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Advance question A phone mistakenly got locked with the pattern of 3 × 3 form, in how many attempts person can try before he can eventually get it right ? Thank you

$$\mathrm{Advance}\:\mathrm{question} \\ $$$$ \\ $$$$\mathrm{A}\:\mathrm{phone}\:\mathrm{mistakenly}\:\mathrm{got}\:\mathrm{locked}\:\mathrm{with}\:\mathrm{the}\: \\ $$$$\mathrm{pattern}\:\mathrm{of}\:\:\mathrm{3}\:×\:\mathrm{3}\:\mathrm{form},\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{attempts} \\ $$$$\mathrm{person}\:\mathrm{can}\:\mathrm{try}\:\mathrm{before}\:\mathrm{he}\:\mathrm{can}\:\mathrm{eventually}\:\mathrm{get} \\ $$$$\mathrm{it}\:\mathrm{right}\:? \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

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∫(df/dx)×(dg/dx) ?

$$\int\frac{\mathrm{df}}{\mathrm{dx}}×\frac{\mathrm{dg}}{\mathrm{dx}}\:\:\:\:\:? \\ $$

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Determine the continuity ortherwise of the following functions a) ((7x^2 +x−3)/((x−2)^2 )) b) x^2 −4x+1 c) f(x) = {_(1 , x=1) ^(((4−x^2 )/(3−(√(x^2 −5)))) , x≠2)

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{continuity}\:\mathrm{ortherwise}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{following}\:\mathrm{functions} \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\:\frac{\mathrm{7x}^{\mathrm{2}} +\mathrm{x}−\mathrm{3}}{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{c}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\left\{_{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:,\:\:\:\:\:\mathrm{x}=\mathrm{1}} ^{\frac{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }{\mathrm{3}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{5}}}\:\:\:\:\:\:,\:\:\:\:\mathrm{x}\neq\mathrm{2}} \right. \\ $$

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((3x^2 −1)/x)+((5x)/(3x^2 −x−1))=((119)/(18))

$$\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}}{{x}}+\frac{\mathrm{5}{x}}{\mathrm{3}{x}^{\mathrm{2}} −{x}−\mathrm{1}}=\frac{\mathrm{119}}{\mathrm{18}} \\ $$

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Question Number 198465 Answers: 0 Comments: 1

The furier series approximation to the forcing function is given by f(t)=5[1+(4/π)((/)((sin120πt)/1)+((sin360πt)/2)+((sin600πt)/3) +.........)] The transfer function for this problem T(s)=((X(s))/(f(s)))=(1/(ms^2 +cs+k)) =(1/(0.001s+1)) 1. plot the amplitude spectrum 2.Obtain the expression for steady displacement X(t)

$${The}\:{furier}\:{series}\:{approximation}\:{to}\: \\ $$$${the}\:{forcing}\:{function}\:{is}\:{given}\:{by}\: \\ $$$${f}\left({t}\right)=\mathrm{5}\left[\mathrm{1}+\frac{\mathrm{4}}{\pi}\left(\frac{}{}\frac{{sin}\mathrm{120}\pi{t}}{\mathrm{1}}+\frac{{sin}\mathrm{360}\pi{t}}{\mathrm{2}}+\frac{{sin}\mathrm{600}\pi{t}}{\mathrm{3}}\right.\right. \\ $$$$\left.\:\left.\:\:\:\:\:+.........\right)\right] \\ $$$${The}\:{transfer}\:{function}\:{for}\:{this} \\ $$$${problem}\:\:{T}\left({s}\right)=\frac{{X}\left({s}\right)}{{f}\left({s}\right)}=\frac{\mathrm{1}}{{ms}^{\mathrm{2}} +{cs}+{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{0}.\mathrm{001}{s}+\mathrm{1}} \\ $$$$\mathrm{1}.\:{plot}\:{the}\:{amplitude}\:{spectrum}\: \\ $$$$\mathrm{2}.{Obtain}\:{the}\:{expression}\:{for}\:{steady}\: \\ $$$$\:\:\:\:\:\:\:\:{displacement}\:{X}\left({t}\right) \\ $$

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Please suggest youtube playlist to prepare one for mathematics olympiad. Thanks in advance.

$${Please}\:{suggest}\:{youtube}\:{playlist}\:{to} \\ $$$${prepare}\:{one}\:{for}\:{mathematics}\:{olympiad}. \\ $$$${Thanks}\:{in}\:{advance}. \\ $$$$ \\ $$

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