g}\:{cos}\theta,\:{a}>\mathrm{0}.\:\mathrm{its}\:\mathrm{period}\:\mathrm{is}\: \\ $$$$\mathrm{A}.\:\mathrm{2}\pi\sqrt{\frac{\mathrm{8}{a}}{\mathrm{9}{g}}} \\ $$$$\mathrm{B}.\:\frac{\mathrm{3}\pi}{\mathrm{8}}\sqrt{\frac{{a}}{{g}}} \\ $$$$\mathrm{C}.\:\mathrm{2}\pi\sqrt{\frac{\mathrm{9}{g}}{\mathrm{8}{a}}} \\…