Question Number 80917 by jagoll last updated on 08/Feb/20 $$\frac{\sqrt{\mathrm{18}−\mathrm{7}{x}−{x}^{\mathrm{2}} }}{\mathrm{2}{x}+\mathrm{9}}\:\geqslant\:\frac{\sqrt{\mathrm{18}−\mathrm{7}{x}−{x}^{\mathrm{2}} }}{{x}+\mathrm{8}} \\ $$ Answered by john santu last updated on 08/Feb/20 $$\left({i}\right)\:{x}^{\mathrm{2}} −\mathrm{7}{x}−\mathrm{18}\leqslant\mathrm{0}\:\Rightarrow−\mathrm{9}\leqslant{x}\leqslant\mathrm{2} \\…
Question Number 15232 by tawa tawa last updated on 08/Jun/17 $$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{a}\:\:\mathrm{does}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system}\:\mathrm{have}\:\mathrm{a}\:\mathrm{non}\:\mathrm{trivial}\: \\ $$$$\mathrm{solution}\: \\ $$$$\mathrm{ax}_{\mathrm{1}} \:+\:\mathrm{3x}_{\mathrm{2}} \:−\:\mathrm{2x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$−\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{4x}_{\mathrm{2}} \:+\:\mathrm{ax}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$\mathrm{5x}_{\mathrm{1}}…
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Question Number 14596 by tawa tawa last updated on 02/Jun/17 Commented by Tinkutara last updated on 03/Jun/17 $$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{radii}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bottom} \\ $$$$\mathrm{circular}\:\mathrm{part}\:\mathrm{of}\:\mathrm{cylinder}\:\mathrm{and}\:\mathrm{ends}\:\mathrm{of} \\ $$$$\mathrm{frustum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone}?\:\mathrm{Why}\:\mathrm{these}\:\mathrm{are} \\ $$$$\mathrm{different}?\:\mathrm{These}\:\mathrm{should}\:\mathrm{be}\:\mathrm{same}! \\…
Question Number 145652 by imjagoll last updated on 07/Jul/21 Answered by john_santu last updated on 07/Jul/21 $${area}\:{of}\:{square}\:=\:\left(\mathrm{4}+{y}\right)^{\mathrm{2}} \\ $$$${let}\:{length}\:{side}\:{of}\:{area}\:{I}\:=\:{x} \\ $$$${then}\:{area}\:{of}\:{I}=\:\mathrm{4}{x}\: \\ $$$${the}\:{sum}\:{area}\:{of}\:\mathrm{3},\mathrm{4},\mathrm{5}\:=\:\mathrm{12}{x}\:=\:{xy} \\ $$$${then}\:{we}\:{get}\:{y}=\mathrm{12}\:{and}\:{area}\:{of}\:{square}…
Question Number 13998 by tawa tawa last updated on 26/May/17 Commented by ajfour last updated on 26/May/17 Answered by ajfour last updated on 26/May/17 $${A}=\frac{\mathrm{1}}{\mathrm{2}}{r}^{\mathrm{2}}…
Question Number 13978 by tawa tawa last updated on 25/May/17 Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 26/May/17 $$\left.{a}\right){h}^{\mathrm{2}} =\mathrm{13}^{\mathrm{2}} −\left(\mathrm{8}^{\mathrm{2}} +\mathrm{6}^{\mathrm{2}} \right)/\mathrm{4}=\mathrm{169}−\mathrm{25}=\mathrm{144} \\ $$$$\Rightarrow{h}=\mathrm{12} \\…
Question Number 79404 by jagoll last updated on 25/Jan/20 $$\mathrm{for}\:\mathrm{every}\:\mathrm{real}\:\mathrm{number}\:\mathrm{a}\:,\:\mathrm{b}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{4a}−\mathrm{6b}=\mathrm{2}.\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\: \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{expression}\: \\ $$$$\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{8a}−\mathrm{10b}+\mathrm{41}}\:? \\…
Question Number 13706 by tawa tawa last updated on 22/May/17 $$\mathrm{The}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{circular}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{5}\:\mathrm{litres}\:.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{volumes}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{parts}\:\mathrm{into}\:\mathrm{which}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{base}\:,\:\mathrm{One}\:\mathrm{third} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{way}\:\mathrm{down}\:\mathrm{from}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{to}\:\mathrm{the}\:\mathrm{base}.\:\mathrm{Give}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest} \\ $$$$\mathrm{ml}. \\ $$ Answered by ajfour last updated on…