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Given-a-polynomial-f-x-where-f-x-x-3-ax-2-3x-b-and-x-1-is-a-factor-of-f-x-and-f-x-12-at-point-2-4-find-the-values-of-a-and-b-hence-factorise-f-x-completely-

Question Number 38910 by Rio Mike last updated on 01/Jul/18 $${Given}\:{a}\:{polynomial}\:{f}\left({x}\right)\:{where} \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:{ax}\:^{\mathrm{2}} \:+\:\mathrm{3}{x}\:+\:{b} \\ $$$${and}\:\left(\:{x}−\:\mathrm{1}\right)\:{is}\:{a}\:{factor}\:{of}\:{f}\left({x}\right) \\ $$$${and}\:{f}\:'\left({x}\right)=\:\:\mathrm{12}\:{at}\:{point}\:\left(\:\mathrm{2},\mathrm{4}\right) \\ $$$${find}\:{the}\:{values}\:{of}\:{a}\:{and}\:{b} \\ $$$${hence}\:{factorise}\:{f}\left({x}\right)\:{completely} \\ $$$$…

Find-the-equation-of-the-perpendicular-bisector-of-the-line-segment-joining-the-points-1-3-and-5-1-

Question Number 38880 by Rio Mike last updated on 30/Jun/18 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{perpendicular} \\ $$$${bisector}\:{of}\:{the}\:{line}\:{segment}\:{joining} \\ $$$${the}\:{points}\:\left(\mathrm{1},\mathrm{3}\right)\:{and}\:\left(\mathrm{5},\mathrm{1}\right) \\ $$ Answered by MrW3 last updated on 30/Jun/18 $${eqn}\:{of}\:{line}\:{joining}\:\left(\mathrm{1},\mathrm{3}\right)\:{and}\:\left(\mathrm{5},\mathrm{1}\right):…

solve-for-0-pi-the-equations-a-cos-2-pi-2-1-2-b-cos-3-sin-0-

Question Number 38881 by Rio Mike last updated on 30/Jun/18 $${solve}\:{for}\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\pi,\:{the}\:{equations} \\ $$$$\left.{a}\right)_{} \:\mathrm{cos}\:\left(\mathrm{2}\theta\:−\:\frac{\pi}{\mathrm{2}}\right)=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.{b}\right)\:\mathrm{cos}\:\theta\:−\:\sqrt{\mathrm{3}}\:{sin}\:\theta\:=\:\mathrm{0} \\ $$ Answered by MrW3 last updated on 30/Jun/18…

Find-the-equation-of-the-line-through-2-3-which-make-angles-45-with-the-line-2x-y-2-

Question Number 38879 by Rio Mike last updated on 30/Jun/18 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{line}\:{through} \\ $$$$\left(\mathrm{2},−\mathrm{3}\right)\:{which}\:{make}\:{angles}\:\mathrm{45}°\:{with} \\ $$$${the}\:{line}\:\mathrm{2}{x}\:−\:{y}\:=\:\mathrm{2}. \\ $$ Answered by MrW3 last updated on 30/Jun/18 $${line}\:\mathrm{2}{x}−{y}=\mathrm{2}:…

Find-the-equation-on-a-line-joining-the-points-A-2x-4-B-x-3-and-C-4-3-

Question Number 38878 by Rio Mike last updated on 30/Jun/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{on}\:\mathrm{a}\:\mathrm{line}\:\mathrm{joining} \\ $$$$\mathrm{the}\:\mathrm{points}\:\mathrm{A}\left(\mathrm{2}{x},\mathrm{4}\right),{B}\left({x},\mathrm{3}\right)\:{and}\: \\ $$$${C}\left(\mathrm{4},\mathrm{3}\right) \\ $$ Answered by $@ty@m last updated on 01/Jul/18 $${Eqn}.\:{of}\:{line}\:{passing}\:{through}…

Evaluate-1-2-3-8-3-16-5-64-

Question Number 104406 by Don08q last updated on 21/Jul/20 $$\:\:\:\:\mathrm{Evaluate} \\ $$$$\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{8}}\:+\:\frac{\mathrm{3}}{\mathrm{16}}\:+\:\frac{\mathrm{5}}{\mathrm{64}}\:+\:….. \\ $$ Commented by Don08q last updated on 21/Jul/20 $$\:\frac{\mathrm{1}×\mathrm{2}}{\mathrm{4}^{\mathrm{1}} }\:+\:\frac{\mathrm{2}×\mathrm{3}}{\mathrm{4}^{\mathrm{2}} }\:+\:\frac{\mathrm{3}×\mathrm{4}}{\mathrm{4}^{\mathrm{3}} }\:+\:\frac{\mathrm{4}×\mathrm{5}}{\mathrm{4}^{\mathrm{4}}…