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Category: Differentiation

Question-130780

Question Number 130780 by LYKA last updated on 28/Jan/21 Commented by kaivan.ahmadi last updated on 29/Jan/21 $$\overset{\rightarrow} {{b}}=\left(\mathrm{2},−\mathrm{1},\mathrm{1}\right)\Rightarrow\mid\overset{\rightarrow} {{b}}\mid=\sqrt{\mathrm{6}}\Rightarrow\overset{\rightarrow} {{u}}=\frac{\overset{\rightarrow} {{b}}}{\mid\overset{\rightarrow} {{b}}\mid}=\left(\frac{\mathrm{2}}{\:\sqrt{\mathrm{6}}},\frac{−\mathrm{1}}{\:\sqrt{\mathrm{6}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{6}}}\right) \\ $$$$\bigtriangledown{f}=\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{yz},\mathrm{3}{y}^{\mathrm{2}}…

A-metal-rain-gutter-is-to-have-3-inch-and-a-3-inch-bottom-the-sides-making-an-equal-angle-with-the-bottom-What-should-be-in-order-to-maximize-carrying-capasity-of-the-gutter-

Question Number 130582 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{A}\:\mathrm{metal}\:\mathrm{rain}\:\mathrm{gutter}\:\mathrm{is}\:\mathrm{to}\:\mathrm{have}\:\mathrm{3}−\mathrm{inch}\:\mathrm{and} \\ $$$$\mathrm{a}\:\mathrm{3}−\mathrm{inch}\:\mathrm{bottom}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{making}\:\mathrm{an}\:\mathrm{equal} \\ $$$$\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{bottom}.\:\mathrm{What}\:\mathrm{should}\: \\ $$$$\theta\:\mathrm{be}\:\mathrm{in}\:\mathrm{order}\:\mathrm{to}\:\mathrm{maximize}\:\mathrm{carrying}\:\mathrm{capasity} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{gutter}\:? \\ $$ Answered by EDWIN88 last updated…

Find-the-angle-between-y-2-8x-and-x-2-y-2-16-at-their-point-of-intersection-for-which-y-is-positive-

Question Number 130294 by bramlexs22 last updated on 24/Jan/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{y}^{\mathrm{2}} =\mathrm{8x}\: \\ $$$$\mathrm{and}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{16}\:\mathrm{at}\:\mathrm{their}\:\mathrm{point}\:\mathrm{of} \\ $$$$\mathrm{intersection}\:\mathrm{for}\:\mathrm{which}\:\mathrm{y}\:\mathrm{is}\:\mathrm{positive} \\ $$ Answered by benjo_mathlover last updated on…

The-closest-distance-from-the-point-on-the-ellipse-2x-2-y-2-8-to-the-line-y-5x-is-

Question Number 130213 by benjo_mathlover last updated on 23/Jan/21 $$\:\mathrm{The}\:\mathrm{closest}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\mathrm{on}\: \\ $$$$\mathrm{the}\:\mathrm{ellipse}\:\mathrm{2x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} =\mathrm{8}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}=\mathrm{5x} \\ $$$$\mathrm{is}\:\_\_ \\ $$ Answered by liberty last updated on 23/Jan/21…