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Category: Mensuration

Question-24605

Question Number 24605 by ajfour last updated on 22/Nov/17 Commented by ajfour last updated on 22/Nov/17 $${Find}\:{the}\:{central}\:{octagonal}\:{area} \\ $$$${if}\:{ABCD}\:{is}\:{a}\:{square}\:{and}\:{points} \\ $$$${P},\:{Q},\:{R},\:{and}\:{S}\:{are}\:{the}\:{midpoints} \\ $$$${of}\:{its}\:{sides}.\:{Take}\:{edge}\:{length}\:{of} \\ $$$${square}\:{to}\:{be}\:{unity}.…

each-vertex-of-a-cube-is-to-be-labeled-with-an-integer-1-through-8-with-each-integer-being-used-once-in-such-a-way-that-the-sum-of-the-four-numbers-on-the-vertices-of-a-face-is-the-same-for-each-fa

Question Number 90122 by M±th+et£s last updated on 21/Apr/20 $${each}\:{vertex}\:{of}\:{a}\:{cube}\:{is}\:{to}\:{be}\:{labeled} \\ $$$${with}\:{an}\:{integer}\:\mathrm{1}\:{through}\:\mathrm{8}\:,\:{with} \\ $$$${each}\:{integer}\:{being}\:{used}\:{once},{in}\:{such} \\ $$$${a}\:{way}\:{that}\:{the}\:{sum}\:{of}\:{the}\:{four}\:{numbers} \\ $$$${on}\:{the}\:{vertices}\:{of}\:{a}\:{face}\:{is}\:{the}\:{same}\: \\ $$$${for}\:{each}\:{face}.{Arrangements}\:{that}\:{can} \\ $$$${be}\:{obtained}\:{from}\:{each}\:{other}\:{through} \\ $$$${rotations}\:{of}\:{the}\:{cube}\:{are}\:{considered} \\…

lim-x-0-tanx-x-1-x-2-

Question Number 155625 by puissant last updated on 02/Oct/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{{tanx}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} =\:? \\ $$ Answered by yeti123 last updated on 03/Oct/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{tan}\:{x}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}…