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Question-182253

Question Number 182253 by Tawa11 last updated on 06/Dec/22 Commented by Tawa11 last updated on 06/Dec/22 $$\mathrm{Sirs},\:\mathrm{see}\:\mathrm{whag}\:\mathrm{I}\:\mathrm{did}. \\ $$$$\:\:\mathrm{h}\:\:=\:\:\mathrm{5}\:\:+\:\:\mathrm{30t}\:\:−\:\:\mathrm{5t}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\mathrm{h}'\:\:\:=\:\:\:\mathrm{30}\:\:\:−\:\:\:\mathrm{10t} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{10t}\:\:\:=\:\:\:\mathrm{30} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{t}\:\:\:=\:\:\:\frac{\mathrm{30}}{\mathrm{10}}…

Given-the-equality-1-3-5-2p-1-p-1-2-p-N-Show-this-equality-is-true-when-we-replace-p-by-p-1-

Question Number 116685 by mathocean1 last updated on 05/Oct/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{equality}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+…+\left(\mathrm{2p}+\mathrm{1}\right)=\left(\mathrm{p}+\mathrm{1}\right)^{\mathrm{2}\:} \:\:\:\mathrm{p}\:\in\:\mathbb{N}^{\ast} \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{this}\:\mathrm{equality}\:\mathrm{is}\:\mathrm{true}\:\mathrm{when} \\ $$$$\mathrm{we}\:\mathrm{replace}\:\mathrm{p}\:\mathrm{by}\:\mathrm{p}+\mathrm{1} \\ $$ Answered by TANMAY PANACEA…

solve-1-2-2h-3-2-h-1-

Question Number 116610 by moh175 last updated on 05/Oct/20 $$ \\ $$$$\:\:\:\:\:{solve}\:: \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}{h}} \:+\:\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{{h}} \:=\:\mathrm{1} \\ $$ Commented by Dwaipayan Shikari last updated on…

Find-constant-a-b-so-that-y-t-t-3-e-2t-is-solution-of-IVP-y-ay-e-2t-y-0-b-

Question Number 182139 by Mastermind last updated on 04/Dec/22 $$\mathrm{Find}\:\mathrm{constant}\:\mathrm{a},\:\mathrm{b},\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{y}\left(\mathrm{t}\right)=\left(\mathrm{t}+\mathrm{3}\right)\mathrm{e}^{\mathrm{2t}} \:\mathrm{is}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{IVP} \\ $$$$\mathrm{y}^{'} =\mathrm{ay}+\mathrm{e}^{\mathrm{2t}} ,\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{b} \\ $$$$ \\ $$$$. \\ $$ Commented by…

1-8-1-18-1-30-1-44-1-60-1-78-1-98-1-120-

Question Number 116480 by Dwaipayan Shikari last updated on 04/Oct/20 $$\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{44}}+\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{78}}+\frac{\mathrm{1}}{\mathrm{98}}+\frac{\mathrm{1}}{\mathrm{120}}+…….. \\ $$ Answered by Olaf last updated on 04/Oct/20 $${u}_{{n}} \:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{7}{n}}\:=\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{7}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{7}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+\mathrm{7}}\right) \\ $$$$\underset{{n}=\mathrm{1}}…