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Question Number 225664 Answers: 0 Comments: 0

If a(x)=1 and W_(n=−1) ^(Qw_(fr.) ((1/(x−1))×x)) a′′(ust^n x)=0; What value of Tk(x^2 )? (This is nonstandartmath exercise)

$${If}\:{a}\left({x}\right)=\mathrm{1}\:{and}\:\underset{{n}=−\mathrm{1}} {\overset{{Qw}_{{fr}.} \left(\frac{\mathrm{1}}{{x}−\mathrm{1}}×{x}\right)} {{W}}a}''\left({ust}^{{n}} {x}\right)=\mathrm{0}; \\ $$$${What}\:{value}\:{of}\:{Tk}\left({x}^{\mathrm{2}} \right)? \\ $$$$\left({This}\:{is}\:{nonstandartmath}\:{exercise}\right) \\ $$

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A gun, kept on a straight horizontal road, is used to hit a car travelling along the same road away from it with a uniform speed of 72 km/h. The car is at a distance of 500 m from the gun, when the gun is fired at an angle of 45° with the horizontal. Find the distance of the car from the gun, when the shell hits it. g = 10m/s²

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what′s the matter? yesterday the app was not accessible for many hours. now it seems to work normally again. but actually it doesn′t, at least with me. when i tip “view older” to scroll through the old posts, the app crashes always at some point, showing a message “Math Editor isn′t responding. × Close it ⊝ Wait” are you also experiencing the same problem? what has happened since yesterday?

$${what}'{s}\:{the}\:{matter}? \\ $$$${yesterday}\:{the}\:{app}\:{was}\:{not}\:{accessible} \\ $$$${for}\:{many}\:{hours}.\:{now}\:{it}\:{seems}\:{to} \\ $$$${work}\:{normally}\:{again}.\:{but}\:{actually} \\ $$$${it}\:{doesn}'{t},\:{at}\:{least}\:{with}\:{me}.\:{when} \\ $$$${i}\:{tip}\:``\boldsymbol{{view}}\:\boldsymbol{{older}}''\:{to}\:{scroll}\:{through} \\ $$$${the}\:{old}\:{posts},\:{the}\:{app}\:{crashes}\:{always} \\ $$$${at}\:{some}\:{point},\:{showing}\:{a}\:{message} \\ $$$$``{Math}\:{Editor}\:{isn}'{t}\:{responding}. \\ $$$$×\:{Close}\:{it} \\ $$$$\circleddash\:{Wait}'' \\ $$$${are}\:{you}\:{also}\:{experiencing}\:{the}\:{same} \\ $$$${problem}?\: \\ $$$${what}\:{has}\:{happened}\:{since}\:{yesterday}? \\ $$

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Question Number 223255 Answers: 2 Comments: 0

Which of the following complex numbers is equivalent to ((3−5i)/(8+2i))?(Note: i=(√(−1))) A)(3/8)−((5i)/2) B)(3/8)+((5i)/2) C)(7/(34))−((23i)/(34)) D)(7/(34))+((23i)/(34))

$${Which}\:{of}\:{the}\:{following}\:{complex} \\ $$$${numbers}\:{is}\:{equivalent}\:{to}\:\frac{\mathrm{3}−\mathrm{5}{i}}{\mathrm{8}+\mathrm{2}{i}}?\left({Note}:\:{i}=\sqrt{\left.−\mathrm{1}\right)}\right. \\ $$$$\left.{A}\right)\frac{\mathrm{3}}{\mathrm{8}}−\frac{\mathrm{5}{i}}{\mathrm{2}} \\ $$$$ \\ $$$$\left.{B}\right)\frac{\mathrm{3}}{\mathrm{8}}+\frac{\mathrm{5}{i}}{\mathrm{2}} \\ $$$$\: \\ $$$$\left.{C}\right)\frac{\mathrm{7}}{\mathrm{34}}−\frac{\mathrm{23}{i}}{\mathrm{34}} \\ $$$$ \\ $$$$\left.{D}\right)\frac{\mathrm{7}}{\mathrm{34}}+\frac{\mathrm{23}{i}}{\mathrm{34}} \\ $$

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Prove that the following identity holds : Σ_(λ∈Z[i]) ((1/((1 + 3λ)^3 ))) = ((π^(9/2) (√(1 + (√(3 )))))/(2^(5/4) 3^(27/8) Γ((3/4))^6 )) Where Z[i] = {a + bi : a,b ∈ Z} denotes gaussian integers !

$$ \\ $$$$\:\:\:\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following}\:\mathrm{identity}\:\mathrm{holds}\::\:\:\:\: \\ $$$$\:\:\:\underset{\lambda\in\mathbb{Z}\left[{i}\right]} {\sum}\:\left(\frac{\mathrm{1}}{\left(\mathrm{1}\:+\:\mathrm{3}\lambda\right)^{\mathrm{3}} }\right)\:=\:\frac{\pi^{\mathrm{9}/\mathrm{2}} \:\sqrt{\mathrm{1}\:+\:\sqrt{\mathrm{3}\:}}}{\mathrm{2}^{\mathrm{5}/\mathrm{4}} \:\:\mathrm{3}^{\mathrm{27}/\mathrm{8}} \:\Gamma\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{6}} \:}\:\:\:\:\: \\ $$$$\:\:\:\:\mathrm{Where}\:\mathbb{Z}\left[{i}\right]\:=\:\left\{{a}\:+\:{bi}\::\:{a},{b}\:\in\:\mathbb{Z}\right\}\:\mathrm{denotes}\:\mathrm{gaussian}\:\mathrm{integers}\:!\:\:\:\:\:\:\:\:\: \\ $$$$\: \\ $$

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Question Number 222783 Answers: 1 Comments: 0

(1/5)x^5 −(5/3)x^3 +4x+2

$$ \\ $$$$ \frac{\mathrm{1}}{\mathrm{5}}{x}^{\mathrm{5}} −\frac{\mathrm{5}}{\mathrm{3}}{x}^{\mathrm{3}} +\mathrm{4}{x}+\mathrm{2} \\ $$$$ \\ $$

Question Number 222781 Answers: 1 Comments: 0

a x^3 +ax^2 +3ax+2

$$ \\ $$$$ \:{a}\: {x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +\mathrm{3}{ax}+\mathrm{2} \\ $$

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