Question Number 74322 by naka3546 last updated on 22/Nov/19 $${Let}\:\: \\ $$$${k}\:\:=\:\:\frac{\left({xy}\:+\:{yz}\:+\:{zx}\right)\left({x}\:+\:{y}\:+\:{z}\right)}{\left({x}\:+\:{y}\right)\left({y}\:+\:{z}\right)\left({z}\:+\:{x}\right)} \\ $$$${Find}\:\:{the}\:\:{minimum}\:\:{and}\:\:{maximum}\:\:{value}\:\:{of}\:\:\:{k}\:. \\ $$ Answered by MJS last updated on 23/Nov/19 $${k}−\mathrm{1}=\frac{{xyz}}{\left({x}+{y}\right)\left({x}+{z}\right)\left({y}+{z}\right)} \\…
Question Number 8757 by FilupSmith last updated on 26/Oct/16 $$\mathrm{A}\:\mathrm{balloon}\:\mathrm{is}\:\mathrm{inflated}\:\mathrm{such}\:\mathrm{that}\:\mathrm{every} \\ $$$$\mathrm{point}\:\mathrm{expands}\:\mathrm{at}\:{a}\:\mathrm{units}/\mathrm{second}. \\ $$$$ \\ $$$$\mathrm{An}\:\mathrm{ant}\:\mathrm{runs}\:\mathrm{from}\:\mathrm{one}\:\mathrm{point}\:\boldsymbol{{A}}\:\mathrm{to}\:\mathrm{another} \\ $$$$\mathrm{point}\:\boldsymbol{{B}}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{ant}\:\mathrm{moves}\:{b}\:\mathrm{units}/\mathrm{second}, \\ $$$$\mathrm{what}\:\mathrm{will}\:\mathrm{influence}\:\mathrm{if}\:\mathrm{or}\:\mathrm{not}\:\mathrm{the}\:\mathrm{ant}\:\mathrm{will} \\ $$$$\mathrm{ever}\:\mathrm{reach}\:\mathrm{point}\:\boldsymbol{{B}}? \\ $$ Commented…
Question Number 74293 by Mr. K last updated on 21/Nov/19 Commented by Mr. K last updated on 21/Nov/19 $${ABCD}\:{id}\:{a}\:{quadrilateral},\:{cos}\theta=\frac{\sqrt{\mathrm{7}}}{\mathrm{4}}. \\ $$$${AE}=\mathrm{1},\:{BE}=\mathrm{4},\:{CE}=\mathrm{3}\:{and}\:{DE}=\mathrm{2}. \\ $$$${Find}\:{the}\:{area}\:{of}\:{the}\:{quadrilateral}. \\ $$…
Question Number 139825 by mathdave last updated on 01/May/21 Commented by mr W last updated on 01/May/21 $${rate}\:{of}\:{changing}\:{of}\:{distance}\:{is}\:{the} \\ $$$${sum}\:{of}\:{the}\:{speeds}\:{of}\:{the}\:{cars}: \\ $$$${case}\:\mathrm{1}: \\ $$$$−\left(\mathrm{50}+\mathrm{40}\right)=−\mathrm{90}\:{km}/{h}\:{if}\:{A}\:{was}\:{to} \\…
Question Number 139815 by mohammad17 last updated on 01/May/21 Commented by mohammad17 last updated on 01/May/21 $${solve}\:{by}\:{Gauss}\:{Jordan}\:? \\ $$ Commented by EDWIN88 last updated on…
Question Number 139818 by Study last updated on 01/May/21 $${x}^{\mathrm{4}} −\mathrm{22}{x}^{\mathrm{2}} +{x}−\mathrm{114}=\mathrm{0} \\ $$$${x}=? \\ $$ Answered by MJS_new last updated on 01/May/21 $$\mathrm{exact}\:\mathrm{solution}\:\mathrm{too}\:\mathrm{complicated},\:\mathrm{approximation} \\…
Question Number 8740 by 123456 last updated on 25/Oct/16 $${x}_{\mathrm{1},\mathrm{1}} =\mathrm{1} \\ $$$${x}_{{n}+\mathrm{1},{m}} ={x}_{{n},{m}} +{m} \\ $$$${x}_{{n},{m}+\mathrm{1}} ={nx}_{{n},{m}} −\mathrm{1} \\ $$$${x}_{\mathrm{2},\mathrm{2}} =? \\ $$ Commented…
Question Number 74267 by smartsmith459@gmail.com last updated on 21/Nov/19 $$\mathrm{1}\:\:{what}\:{is}\:{the}\:{order}\:{and}\:{the}\:{degree}\:{of}\:{the}\:{differential}\:{equation} \\ $$$$\frac{{d}^{\mathrm{3}} {Z}}{{dt}^{\mathrm{3}} }\:+\left(\frac{{dZ}}{{dt}}\right)^{\mathrm{4}} \:−\:{y}^{\mathrm{5}} \:={e}^{−\mathrm{2}{x}} . \\ $$$$\left.\mathrm{2}\right)\:\:\mathrm{2}{x}\frac{{d}^{\mathrm{5}} {y}}{{dx}^{\mathrm{5}} }\:+\:\mathrm{5}{x}^{\mathrm{2}} \:\left(\frac{{dy}}{{dx}}\:\right)^{\mathrm{4}} \:−\:{xy}^{\mathrm{2}} \:=\:\mathrm{0}. \\…
Question Number 74265 by Maclaurin Stickker last updated on 21/Nov/19 $${Determine}\:{the}\:{values}\:{of}\:{m}\in\mathbb{R}\:{for}\: \\ $$$${which}\:{the}\:{function}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{mx}+{m}}} \\ $$$${is}\:{the}\:{set}\:{of}\:{real}\:{numbers}. \\ $$ Answered by MJS last updated on 21/Nov/19…
Question Number 8721 by swapnil last updated on 24/Oct/16 $$\mathrm{If}\:\mathrm{z}\in\mathrm{C}\:\mathrm{satisfies} \\ $$$$\mid\mathrm{z}^{\mathrm{3}} +\mathrm{z}^{−\mathrm{3}} \mid\leqslant\mathrm{2} \\ $$$${t}\mathrm{hen}\:\mathrm{maximum}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\mid\mathrm{z}+\mathrm{z}^{−\mathrm{1}} \mid\mathrm{is}? \\ $$ Commented by 123456 last updated on…