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Category: Arithmetic

prove-n-1-9n-4-3n-3n-1-3n-2-3-2-ln-3-

Question Number 97956 by  M±th+et+s last updated on 10/Jun/20 $${prove} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{9}{n}+\mathrm{4}}{\mathrm{3}{n}\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}=\frac{\mathrm{3}}{\mathrm{2}}−{ln}\left(\mathrm{3}\right) \\ $$ Answered by maths mind last updated on 13/Jun/20 $$=\underset{{n}\geqslant\mathrm{1}}…

1-2-9-21-1-3-1-2-9-21-1-3-

Question Number 163408 by mathlove last updated on 06/Jan/22 $$\sqrt[{\mathrm{3}}]{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}}+\sqrt[{\mathrm{3}}]{\mathrm{1}−\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}}=? \\ $$ Answered by mr W last updated on 06/Jan/22 $$\sqrt[{\mathrm{3}}]{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}}+\sqrt[{\mathrm{3}}]{\mathrm{1}−\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}}={x} \\ $$$$\left.\mathrm{1}+\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}+\mathrm{1}−\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}+\mathrm{3}{x}\sqrt[{\mathrm{3}}]{\left(\mathrm{1}+\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}\right)\left(\mathrm{1}−\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}\right.}\right)={x}^{\mathrm{3}} \\ $$$${x}^{\mathrm{3}}…

A-small-ball-is-dropped-from-a-height-of-1m-into-a-horizontal-floor-Each-time-it-rebounces-to-3-5-of-the-height-it-has-fallen-a-show-that-when-the-ball-strikes-the-ground-for-the-third-time-it-has-

Question Number 32312 by NECx last updated on 23/Mar/18 $${A}\:{small}\:{ball}\:{is}\:{dropped}\:{from}\:{a}\: \\ $$$${height}\:{of}\:\mathrm{1}{m}\:{into}\:{a}\:{horizontal} \\ $$$${floor}.{Each}\:{time}\:{it}\:{rebounces}\:{to} \\ $$$$\mathrm{3}/\mathrm{5}\:{of}\:{the}\:{height}\:{it}\:{has}\:{fallen}. \\ $$$$\left.{a}\right){show}\:{that}\:{when}\:{the}\:{ball}\:{strikes} \\ $$$${the}\:{ground}\:{for}\:{the}\:{third}\:{time}\:,{it} \\ $$$${has}\:{travelled}\:{a}\:{distance}\:{of}\:\mathrm{2}.\mathrm{92}{m} \\ $$$$\left.{b}\right){Show}\:{that}\:{the}\:{total}\:{distance} \\…

Question-163340

Question Number 163340 by mathlove last updated on 06/Jan/22 Answered by Rasheed.Sindhi last updated on 06/Jan/22 $$\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{{a}+{b}}={a}−{b} \\ $$$$=\left[\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}−\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right)\right] \\ $$$$=\left[\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right] \\ $$$$\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right)=\mathrm{2}×\frac{\mathrm{100}}{\mathrm{101}}=\frac{\mathrm{200}}{\mathrm{101}}\:\:\:\left({b}\right)\checkmark…

A-M-n-n-A-3-O-Find-A-2I-1-

Question Number 162960 by mnjuly1970 last updated on 02/Jan/22 $$ \\ $$$$\:\:\:\:\mathrm{A}\:\in\:\mathrm{M}_{\:{n}×{n}} \:\:,\:\:\:\mathrm{A}^{\:\mathrm{3}} =\:\overset{−} {\mathrm{O}}\:\: \\ $$$$\:\:\:\:\:\mathrm{Find}\:,\:\:\:\:\:\:\:\:\left(\:\mathrm{A}−\mathrm{2I}\:\right)^{\:−\mathrm{1}} =? \\ $$$$ \\ $$ Answered by mathmax…

4men-clear-a-farm-for-8-days-and-are-paid-24-How-long-will-6-men-take-to-clear-the-same-farm-if-they-are-paid-360-

Question Number 162951 by Ar Brandon last updated on 02/Jan/22 $$\mathrm{4men}\:\mathrm{clear}\:\mathrm{a}\:\mathrm{farm}\:\mathrm{for}\:\mathrm{8}\:\mathrm{days}\:\mathrm{and}\:\mathrm{are}\:\mathrm{paid}\:\mathrm{24\$} \\ $$$$\mathrm{How}\:\mathrm{long}\:\mathrm{will}\:\mathrm{6}\:\mathrm{men}\:\mathrm{take}\:\mathrm{to}\:\mathrm{clear}\:\mathrm{the}\:\mathrm{same}\:\mathrm{farm} \\ $$$$\mathrm{if}\:\mathrm{they}\:\mathrm{are}\:\mathrm{paid}\:\mathrm{360\$}\:? \\ $$ Commented by mr W last updated on 03/Jan/22…

E-x-denotes-the-integer-part-of-x-x-0-1-determine-E-x-x-and-E-x-x-x-calcul-lim-x-0-E-x-x-x-please-i-need-help-please-

Question Number 96930 by pticantor last updated on 21/Jun/20 $${E}\left({x}\right)\:{denotes}\:{the}\:{integer}\:{part}\:{of}\:{x}\: \\ $$$$\left.{x}\in\right]\mathrm{0};\mathrm{1}\left[\:{determine}:\right. \\ $$$$\boldsymbol{{E}}\left(\boldsymbol{{x}}^{\boldsymbol{{x}}} \right)\:\boldsymbol{{and}}\:\boldsymbol{{E}}\left(\boldsymbol{{x}}^{\boldsymbol{{x}}^{\boldsymbol{{x}}} } \right)\: \\ $$$$\boldsymbol{{calcul}}\:\boldsymbol{{li}}\underset{{x}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\:\boldsymbol{{E}}\left(\boldsymbol{{x}}^{\boldsymbol{{x}}^{\boldsymbol{{x}}} } \right) \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{i}}\:\boldsymbol{{need}}\:\boldsymbol{{help}}\:\boldsymbol{{please}} \\…