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Author: Tinku Tara

xcos-a-ysin-b-1-xsin-ycos-a-2-sin-2-b-2-cos-2-Eliminate-

Question Number 207594 by MATHEMATICSAM last updated on 19/May/24 $$\frac{{x}\mathrm{cos}\theta}{{a}}\:+\:\frac{{y}\mathrm{sin}\theta}{{b}}\:=\:\mathrm{1} \\ $$$${x}\mathrm{sin}\theta\:−\:{y}\mathrm{cos}\theta\:=\:\sqrt{{a}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \theta\:+\:{b}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \theta} \\ $$$$\mathrm{Eliminate}\:\theta. \\ $$ Answered by Frix last updated…

2-sinx-cosx-1-

Question Number 207588 by hardmath last updated on 19/May/24 $$\sqrt{\mathrm{2}}\:\mathrm{sin}\boldsymbol{\mathrm{x}}\:\:+\:\:\mathrm{cos}\boldsymbol{\mathrm{x}}\:\:\geqslant\:\:\mathrm{1} \\ $$ Answered by mr W last updated on 19/May/24 $$\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{3}}}\:\mathrm{sin}\:{x}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:\mathrm{cos}\:{x}\geqslant\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\mathrm{sin}\:\alpha\:\:\mathrm{sin}\:{x}+\mathrm{cos}\:\alpha\:\mathrm{cos}\:{x}\geqslant\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$${with}\:\alpha=\mathrm{cos}^{−\mathrm{1}}…

The-real-roots-of-the-equation-x-2-6x-c-0-differ-by-2n-where-n-is-a-real-non-zero-Show-that-n-2-9-c-Given-that-the-roots-also-have-opposite-signs-find-the-set-of-possible-values-of-n-

Question Number 207546 by pete last updated on 18/May/24 $$\mathrm{The}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{2}} +\mathrm{6x}+\mathrm{c}=\mathrm{0} \\ $$$$\mathrm{differ}\:\mathrm{by}\:\mathrm{2n},\:\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{non}−\mathrm{zero}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{n}^{\mathrm{2}} =\mathrm{9}−\mathrm{c} \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{also}\:\mathrm{have}\:\mathrm{opposite} \\ $$$$\mathrm{signs},\:\mathrm{find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n} \\ $$ Answered by A5T…

lim-oo-1-oo-x-n-1-x-n-2-dx-

Question Number 207547 by SANOGO last updated on 18/May/24 $${lim}\rightarrow+{oo}\:\int_{\mathrm{1}} ^{+{oo}} \:\frac{{x}^{{n}} }{\mathrm{1}+{x}^{{n}+\mathrm{2}} }{dx}\:=? \\ $$ Commented by SWPlaysMC last updated on 18/May/24 $$\mathrm{Just}\:\mathrm{so}\:\mathrm{you}\:\mathrm{know},\:\mathrm{the}\:\mathrm{infinity}\:\mathrm{symbol}\:\mathrm{is}\:\infty\:\mathrm{and}\:\mathrm{not}\:“{oo}'' \\…