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Question Number 218855    Answers: 0   Comments: 0

(√3)x^2 =(√((64−x^2 )(x^2 −4)))+(√((81−x^2 )(x^2 −1)))+(√((49−x^2 )(x^2 −1)))solve

$$\sqrt{\mathrm{3}}{x}^{\mathrm{2}} =\sqrt{\left(\mathrm{64}−{x}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} −\mathrm{4}\right)}+\sqrt{\left(\mathrm{81}−{x}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} −\mathrm{1}\right)}+\sqrt{\left(\mathrm{49}−{x}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} −\mathrm{1}\right)}\boldsymbol{{solve}} \\ $$

Question Number 218853    Answers: 5   Comments: 0

Question Number 218854    Answers: 3   Comments: 0

Question Number 218850    Answers: 1   Comments: 0

Question Number 218849    Answers: 0   Comments: 0

Question Number 218848    Answers: 0   Comments: 0

Question Number 218846    Answers: 1   Comments: 0

Question Number 218844    Answers: 5   Comments: 0

Question Number 218845    Answers: 2   Comments: 0

Question Number 218836    Answers: 3   Comments: 0

Question Number 218835    Answers: 1   Comments: 0

Question Number 218834    Answers: 0   Comments: 0

Question Number 218833    Answers: 3   Comments: 0

Question Number 218832    Answers: 0   Comments: 0

Question Number 218975    Answers: 0   Comments: 0

In physics , Flux integral ∮_( ∂S) F^→ ∙ dS^→ is a concept that widely used in eletric equation or Heat Eqaution for example..... ∮_( A) D^→ ∙dA^→ =Q_0 (Gauss law) D^→ is displayment field ∮_( S) B^→ ∙dA^→ =0 (Gauss law for magnetic) B^→ is Magnetic field and in Heat Flux (∂E_(in) /∂t)−(∂E_(out) /∂t)=∮_( S) 𝛗_q ^→ ∙dS^→ But in mathematic it seems that Surface integral in the vector field is only extended version of the integral,why mathematic don′t use surface integral like physics...??? i really curious

$$\mathrm{In}\:\mathrm{physics}\:,\:\mathrm{Flux}\:\mathrm{integral}\:\oint_{\:\partial\boldsymbol{\mathcal{S}}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\:\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{S}}}\:\mathrm{is}\:\mathrm{a}\: \\ $$$$\mathrm{concept}\:\mathrm{that}\:\mathrm{widely}\:\mathrm{used}\:\mathrm{in}\:\mathrm{eletric}\:\mathrm{equation}\:\mathrm{or} \\ $$$$\mathrm{Heat}\:\mathrm{Eqaution} \\ $$$$\mathrm{for}\:\mathrm{example}.....\: \\ $$$$\oint_{\:{A}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{D}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{A}}}={Q}_{\mathrm{0}} \:\left(\mathrm{Gauss}\:\mathrm{law}\right)\:\overset{\rightarrow} {\boldsymbol{\mathrm{D}}}\:\mathrm{is}\:\mathrm{displayment}\:\mathrm{field} \\ $$$$\oint_{\:{S}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{B}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{A}}}=\mathrm{0}\:\left(\mathrm{Gauss}\:\mathrm{law}\:\mathrm{for}\:\mathrm{magnetic}\right)\:\overset{\rightarrow} {\boldsymbol{\mathrm{B}}}\:\mathrm{is}\:\mathrm{Magnetic}\:\mathrm{field} \\ $$$$\mathrm{and}\:\mathrm{in}\:\mathrm{Heat}\:\mathrm{Flux} \\ $$$$\frac{\partial\mathrm{E}_{\mathrm{in}} }{\partial{t}}−\frac{\partial\mathrm{E}_{\mathrm{out}} }{\partial{t}}=\oint_{\:{S}} \:\overset{\rightarrow} {\boldsymbol{\phi}}_{\mathrm{q}} \centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{S}}}\:\: \\ $$$$\mathrm{But}\:\mathrm{in}\:\mathrm{mathematic}\:\mathrm{it}\:\mathrm{seems}\:\mathrm{that}\:\mathrm{Surface}\:\mathrm{integral} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{vector}\:\mathrm{field}\:\mathrm{is}\:\mathrm{only}\:\mathrm{extended}\:\mathrm{version}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{integral},\mathrm{why}\:\mathrm{mathematic}\:\mathrm{don}'\mathrm{t}\:\mathrm{use}\:\mathrm{surface}\:\mathrm{integral} \\ $$$$\mathrm{like}\:\mathrm{physics}...???\:\mathrm{i}\:\mathrm{really}\:\mathrm{curious}\: \\ $$

Question Number 218820    Answers: 1   Comments: 0

Question Number 218813    Answers: 3   Comments: 0

Question Number 218812    Answers: 5   Comments: 0

Question Number 218799    Answers: 0   Comments: 1

For those who are interested in cryptography. The below text has been encrypted using Vigenere cipher, such that numbers, punctuation marks and the letter E^(..) have remained the same. A keyword of length 9 has been used, which starts with the letter K. Decrypt the text.

$$\mathrm{For}\:\mathrm{those}\:\mathrm{who}\:\mathrm{are}\:\mathrm{interested}\:\mathrm{in}\:\mathrm{cryptography}. \\ $$$$\mathrm{The}\:\mathrm{below}\:\mathrm{text}\:\mathrm{has}\:\mathrm{been}\:\mathrm{encrypted}\:\mathrm{using} \\ $$$$\mathrm{Vigenere}\:\mathrm{cipher},\:\mathrm{such}\:\mathrm{that}\:\mathrm{numbers},\:\mathrm{punctuation} \\ $$$$\mathrm{marks}\:\mathrm{and}\:\mathrm{the}\:\mathrm{letter}\:\overset{..} {\mathrm{E}}\:\mathrm{have}\:\mathrm{remained}\:\mathrm{the}\:\mathrm{same}. \\ $$$$\mathrm{A}\:\mathrm{keyword}\:\mathrm{of}\:\mathrm{length}\:\mathrm{9}\:\mathrm{has}\:\mathrm{been}\:\mathrm{used},\:\mathrm{which} \\ $$$$\mathrm{starts}\:\mathrm{with}\:\mathrm{the}\:\mathrm{letter}\:\mathrm{K}.\:\mathrm{Decrypt}\:\mathrm{the}\:\mathrm{text}. \\ $$

Question Number 218997    Answers: 1   Comments: 0

Question Number 218792    Answers: 0   Comments: 0

Question Number 218785    Answers: 0   Comments: 0

Question Number 218781    Answers: 1   Comments: 0

prove: ∫_0 ^(π/4) arccos ((√2)/( (√(3−tan^2 x)))) dx=(π^2 /(24))

$$\mathrm{prove}: \\ $$$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\mathrm{arccos}\:\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{3}−\mathrm{tan}^{\mathrm{2}} \:{x}}}\:{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{24}} \\ $$

Question Number 218780    Answers: 2   Comments: 1

Question Number 218779    Answers: 3   Comments: 0

Question Number 218778    Answers: 4   Comments: 0

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