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Let-P-be-the-point-a-2-t-2-1-t-2-a-t-1-t-Find-the-locus-of-P-as-t-varies-

Question Number 141446 by ZiYangLee last updated on 19/May/21 $$\mathrm{Let}\:\mathrm{P}\:\mathrm{be}\:\mathrm{the}\:\mathrm{point}\:\left(\frac{{a}}{\mathrm{2}}\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right),{a}\left({t}−\frac{\mathrm{1}}{{t}}\right)\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{P},\:\mathrm{as}\:{t}\:\mathrm{varies}. \\ $$ Answered by 1549442205PVT last updated on 19/May/21 $$\mathrm{Let}\:\mathrm{P}\:\mathrm{be}\:\mathrm{the}\:\mathrm{point}\:\left(\frac{{a}}{\mathrm{2}}\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}}…

Question-75851

Question Number 75851 by aliesam last updated on 18/Dec/19 Answered by MJS last updated on 18/Dec/19 $$\mathrm{10}\frac{\mathrm{8}+\mathrm{6i}}{\mathrm{3}−\mathrm{i}}=\mathrm{18}+\mathrm{26i}=\left(\mathrm{3}+\mathrm{i}\right)^{\mathrm{3}} \\ $$$$\left({x}+{y}\mathrm{i}\right)^{\mathrm{3}} ={x}^{\mathrm{3}} −\mathrm{3}{xy}^{\mathrm{2}} +\left(\mathrm{3}{x}^{\mathrm{2}} {y}−{y}^{\mathrm{3}} \right)\mathrm{i} \\…

Given-the-increasing-sequence-1-4-8-13-a-Find-U-2019-b-Find-S-2019-U-n-is-nth-term-of-the-sequence-S-n-is-sum-of-n-term-of-the-sequence-Arithmetic-Sequence-Deg

Question Number 75818 by naka3546 last updated on 18/Dec/19 $${Given}\:\:{the}\:\:{increasing}\:\:{sequence}\:: \\ $$$$\mathrm{1},\:\mathrm{4},\:\mathrm{8},\:\mathrm{13},\:… \\ $$$${a}.\:{Find}\:\:{U}_{\mathrm{2019}} \\ $$$${b}.\:{Find}\:\:{S}_{\mathrm{2019}} \\ $$$${U}_{{n}} \:\:{is}\:\:{nth}−{term}\:\:{of}\:\:{the}\:\:{sequence} \\ $$$${S}_{{n}} \:\:{is}\:\:{sum}\:\:{of}\:\:{n}\:−\:{term}\:\:{of}\:\:{the}\:\:{sequence} \\ $$$${Arithmetic}\:\:{Sequence}\:\:{Degree}\:\:{Two} \\…