Question Number 160090 by abdullah_ff last updated on 24/Nov/21 $$\mathrm{There}\:\mathrm{are}\:\mathrm{40}\:\mathrm{oranges},\:\mathrm{20}\:\mathrm{apples},\:\mathrm{and}\: \\ $$$$\mathrm{20}\:\mathrm{lemons}\:\mathrm{in}\:\mathrm{a}\:\mathrm{bag}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{minimum}\:\mathrm{number}\:\mathrm{of}\:\mathrm{fruits}\:\mathrm{that}\:\mathrm{you}\: \\ $$$$\mathrm{have}\:\mathrm{to}\:\mathrm{take}\:\mathrm{out}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{with}\:\mathrm{your}\: \\ $$$$\mathrm{eyes}\:\mathrm{closed}\:\mathrm{before}\:\mathrm{you}\:\mathrm{are}\:\mathrm{sure}\:\mathrm{that}\: \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{them}\:\mathrm{is}\:\mathrm{an}\:\mathrm{orange}? \\ $$ Commented by mr…
Question Number 29012 by mrW2 last updated on 03/Feb/18 Commented by mrW2 last updated on 03/Feb/18 $${See}\:{Q}\mathrm{28940} \\ $$$${A},{B},{C}\:{are}\:{three}\:{points}\:{on}\:{the}\:{roof}. \\ $$$${Find}\:{the}\:{tension}\:{in}\:{the}\:{threads}. \\ $$$${Assume}\:{all}\:{threads}\:{are}\:{taut}. \\ $$…
Question Number 160065 by Kunal12588 last updated on 24/Nov/21 $$\mathrm{The}\:\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{non}-\mathrm{negative}\:\mathrm{integer}\:{a} \\ $$$$\mathrm{for}\:\mathrm{which}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left\{\frac{−{ax}+\mathrm{sin}\left({x}−\mathrm{1}\right)+{a}}{{x}+\mathrm{sin}\left({x}−\mathrm{1}\right)−\mathrm{1}}\right\}^{\frac{\mathrm{1}−{x}}{\:\mathrm{1}−\sqrt{{x}}}} =\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{is}\:……..? \\ $$ Commented by Kunal12588 last updated on 24/Nov/21…
Question Number 160025 by Alamgir143ap last updated on 23/Nov/21 Commented by abdullah_ff last updated on 24/Nov/21 $$\mathrm{Dear}\:\mathrm{Alamgir}\:\mathrm{sir},\:\mathrm{please}\:\mathrm{clearify}\:\mathrm{what} \\ $$$$\:\mathrm{you}\:\mathrm{want}\:\mathrm{to}\:\mathrm{know}.\: \\ $$$$ \: \: \: \:…
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Question Number 28938 by mondodotto@gmail.com last updated on 01/Feb/18 Commented by Cheyboy last updated on 02/Feb/18 $${let}\:{andre}'{s}\:{money}\:{be}=\:{x} \\ $$$${let}\:{Bob}'{s}\:{money}\:{be}={y} \\ $$$${x}−\mathrm{20}={y}+\mathrm{20}\Rightarrow\left(\mathrm{1}\right) \\ $$$$\mathrm{2}\left({y}−\mathrm{22}\right)={x}+\mathrm{22}\Rightarrow\left(\mathrm{2}\right) \\ $$$${x}−{y}=\mathrm{40}…
Question Number 159994 by mathocean1 last updated on 23/Nov/21 $$ \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{le}\:\mathrm{quotient}\:\mathrm{d}'\mathrm{un} \\ $$$$\mathrm{nombe}\:\mathrm{rationnel}\:\mathrm{et}\:\mathrm{dun}\:\mathrm{nombre}\: \\ $$$$\mathrm{irr}{a}\mathrm{tionnel}\:\mathrm{est}\:\mathrm{irrationnel} \\ $$ Answered by Tokugami last updated on 23/Nov/21…
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Question Number 159962 by bounhome last updated on 23/Nov/21 $${show}\:{me}:\:{these}\:{are}\:{the}\:{cauchy}\:{criterion}.\:{please} \\ $$$$\mathrm{1}.\left(\frac{{n}+\mathrm{1}}{{n}}\right) \\ $$$$\mathrm{2}.\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{1}}{\mathrm{3}!}+…+\frac{\mathrm{1}}{{n}!}\right) \\ $$$$\mathrm{3}.\:\left(\left(−\mathrm{1}\right)^{{n}} \right) \\ $$$$\mathrm{4}.\:{n}+\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}} \\ $$$$\mathrm{5}.\left(\mathrm{1}{nm}\right) \\ $$$$ \\…