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If-we-had-a-maze-which-was-contained-within-the-shape-of-a-square-and-it-has-one-enterence-on-its-edge-and-a-centre-point-from-which-you-start-If-you-move-randomly-you-will-naturally-escape-Now

Question Number 5150 by FilupSmith last updated on 21/Apr/16 $$\mathrm{If}\:\mathrm{we}\:\mathrm{had}\:\mathrm{a}\:\mathrm{maze},\:\mathrm{which}\:\mathrm{was}\:\mathrm{contained} \\ $$$$\mathrm{within}\:\mathrm{the}\:\mathrm{shape}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square},\:\mathrm{and}\:\mathrm{it}\:\mathrm{has} \\ $$$$\mathrm{one}\:\mathrm{enterence}\:\mathrm{on}\:\mathrm{its}\:\mathrm{edge},\:\mathrm{and}\:\mathrm{a}\:\mathrm{centre} \\ $$$$\mathrm{point}\:\mathrm{from}\:\mathrm{which}\:\mathrm{you}\:\mathrm{start},\:\mathrm{If}\:\mathrm{you}\:\mathrm{move} \\ $$$$\mathrm{randomly},\:\mathrm{you}\:\mathrm{will}\:\mathrm{naturally}\:\mathrm{escape}. \\ $$$$ \\ $$$$\mathrm{Now},\:\mathrm{lets}\:\mathrm{say}\:\mathrm{the}\:\mathrm{maze}\:\mathrm{itself}\:\mathrm{is}\:\mathrm{generated} \\ $$$$\mathrm{at}\:\mathrm{completely}\:\mathrm{random}\:\mathrm{odds}. \\…

2-to-the-power-x-2-to-the-power-x-1-3-lt-0-ease-ans-asap-

Question Number 5130 by Apoorva last updated on 16/Apr/16 $$\mathrm{2}\:{to}\:{the}\:{power}\:{x}+\mathrm{2}\:{to}\:{the}\:{power}\:\left(−{x}+\mathrm{1}\right)−\mathrm{3}<\mathrm{0}.{ease}\:{ans}\:{asap} \\ $$ Commented by prakash jain last updated on 17/Apr/16 $$\mathrm{2}^{\left({x}+\mathrm{2}\right)^{\left(−{x}+\mathrm{1}\right)−\mathrm{3}} } <\mathrm{0} \\ $$$$\mathrm{If}\:{x}\in\mathbb{R}\:\mathrm{then}\:\mathrm{2}^{\left({x}+\mathrm{2}\right)^{\left(−{x}+\mathrm{1}\right)−\mathrm{3}}…

Lets-say-person-1-punches-a-bag-and-the-punch-is-fast-from-start-to-finish-Lets-say-person-2-does-a-punch-but-only-the-final-part-of-the-punch-is-fast-How-will-the-forces-differ-in-these-punches-

Question Number 5122 by FilupSmith last updated on 16/Apr/16 $$\mathrm{Lets}\:\mathrm{say}\:\mathrm{person}\:\mathrm{1}\:\mathrm{punches}\:\mathrm{a}\:\mathrm{bag}\:\mathrm{and}\: \\ $$$$\mathrm{the}\:\mathrm{punch}\:\mathrm{is}\:\mathrm{fast}\:\mathrm{from}\:\mathrm{start}\:\mathrm{to}\:\mathrm{finish}. \\ $$$$ \\ $$$$\mathrm{Lets}\:\mathrm{say}\:\mathrm{person}\:\mathrm{2}\:\mathrm{does}\:\mathrm{a}\:\mathrm{punch}\:\mathrm{but} \\ $$$$\mathrm{only}\:\mathrm{the}\:\mathrm{final}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{punch}\:\mathrm{is}\:\mathrm{fast}. \\ $$$$ \\ $$$$\mathrm{How}\:\mathrm{will}\:\mathrm{the}\:\mathrm{forces}\:\mathrm{differ}\:\mathrm{in}\:\mathrm{these}\:\mathrm{punches}? \\ $$$$ \\…

lim-x-pi-2-sin-x-cos-x-tan-x-

Question Number 70653 by naka3546 last updated on 06/Oct/19 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\:\left(\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\right)^{\mathrm{tan}\:{x}} \:\:=\:\:… \\ $$ Commented by kaivan.ahmadi last updated on 06/Oct/19 $${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \left({sinx}−{cosx}−\mathrm{1}\right){tanx}= \\ $$$${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}}…

Let-f-x-cos-1-x-cos-1-x-1-find-the-range-of-f-

Question Number 136186 by ZiYangLee last updated on 19/Mar/21 $$\mathrm{Let}\:{f}\left({x}\right)=\mathrm{cos}^{−\mathrm{1}} {x}+\mathrm{cos}^{−\mathrm{1}} \left({x}−\mathrm{1}\right),\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{f}. \\ $$ Answered by ZiYangLee last updated on 19/Mar/21 $$\mathrm{Ans}:\:\left[\frac{\pi}{\mathrm{2}},\frac{\mathrm{3}\pi}{\mathrm{2}}\right] \\…