Question Number 21771 by Tinkutara last updated on 03/Oct/17 $$\mathrm{The}\:\mathrm{result}\:\mathrm{of}\:\mathrm{11}\:\mathrm{chess}\:\mathrm{matches}\:\left(\mathrm{as}\:\mathrm{win},\right. \\ $$$$\left.\mathrm{lose}\:\mathrm{or}\:\mathrm{draw}\right)\:\mathrm{are}\:\mathrm{to}\:\mathrm{be}\:\mathrm{forecast}.\:\mathrm{Out}\:\mathrm{of} \\ $$$$\mathrm{all}\:\mathrm{possible}\:\mathrm{forecasts},\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{8}\:\mathrm{correct}\:\mathrm{and}\:\mathrm{3}\:\mathrm{incorrect} \\ $$$$\mathrm{results}\:\mathrm{can}\:\mathrm{be}\:\mathrm{forecast}\:\mathrm{is} \\ $$ Terms of Service Privacy Policy…
Question Number 152840 by liberty last updated on 02/Sep/21 Answered by MJS_new last updated on 04/Sep/21 $$\mathrm{transforming}\:\Rightarrow \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\left({y}^{\mathrm{2}} +\mathrm{3}\right){x}−{y}\left(\mathrm{3}{y}+\mathrm{1}\right)=\mathrm{0} \\ $$$${x}^{\mathrm{2}} −\frac{\mathrm{1}}{{y}}{x}+{y}^{\mathrm{2}}…
Question Number 21768 by Tinkutara last updated on 03/Oct/17 $$\mathrm{Six}\:\mathrm{cards}\:\mathrm{and}\:\mathrm{six}\:\mathrm{envelopes}\:\mathrm{are}\:\mathrm{numbered} \\ $$$$\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6}\:\mathrm{and}\:\mathrm{cards}\:\mathrm{are}\:\mathrm{to}\:\mathrm{be}\:\mathrm{placed} \\ $$$$\mathrm{in}\:\mathrm{envelopes}\:\mathrm{so}\:\mathrm{that}\:\mathrm{each}\:\mathrm{envelope} \\ $$$$\mathrm{contains}\:\mathrm{exactly}\:\mathrm{one}\:\mathrm{card}\:\mathrm{and}\:\mathrm{no}\:\mathrm{card} \\ $$$$\mathrm{is}\:\mathrm{placed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{envelope}\:\mathrm{bearing}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{number}\:\mathrm{and}\:\mathrm{moreover}\:\mathrm{the}\:\mathrm{card} \\ $$$$\mathrm{numbered}\:\mathrm{1}\:\mathrm{is}\:\mathrm{always}\:\mathrm{placed}\:\mathrm{in}\:\mathrm{envelope} \\ $$$$\mathrm{numbered}\:\mathrm{2}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways} \\…
Question Number 87302 by M±th+et£s last updated on 03/Apr/20 $${for}\:\mid{z}−\mathrm{1}\mid=\mathrm{1}\:{show}\:{that} \\ $$$${tan}\left(\frac{{arg}\left({z}−\mathrm{1}\right)}{\mathrm{2}}\right)−\frac{\mathrm{2}{i}}{{z}}=−\mathrm{1} \\ $$ Commented by MJS last updated on 04/Apr/20 $$\mathrm{tan}\:\frac{\mathrm{arg}\:\left({z}−\mathrm{1}\right)}{\mathrm{2}}\:\in\mathbb{R} \\ $$$$−\frac{\mathrm{2i}}{{z}}\notin\mathbb{R}\:\forall\:{z}={a}+{b}\mathrm{i};\:{a}\neq\mathrm{0} \\…
Question Number 21766 by Tinkutara last updated on 03/Oct/17 $$\mathrm{There}\:\mathrm{are}\:\mathrm{3}\:\mathrm{apartments}\:{A},\:{B}\:\mathrm{and}\:{C}\:\mathrm{for} \\ $$$$\mathrm{rent}\:\mathrm{in}\:\mathrm{a}\:\mathrm{building}.\:\mathrm{Each}\:\mathrm{apartment}\:\mathrm{will} \\ $$$$\mathrm{accept}\:\mathrm{either}\:\mathrm{3}\:\mathrm{or}\:\mathrm{4}\:\mathrm{occupants}.\:\mathrm{The} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{of}\:\mathrm{renting}\:\mathrm{the} \\ $$$$\mathrm{apartments}\:\mathrm{to}\:\mathrm{10}\:\mathrm{students} \\ $$ Answered by mrW1 last updated…
Question Number 152839 by mnjuly1970 last updated on 02/Sep/21 $$ \\ $$$$\:\:\:\mathrm{Prove}\:\:\mathrm{that}\:: \\ $$$$ \\ $$$$\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{ln}^{\:\mathrm{3}} \:\left(\mathrm{1}\:+\:{x}\:\right)}{{x}^{\:\mathrm{2}} }{dx}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\:\zeta\:\left(\mathrm{3}\:\right)−\:\mathrm{2ln}^{\:\mathrm{3}} \left(\:\mathrm{2}\:\right)\:\:\:\:\:\:\:\:\blacksquare \\ $$$$\:\:\:\:\:\:\:\mathrm{Prepared}\:\mathrm{by}:\:\:\:\:\:\:\mathrm{M}.\mathrm{N} \\ $$$$…
Question Number 87301 by M±th+et£s last updated on 03/Apr/20 Commented by mathmax by abdo last updated on 04/Apr/20 $${let}\:\:{I}\:=\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{\mathrm{2}\left[{x}\right]^{\mathrm{2}} \:+\left[{x}\right]}\:\Rightarrow\:{I}\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\int_{{n}} ^{{n}+\mathrm{1}}…
Question Number 87298 by ajfour last updated on 03/Apr/20 $${If}\:{y}=\mathrm{sin}\:{x}\:,\:\:{x}=\mathrm{0}\:{to}\:{x}=\mathrm{2}\pi\:{is} \\ $$$${revolved}\:{about}\:{the}\:{x}-{axis},\:{find} \\ $$$${the}\:{surface}\:{of}\:{the}\:{solid}\:{of} \\ $$$${revolution}. \\ $$ Answered by ajfour last updated on 04/Apr/20…
Question Number 87296 by ajfour last updated on 03/Apr/20 $${If}\:\:{ellipse}\:\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:\:\left({a}>{b}\right) \\ $$$${is}\:{rotated}\:{about}\:{x}-{axis},\:{find}\:{the} \\ $$$${surface}\:{of}\:{the}\:{solid}\:{of}\:{revolution}. \\ $$ Answered by mr W last…
Question Number 152834 by liberty last updated on 02/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com