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Category: Geometry

Question-153226

Question Number 153226 by ajfour last updated on 05/Sep/21 Commented by mr W last updated on 05/Sep/21 $${x}^{\mathrm{3}} +{x}−{c}=\mathrm{0} \\ $$$$\Rightarrow{x}=\sqrt[{\mathrm{3}}]{\sqrt{\frac{\mathrm{1}}{\mathrm{27}}+\frac{{c}^{\mathrm{2}} }{\mathrm{4}}}+\frac{{c}}{\mathrm{2}}}−\sqrt[{\mathrm{3}}]{\sqrt{\frac{\mathrm{1}}{\mathrm{27}}+\frac{{c}^{\mathrm{2}} }{\mathrm{4}}}−\frac{{c}}{\mathrm{2}}} \\ $$$${any}\:{other}\:{ways}\:{to}\:{solve}?…

Question-87671

Question Number 87671 by TawaTawa1 last updated on 05/Apr/20 Commented by TawaTawa1 last updated on 05/Apr/20 $$\mathrm{I}\:\mathrm{got}\:\:\mathrm{10}.\mathrm{5}\:\mathrm{m}^{\mathrm{2}\:} \:\:\mathrm{but}\:\mathrm{am}\:\mathrm{not}\:\mathrm{sure}. \\ $$$$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{check}. \\ $$ Commented by Tony…

A-boy-ran-around-a-circular-part-of-radius-14m-in-15s-Calculate-the-average-velocity-and-the-average-speed-

Question Number 22112 by tawa tawa last updated on 11/Oct/17 $$\mathrm{A}\:\mathrm{boy}\:\mathrm{ran}\:\mathrm{around}\:\mathrm{a}\:\mathrm{circular}\:\mathrm{part}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{14m}\:\mathrm{in}\:\mathrm{15s}.\:\mathrm{Calculate}\:\mathrm{the}\: \\ $$$$\mathrm{average}\:\mathrm{velocity}\:\mathrm{and}\:\mathrm{the}\:\mathrm{average}\:\mathrm{speed}. \\ $$ Answered by $@ty@m last updated on 11/Oct/17 $${Average}\:{Verlocity}=\frac{{Displacement}}{{time}} \\ $$$$=\frac{\mathrm{0}}{\mathrm{15}}=\mathrm{0}…

Question-87630

Question Number 87630 by mr W last updated on 05/Apr/20 Commented by mr W last updated on 05/Apr/20 $${ajfour}\:{sir}\:{has}\:{put}\:{this}\:{question}: \\ $$$${find}\:{the}\:{radius}\:{r}\:{of}\:{the}\:{small}\:{circles} \\ $$$${in}\:{terms}\:{of}\:{the}\:{parameters}\:{a}\:{and}\:{b} \\ $$$${of}\:{the}\:{ellipse}\:\left({a}\geqslant{b}\right).…

Let-ABC-be-a-triangle-and-h-a-the-altitude-through-A-Prove-that-b-c-2-a-2-4h-a-2-As-usual-a-b-c-denote-the-sides-BC-CA-AB-respectively-

Question Number 22079 by Tinkutara last updated on 10/Oct/17 $$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{and}\:{h}_{{a}} \:\mathrm{the} \\ $$$$\mathrm{altitude}\:\mathrm{through}\:{A}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\left({b}\:+\:{c}\right)^{\mathrm{2}} \:\geqslant\:{a}^{\mathrm{2}} \:+\:\mathrm{4}{h}_{{a}} ^{\mathrm{2}} . \\ $$$$\left(\mathrm{As}\:\mathrm{usual}\:{a},\:{b},\:{c}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sides}\:{BC},\right. \\ $$$$\left.{CA},\:{AB}\:\mathrm{respectively}.\right) \\ $$…