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Question Number 211400    Answers: 3   Comments: 0

∫_0 ^1 ((x^3 −3x^2 +3x−1)/(x^4 +4x^3 +6x^2 +4x+1))dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{1}}{dx} \\ $$$$ \\ $$

Question Number 211399    Answers: 0   Comments: 1

∫(dx/((1+x^4 )(√(1+x^4 −x^2 ))))

$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{4}} −{x}^{\mathrm{2}} }} \\ $$$$ \\ $$

Question Number 211398    Answers: 1   Comments: 0

Question Number 211393    Answers: 3   Comments: 1

Question Number 211392    Answers: 1   Comments: 0

△ABC. cos C=((sin A + cos A)/2)=((sin B + cos B)/2). Find cos C.

$$\bigtriangleup{ABC}.\:\mathrm{cos}\:{C}=\frac{\mathrm{sin}\:{A}\:+\:\mathrm{cos}\:{A}}{\mathrm{2}}=\frac{\mathrm{sin}\:{B}\:+\:\mathrm{cos}\:{B}}{\mathrm{2}}. \\ $$$$\mathrm{Find}\:\mathrm{cos}\:{C}. \\ $$

Question Number 211383    Answers: 2   Comments: 1

Question Number 211381    Answers: 2   Comments: 1

Question Number 211377    Answers: 0   Comments: 0

The irrational number ^3 (√(^3 (√2)−1)) is written as^3 (√p) +^3 (√q) +^3 (√r) what is p, q, r ?

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{irrational}}\:\boldsymbol{\mathrm{number}}\: \\ $$$$\:^{\mathrm{3}} \sqrt{\:^{\mathrm{3}} \sqrt{\mathrm{2}}−\mathrm{1}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{written}}\:\boldsymbol{\mathrm{as}}\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{p}}}\:+\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{q}}}\:+\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{r}}}\: \\ $$$$\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{p}},\:\boldsymbol{\mathrm{q}},\:\boldsymbol{\mathrm{r}}\:? \\ $$

Question Number 211374    Answers: 0   Comments: 0

Evaluate: Σ_(k=1) ^n (((sin (2^(k+4) θ))/(sin (2^k θ)))).

$$\mathrm{Evaluate}:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{sin}\:\left(\mathrm{2}^{{k}+\mathrm{4}} \theta\right)}{\mathrm{sin}\:\left(\mathrm{2}^{\mathrm{k}} \theta\right)}\right). \\ $$

Question Number 211373    Answers: 3   Comments: 0

Question Number 211365    Answers: 2   Comments: 0

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

$$\:\:\:\:\underbrace{\:} \\ $$

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?

$$\boldsymbol{\mathrm{Dterminer}}\:\boldsymbol{\mathrm{le}}\:\boldsymbol{\mathrm{nombre}}\:\boldsymbol{\mathrm{total}}\:\:\boldsymbol{\mathrm{des}}\:\boldsymbol{\mathrm{nombres}}\: \\ $$$$\boldsymbol{\mathrm{de}}\:\left(\mathrm{3}\:\boldsymbol{\mathrm{chiffres}}\right)\boldsymbol{\mathrm{qui}}\:\boldsymbol{\mathrm{sont}}\:\boldsymbol{\mathrm{impair}}\left(\:\boldsymbol{\mathrm{et}}\right)\:\boldsymbol{\mathrm{divisibles}}\: \\ $$$$\boldsymbol{\mathrm{par}}\:\mathrm{9}\:\:\:\boldsymbol{\mathrm{compris}}\:\boldsymbol{\mathrm{entre}}\:\mathrm{100}\:\boldsymbol{\mathrm{et}}\:\mathrm{500}.? \\ $$$$\boldsymbol{\mathrm{formule}}\:\boldsymbol{\mathrm{si}}\:\boldsymbol{\mathrm{c}}\:\boldsymbol{\mathrm{est}}\:\boldsymbol{\mathrm{possible}}? \\ $$$$ \\ $$

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)?

$$\mathrm{soit}\:\mathrm{le}\:\mathrm{systeme}\:\mathrm{d}\:\mathrm{equatiins} \\ $$$$\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}\:\:\:\:=\mathrm{7} \\ $$$$\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\mathrm{9} \\ $$$$\:\:\boldsymbol{\mathrm{xyz}}\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{5} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{z}}}? \\ $$

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

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