Category: Geometry

Question Number 1611 by Rasheed Soomro last updated on 26/Aug/15 $$\mathrm{A}\mathrm{right}\mathrm{angled}\mathrm{triangle}\mathrm{has}\mathrm{fixed}\mathrm{hypotenuse}\mathrm{measuring}$$$$\mathrm{h}\mathrm{units}.\mathrm{What}\mathrm{are}\mathrm{the}\mathrm{measures}\mathrm{of}\mathrm{its}\mathrm{legs},$$$$\mathrm{for}\mathbf{maximum}\mathbf{perimeter}\mathrm{P}\mathrm{units}.$$$$\mathrm{Will}\mathrm{the}\mathrm{area}\mathrm{be}\mathrm{also}\mathrm{maximum},\mathrm{when}\mathrm{the}\mathrm{perimeter}\mathrm{be}$$$$\mathrm{maximum}?$$ Commented by Rasheed Soomro…

Question Number 1581 by 112358 last updated on 21/Aug/15 $$Findafunctionf\left(x\right)satisfying$$$$thefollowingequation.$$$${\int }_a^b[\frac{1}{2}{\left\{f\left(x\right)\right\}}^2-\sqrt{{\left\{f\left(x\right)\right\}}^2+{\left\{\frac{d}{dx}\left(f\left(x\right)\right)\right\}}^2}]dx=0$$$$b>0,a>0,b\ne a.$$ Commented by…

Question Number 67102 by TawaTawa last updated on 22/Aug/19 Answered by mr W last updated on 23/Aug/19 Commented by mr W last updated on 23/Aug/19…

Question Number 67071 by TawaTawa last updated on 22/Aug/19 Commented by Prithwish sen last updated on 22/Aug/19 $$\mathrm{a})\mathrm{The}\mathrm{eqn}.\mathrm{of}\mathbf{C}{(\mathrm{x}-8)}^2+{(\mathrm{y}-2)}^2={\mathrm{r}}^2$$$$\because \mathbf{L}\mathrm{is}\mathrm{a}\mathrm{tangent}$$$$\therefore\:\frac{\mathrm{k}.\mathrm{8}−\mathrm{5}.\mathrm{2}−\mathrm{21}}{\:\sqrt{\mathrm{k}^{\mathrm{2}} +\mathrm{25}}}\:=\:\mathrm{r}…

Question Number 67026 by TawaTawa last updated on 21/Aug/19 Commented by Tony Lin last updated on 22/Aug/19 $$\because slopeof{L}_{BC}=tan150°=-\frac{\sqrt{3}}{3}$$$$\therefore L_{BC}:y=-\frac{\sqrt{3}}{3}(x+4)$$$$\because{L}_{{BC}} \bot{L}_{{AB}}…