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Category: Coordinate Geometry

Question-199817

Question Number 199817 by ajfour last updated on 09/Nov/23 Answered by ajfour last updated on 09/Nov/23 $$\left\{{a}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \theta\right)−\frac{\mathrm{sin}\:\theta}{\mathrm{2}\left(\mathrm{1}+\mathrm{sin}\:\theta\right)}\right\}^{\mathrm{2}} \\ $$$$\:\:\:={a}\left\{{a}+\frac{\mathrm{sin}\:\theta}{\mathrm{2cos}\:\theta\left(\mathrm{1}+\mathrm{sin}\:\theta\right)}\right\} \\ $$$${b}=\frac{\mathrm{sin}\:\theta}{\mathrm{2cos}\:\theta\left(\mathrm{1}+\mathrm{sin}\:\theta\right)} \\ $$…

Given-Fibonacci-series-F-1-F-2-1-and-F-n-2-F-n-1-F-n-for-n-gt-0-Find-the-remainder-F-2022-divides-by-5-

Question Number 199625 by cortano12 last updated on 06/Nov/23 $$\mathrm{Given}\:\mathrm{Fibonacci}\:\mathrm{series}\: \\ $$$$\:\mathrm{F}_{\mathrm{1}} =\mathrm{F}_{\mathrm{2}} =\:\mathrm{1}\:\mathrm{and}\:\mathrm{F}_{\mathrm{n}+\mathrm{2}} =\:\mathrm{F}_{\mathrm{n}+\mathrm{1}} +\mathrm{F}_{\mathrm{n}} \\ $$$$\:\mathrm{for}\:\mathrm{n}>\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\: \\ $$$$\:\mathrm{F}_{\mathrm{2022}} \:\mathrm{divides}\:\mathrm{by}\:\mathrm{5}\: \\ $$ Answered by…

Question-198434

Question Number 198434 by cortano12 last updated on 20/Oct/23 Commented by mr W last updated on 20/Oct/23 $${due}\:{to}\:{symmetry} \\ $$$${max}=\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)=\frac{\sqrt{\mathrm{2}}}{\mathrm{4}} \\ $$ Answered by mr…