Question Number 198949 by ArifinTanjung last updated on 26/Oct/23 $$\:\:\frac{\mathrm{5}!×\mathrm{4}!}{\mathrm{3}!×\mathrm{2}!}\:=\:….\:\: \\ $$ Answered by Rasheed.Sindhi last updated on 26/Oct/23 $$\:\:\frac{\mathrm{5}!×\mathrm{4}!}{\mathrm{3}!×\mathrm{2}!}\:=\:\frac{\mathrm{5}!×\cancel{\overset{\mathrm{2}} {\mathrm{4}}}×\cancel{\mathrm{3}!}}{\cancel{\mathrm{3}!}×\cancel{\underset{\mathrm{1}} {\mathrm{2}}}×\mathrm{1}}=\mathrm{2}×\mathrm{5}! \\ $$$$ \\…
Question Number 198950 by ArifinTanjung last updated on 26/Oct/23 $$\mathrm{3x}+\mathrm{2y}=\mathrm{6} \\ $$$$\mathrm{2x}+\mathrm{3y}=\mathrm{6}\:\rightarrow\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:=…? \\ $$ Answered by Rasheed.Sindhi last updated on 26/Oct/23 $$\begin{cases}{\mathrm{3x}+\mathrm{2y}=\mathrm{6}}\\{\mathrm{2x}+\mathrm{3y}=\mathrm{6}}\end{cases}\:\:\:\:\:\:\:\:\:\mathrm{x},\mathrm{y}=? \\ $$$$\mathrm{Adding}:\:\:\mathrm{5}\left(\mathrm{x}+\mathrm{y}\right)=\mathrm{12}\Rightarrow\mathrm{x}+\mathrm{y}=\frac{\mathrm{12}}{\mathrm{5}} \\…
Question Number 199015 by Tawa11 last updated on 26/Oct/23 Answered by Rasheed.Sindhi last updated on 26/Oct/23 $$\sqrt{{a}−{x}}\:+\sqrt{{b}−{x}}\:+\sqrt{{c}−{x}}\:=\mathrm{0} \\ $$$$\sqrt{{a}−{x}}\:=\mathrm{0}\:\wedge\:\sqrt{{b}−{x}}\:=\mathrm{0}\:\wedge\:\sqrt{{c}−{x}}\:=\mathrm{0} \\ $$$${x}={a}={b}={c} \\ $$$$\left({a}+{b}+{c}+\mathrm{3}{x}\right)\left({a}+{b}+{c}−{x}\right)=\mathrm{4}\left({bc}+{ca}+{ab}\right) \\ $$$$\left({x}+{x}+{x}+\mathrm{3}{x}\right)\left({x}+{x}+{x}−{x}\right)=\mathrm{4}\left({x}.{x}+{x}.{x}+{x}.{x}\right)…
Question Number 198951 by ArifinTanjung last updated on 26/Oct/23 $$\sqrt{\mathrm{8}+\sqrt{\mathrm{48}}\:}=….? \\ $$ Commented by mr W last updated on 26/Oct/23 $${are}\:{you}\:{serious}? \\ $$$${you}\:{ask}\:{both}\:{this}\:\sqrt{\mathrm{8}+\sqrt{\mathrm{48}}\:}=…. \\ $$$${and}\:{this}\:\int_{\mathrm{1}}…
Question Number 199011 by necx122 last updated on 26/Oct/23 $${Sum}\:{of}\:{two}\:{irrational}\:{numbers}\:{is}\:\mathrm{1} \\ $$$${less}\:{than}\:{their}\:{product},\:{and}\:\mathrm{8}\:{less}\:{than} \\ $$$${their}\:{sum}\:{of}\:{squares}.\:{Find}\:{the}\:{larger} \\ $$$${of}\:{the}\:{two}\:{numbers}. \\ $$ Commented by nikif99 last updated on 27/Oct/23…
Question Number 199005 by Safojon last updated on 26/Oct/23 Commented by mr W last updated on 29/Oct/23 $${i}\:{got}\:\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{1}°} \\ $$$${solution}\:{see}\:{Q}\mathrm{199226} \\ $$ Commented by Rasheed.Sindhi…
Question Number 198941 by Mingma last updated on 26/Oct/23 Commented by witcher3 last updated on 06/Nov/23 $$\varpi\:\mathrm{what}\:\mathrm{is}\:\mathrm{omega}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 199006 by adhigenz last updated on 26/Oct/23 $$\mathrm{Given}\:\mathrm{that}\:{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{trapezium}\:\mathrm{such}\:\mathrm{that}\:{AD}//{BC}. \\ $$$$\mathrm{The}\:\mathrm{centroid}\:\mathrm{of}\:\bigtriangleup{ABD}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\angle{BCD}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\bigtriangleup{ABC}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\angle{ADC}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 199001 by mnjuly1970 last updated on 26/Oct/23 $$ \\ $$$$\:\mathrm{I}{f}\:,\mathrm{A}\:\in\:\mathrm{M}_{{n}×{n}} \:\:\:,\:\:\mathrm{A}^{\:\mathrm{2}} \:=\:\mathrm{A}\:,\mathrm{1}\neq\:{k}\:\in\mathbb{R}. \\ $$$$\:\:\:\mathrm{F}{ind}\:\:\:\:\left(\:\:\:\mathrm{I}\:−\:{k}\mathrm{A}\:\right)^{\:−\mathrm{1}} \:=\:?\: \\ $$ Answered by MM42 last updated on…
Question Number 198939 by Mingma last updated on 26/Oct/23 Answered by witcher3 last updated on 26/Oct/23 $$\varphi:\mathrm{2}\mathbb{N}\rightarrow\mathbb{Z} \\ $$$$\varphi\left(\mathrm{2n}\right)=\begin{cases}{\mathrm{k}\:\mathrm{if}\:\mathrm{n}=\mathrm{2}\left(\mathrm{2k}+\mathrm{1}\right)}\\{−\mathrm{k}\:\mathrm{if}\:\mathrm{n}=\mathrm{2}.\left(\mathrm{2k}\right)}\end{cases} \\ $$$$\varphi\left(\mathrm{m}\right)=\varphi\left(\mathrm{n}\right)\:\Leftrightarrow\mathrm{m}=\mathrm{n} \\ $$$$\varphi\:\mathrm{injective} \\ $$$$\mathrm{if}\:\:\mathrm{n}\in\mathbb{Z}\:\mathrm{if}\:\mathrm{n}\geqslant\mathrm{0}\:…