Menu Close

Category: Others

Given-that-z-1-R-1-R-j-L-z-2-R-2-z-3-1-j-C-3-and-z-4-R-4-1-j-C-4-and-also-that-z-1-z-3-z-2-z-4-express-R-and-L-in-terms-of-the-real-constants-R-

Question Number 51250 by Tawa1 last updated on 25/Dec/18 $$\mathrm{Given}\:\mathrm{that}\:\:\:\mathrm{z}_{\mathrm{1}} \:=\:\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{R}\:+\:\mathrm{j}\omega\mathrm{L}\:;\:\:\:\mathrm{z}_{\mathrm{2}} \:=\:\mathrm{R}_{\mathrm{2}} \:;\:\:\mathrm{z}_{\mathrm{3}} \:=\:\frac{\mathrm{1}}{\mathrm{j}\omega\mathrm{C}_{\mathrm{3}} } \\ $$$$\mathrm{and}\:\:\mathrm{z}_{\mathrm{4}} \:=\:\mathrm{R}_{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{j}\omega\mathrm{C}_{\mathrm{4}} }\:\:\mathrm{and}\:\mathrm{also}\:\mathrm{that}\:\:\:\mathrm{z}_{\mathrm{1}} \mathrm{z}_{\mathrm{3}} \:\:=\:\:\mathrm{z}_{\mathrm{2}} \mathrm{z}_{\mathrm{4}} \:,\:\:\:\mathrm{express}\:…

If-R-1-j-L-R-3-R-2-R-4-j-1-C-where-R-1-R-2-R-3-R-4-L-and-C-are-real-show-that-L-C-R-2-R-3-2-C-2-R-4-2-1-

Question Number 51248 by Tawa1 last updated on 25/Dec/18 $$\mathrm{If}\:\:\:\:\:\frac{\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{j}\omega\mathrm{L}}{\mathrm{R}_{\mathrm{3}} }\:\:=\:\:\frac{\mathrm{R}_{\mathrm{2}} }{\mathrm{R}_{\mathrm{4}} \:−\:\mathrm{j}\:\frac{\mathrm{1}}{\omega\mathrm{C}}}\:\:,\:\:\:\mathrm{where}\:\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} ,\:\mathrm{R}_{\mathrm{3}} ,\:\mathrm{R}_{\mathrm{4}} ,\:\omega,\:\mathrm{L}\:\mathrm{and}\:\mathrm{C} \\ $$$$\mathrm{are}\:\mathrm{real}\:,\:\:\mathrm{show}\:\mathrm{that}\:\:\:\:\mathrm{L}\:=\:\frac{\mathrm{C}\:\mathrm{R}_{\mathrm{2}} \mathrm{R}_{\mathrm{3}} }{\omega^{\mathrm{2}} \mathrm{C}^{\mathrm{2}} \mathrm{R}_{\mathrm{4}} ^{\mathrm{2}}…

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…