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Question Number 222365 Answers: 1 Comments: 0

Prove ∮_( ∂S) E^→ ∙dS^→ =(ρ_(enc) /𝛜_0 ) E^→ =(r^→ /r^3 )

$$\mathrm{Prove} \\ $$$$\oint_{\:\partial\mathcal{S}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{E}}}\centerdot\mathrm{d}\overset{\rightarrow} {\mathcal{S}}=\frac{\rho_{\mathrm{enc}} }{\boldsymbol{\varepsilon}_{\mathrm{0}} } \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{E}}}=\frac{\overset{\rightarrow} {\boldsymbol{\mathrm{r}}}}{\boldsymbol{\mathrm{r}}^{\mathrm{3}} }\: \\ $$

Question Number 222359 Answers: 0 Comments: 1

(1) [ax^3 +bx^2 +cx+d]_x ′ (2) [x(x−a)^2 ]_x ′ (3) [(x^2 −x)(x^2 −4)]_x ′ (4) [(x+2)(x−5)(x−1)]_x ′

$$\left(\mathrm{1}\right)\:\left[{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}\right]_{{x}} ' \\ $$$$\left(\mathrm{2}\right)\:\left[{x}\left({x}−{a}\right)^{\mathrm{2}} \right]_{{x}} ' \\ $$$$\left(\mathrm{3}\right)\:\left[\left({x}^{\mathrm{2}} −{x}\right)\left({x}^{\mathrm{2}} −\mathrm{4}\right)\right]_{{x}} ' \\ $$$$\left(\mathrm{4}\right)\:\left[\left({x}+\mathrm{2}\right)\left({x}−\mathrm{5}\right)\left({x}−\mathrm{1}\right)\right]_{{x}} ' \\ $$

Question Number 211345 Answers: 0 Comments: 1

Evaluer: (R/(r1+r2))

$$\mathrm{E}\boldsymbol{\mathrm{valuer}}:\:\:\frac{\boldsymbol{\mathrm{R}}}{\boldsymbol{\mathrm{r}}\mathrm{1}+\boldsymbol{\mathrm{r}}\mathrm{2}} \\ $$

Question Number 211344 Answers: 1 Comments: 0

find ∫(dx/(sin^3 (x) cos^5 (x))) .dx

$$\:\:\:{find}\:\int\frac{\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{3}} \left(\boldsymbol{{x}}\right)\:\boldsymbol{{cos}}^{\mathrm{5}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\: \\ $$

Question Number 211340 Answers: 2 Comments: 1

Question Number 211331 Answers: 2 Comments: 0

x=(((√6)+2+(√3)+(√2))/( (√6)+(√3)−2−(√2))) y=(((√6)−(√3)−2+(√2))/( (√6)−(√3)+2−(√2))) x^5 −y^5 =?

$$\:\:\:\:\:\mathrm{x}=\frac{\sqrt{\mathrm{6}}+\mathrm{2}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{6}}+\sqrt{\mathrm{3}}−\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\:\mathrm{y}=\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}−\mathrm{2}+\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}+\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\mathrm{x}^{\mathrm{5}} −\mathrm{y}^{\mathrm{5}} \:=?\: \\ $$

Question Number 211330 Answers: 1 Comments: 0

Question Number 211323 Answers: 2 Comments: 1

Question Number 211321 Answers: 1 Comments: 0

sec θ + tan θ =p (p>1) then ((cosec θ+1)/(cosec θ−1)) =?

$$\:\:\: \mathrm{sec}\:\theta\:+\:\mathrm{tan}\:\theta\:=\mathrm{p}\:\left(\mathrm{p}>\mathrm{1}\right) \\ $$$$\:\:\mathrm{then}\:\frac{\mathrm{cosec}\:\theta+\mathrm{1}}{\mathrm{cosec}\:\theta−\mathrm{1}}\:=? \\ $$

Question Number 211311 Answers: 1 Comments: 0

Dterminer le nombre total des nombres de (3 chiffres)qui sont impair( et) divisibles par 9 compris entre 100 et 500.? formule si c est possible?

Question Number 211310 Answers: 1 Comments: 0

Find: LCD(2^(100) − 1 ; 2^(120) − 1) = ?

$$\mathrm{Find}: \\ $$$$\mathrm{LCD}\left(\mathrm{2}^{\mathrm{100}} \:−\:\mathrm{1}\:\:;\:\:\mathrm{2}^{\mathrm{120}} \:−\:\mathrm{1}\right)\:=\:? \\ $$

Question Number 211315 Answers: 0 Comments: 0

does anyone know if charpit′s method for solving PDE can be used to solve second order pde? Also is it possible to reduce second order PDE to first order?

$$\mathrm{does}\:\mathrm{anyone}\:\mathrm{know}\:\mathrm{if}\:\mathrm{charpit}'\mathrm{s}\:\mathrm{method}\:\mathrm{for}\:\mathrm{solving}\: \\ $$$$\mathrm{PDE}\:\mathrm{can}\:\mathrm{be}\:\mathrm{used}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{second}\:\mathrm{order}\:\mathrm{pde}? \\ $$$$\mathrm{Also}\:\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{reduce}\:\mathrm{second}\:\mathrm{order}\:\mathrm{PDE}\:\mathrm{to}\:\mathrm{first}\:\mathrm{order}? \\ $$

Question Number 211370 Answers: 1 Comments: 0

F(0)=0 F(1)=1 F(n+1)=F(n)+F(n−1) prove: (1/(89))=Σ_(i=1) ^(+∞) 10^(−i) F(i−1)

$${F}\left(\mathrm{0}\right)=\mathrm{0}\:\:\:\:\:\:\:{F}\left(\mathrm{1}\right)=\mathrm{1}\:\:\:\:{F}\left({n}+\mathrm{1}\right)={F}\left({n}\right)+{F}\left({n}−\mathrm{1}\right) \\ $$$${prove}: \\ $$$$\frac{\mathrm{1}}{\mathrm{89}}=\underset{{i}=\mathrm{1}} {\overset{+\infty} {\sum}}\mathrm{10}^{−{i}} {F}\left({i}−\mathrm{1}\right) \\ $$

Question Number 211368 Answers: 1 Comments: 0

soit le systeme d equatiins x+y+z =7 x^2 +y^2 +z^2 =9 xyz =5 (1/x)+(1/y)+(1/z)?

Question Number 211367 Answers: 2 Comments: 1

solve for R^+ x^2 +y^2 −kxy=c^2 y^2 +z^2 −kyz=a^2 z^2 +x^2 −kzx=b^2 (k is constant)

$${solve}\:{for}\:{R}^{+} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{kxy}={c}^{\mathrm{2}} \\ $$$${y}^{\mathrm{2}} +{z}^{\mathrm{2}} −{kyz}={a}^{\mathrm{2}} \\ $$$${z}^{\mathrm{2}} +{x}^{\mathrm{2}} −{kzx}={b}^{\mathrm{2}} \\ $$$$\left({k}\:{is}\:{constant}\right) \\ $$

Question Number 211295 Answers: 2 Comments: 0

lim_(x→0) ((x−sin (sin (sin (....(sin x)))))_(n times) )/x^3 )

$$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left.\mathrm{x}−\underset{\mathrm{n}\:\mathrm{times}} {\underbrace{\mathrm{sin}\:\left(\mathrm{sin}\:\left(\mathrm{sin}\:\left(....\left(\mathrm{sin}\:\mathrm{x}\right)\right)\right)\right)\right)}}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 211294 Answers: 1 Comments: 3

Question Number 211276 Answers: 2 Comments: 0

Prove , in AB^Δ C : ((cosA)/(sin^2 A)) + ((cosB)/(sin^2 B)) +((cosC)/(sin^2 C)) ≥ (r/R) r : incircle radius R: circumcircle radius

$$ \\ $$$$\:\:{Prove}\:,\:{in}\:{A}\overset{\Delta} {{B}C}\:\::\: \\ $$$$ \\ $$$$\:\:\:\:\:\frac{{cosA}}{{sin}^{\mathrm{2}} {A}}\:+\:\frac{{cosB}}{{sin}^{\mathrm{2}} {B}}\:\:+\frac{{cosC}}{{sin}^{\mathrm{2}} {C}}\:\geqslant\:\frac{{r}}{{R}} \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:{r}\::\:{incircle}\:\:{radius} \\ $$$$\:\:\:\:\:{R}:\:{circumcircle}\:\:{radius} \\ $$$$ \\ $$

Question Number 211279 Answers: 1 Comments: 1

Question Number 211265 Answers: 0 Comments: 0

Question Number 211262 Answers: 1 Comments: 0

Question Number 211258 Answers: 1 Comments: 0

Question Number 211255 Answers: 1 Comments: 3

(√(a+(√(b−x))+(√(b−(√(a+x))))))=2x solve for x.

$$\sqrt{{a}+\sqrt{{b}−{x}}+\sqrt{{b}−\sqrt{{a}+{x}}}}=\mathrm{2}{x} \\ $$$${solve}\:{for}\:{x}.\:\:\:\: \\ $$

Question Number 211252 Answers: 1 Comments: 0

Question Number 211251 Answers: 0 Comments: 2

Question Number 211250 Answers: 1 Comments: 0

Find the number of 4 digit numbers so that when decomposed into prime factors, have the sum of prime factors equal to the sum of the exponents?

$${Find}\:{the}\:{number}\:{of}\:\mathrm{4}\:{digit}\:{numbers} \\ $$$$\:{so}\:{that}\:{when}\:{decomposed}\:{into}\:{prime} \\ $$$$\:{factors},\:{have}\:{the}\:{sum}\:{of}\:{prime}\:{factors} \\ $$$$\:{equal}\:{to}\:{the}\:{sum}\:{of}\:{the}\:{exponents}? \\ $$

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