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Category: Permutation and Combination

If-6-x-4-x-then-x-

Question Number 145104 by imjagoll last updated on 02/Jul/21 $$\:\mathrm{If}\:\frac{!\mathrm{6}}{\mathrm{x}}\:−!\mathrm{4}\:=\:!\mathrm{x}\:\mathrm{then}\:\mathrm{x}\:=? \\ $$ Answered by liberty last updated on 02/Jul/21 $$\:\Rightarrow\:\mathrm{265}−\mathrm{9}{x}\:=\:{x}.\left(!{x}\right) \\ $$$${test}\:{x}=\mathrm{5}\: \\ $$$$\Rightarrow\mathrm{265}−\mathrm{45}\:=\:\mathrm{220}\:\wedge\:\mathrm{5}.\left(!\mathrm{5}\right)=\mathrm{5}×\mathrm{44}=\mathrm{220} \\…

how-do-16-people-play-3-matches-in-teams-of-4-but-must-only-be-in-the-same-team-once-

Question Number 79479 by jagoll last updated on 25/Jan/20 $$\mathrm{how}\:\mathrm{do}\:\mathrm{16}\:\mathrm{people}\:\mathrm{play}\:\mathrm{3}\:\mathrm{matches} \\ $$$$\mathrm{in}\:\mathrm{teams}\:\mathrm{of}\:\mathrm{4}\:\mathrm{but}\:\mathrm{must}\:\mathrm{only}\:\mathrm{be} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{same}\:\mathrm{team}\:\mathrm{once}\:?\: \\ $$ Commented by mr W last updated on 25/Jan/20 $${i}\:{don}'{t}\:{understand}\:{the}\:{question}…

what-the-minimum-value-of-f-x-x-2-2x-5-x-2-14x-65-

Question Number 79472 by jagoll last updated on 25/Jan/20 $$\mathrm{what}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{5}}\:+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{14x}+\mathrm{65}} \\ $$ Commented by john santu last updated on 25/Jan/20 $${yes}\:{sir}.\:{haha}\:{this}\:{method}\:{not}\:…

Question-78799

Question Number 78799 by Pratah last updated on 20/Jan/20 Commented by mathmax by abdo last updated on 20/Jan/20 $${convergence}?\:\:\:{let}\:{f}\left({x}\right)=\frac{{ln}\left({x}\right)}{{x}^{\frac{\mathrm{5}}{\mathrm{4}}} }\:\:\:{with}\:{x}\geqslant\mathrm{2}\:\:{we}\:{have} \\ $$$${f}^{'} \left({x}\right)=\frac{\frac{\mathrm{1}}{{x}}{x}^{\frac{\mathrm{5}}{\mathrm{4}}} −\frac{\mathrm{5}}{\mathrm{4}}{x}^{\frac{\mathrm{5}}{\mathrm{4}}−\mathrm{1}} {lnx}}{{x}^{\frac{\mathrm{5}}{\mathrm{2}}}…