Menu Close

Category: None

partial-fraction-in-below-1-x-2-15x-41-x-2-x-3-2-2-4x-2-5x-6-x-1-x-2-4-

Question Number 157869 by joki last updated on 29/Oct/21 $$\mathrm{partial}\:\mathrm{fraction}\:\mathrm{in}\:\mathrm{below}: \\ $$$$\mathrm{1}.\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{15x}+\mathrm{41}}{\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\mathrm{2}.\frac{\mathrm{4x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{6}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{4}\right)} \\ $$ Answered by Rasheed.Sindhi last updated…

Given-that-point-P-a-cos-b-sin-is-a-point-on-the-ellipse-x-2-a-2-y-2-b-2-1-The-tangent-to-the-curve-at-point-P-is-perpendicular-to-a-straight-line-which-passes-through-the-focus-F-ae

Question Number 157867 by ZiYangLee last updated on 29/Oct/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{point}\:{P}\left({a}\:\mathrm{cos}\:\theta,\:{b}\:\mathrm{sin}\:\theta\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}. \\ $$$$\mathrm{The}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{at}\:\mathrm{point}\:{P}\:\:\mathrm{is}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{which}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{focus}, \\ $$$${F}\:\left({ae},\mathrm{0}\right).\:\mathrm{If}\:{N}\:\mathrm{is}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{point},\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:{N}\:\mathrm{is}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…

Make-R-the-subject-of-P-RE-2-R-b-2-

Question Number 92275 by otchereabdullai@gmail.com last updated on 05/May/20 $$\mathrm{Make}\:\mathrm{R}\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}: \\ $$$$\:\:\mathrm{P}=\:\frac{\mathrm{RE}^{\mathrm{2}} }{\left(\mathrm{R}+\mathrm{b}\right)^{\mathrm{2}} } \\ $$ Answered by MJS last updated on 06/May/20 $${P}\left({R}+{b}\right)^{\mathrm{2}} ={E}^{\mathrm{2}}…

a-n-is-a-natural-number-sequence-for-n-0-that-satisfy-recurrence-relation-a-m-n-a-m-n-m-n-1-1-2-a-2m-a-2n-for-m-n-nonnegative-integers-Find-a-2016-

Question Number 157795 by naka3546 last updated on 28/Oct/21 $$\left\{{a}_{{n}} \right\}\:{is}\:{a}\:\:{natural}\:\:{number}\:\:{sequence}\:\:{for}\:\:{n}\:\geqslant\:\mathrm{0}\:\:{that}\:\:{satisfy} \\ $$$${recurrence}\:\:{relation}\:\:{a}_{{m}+{n}} \:+\:{a}_{{m}−{n}} \:−{m}+{n}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({a}_{\mathrm{2}{m}} \:+{a}_{\mathrm{2}{n}} \right)\:,\:\: \\ $$$${for}\:\:\forall\:{m},{n}\:\:{nonnegative}\:\:{integers}\:. \\ $$$${Find}\:\:{a}_{\mathrm{2016}} \:. \\ $$ Answered…