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Question Number 159327 Answers: 4 Comments: 0

Question Number 159325 Answers: 1 Comments: 1

# Trigonometry# solve ( Equation) sin((x/2) ) − 2sin ((x/3) )= 0

$$ \\ $$$$\:\:\:\:\:\:#\:\mathrm{T}{rigonometry}# \\ $$$$\:\:\:\:\:\:\:{solve}\:\left(\:\:\:\mathscr{E}{quation}\right) \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:{sin}\left(\frac{{x}}{\mathrm{2}}\:\right)\:−\:\mathrm{2}{sin}\:\left(\frac{{x}}{\mathrm{3}}\:\right)=\:\mathrm{0}\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$

Question Number 159322 Answers: 1 Comments: 0

P(z)=(1+i(√3))z^2 −(−4+4i)z+2icos((π/5))−2sin((π/5)) Let S denote the sum of roots of P(z) a) Express S in algebraic form then in exponential form. b. Deduce the exact values of cos(((5π)/(12))) and sin(((5π)/(12))).

$$\mathrm{P}\left(\mathrm{z}\right)=\left(\mathrm{1}+{i}\sqrt{\mathrm{3}}\right){z}^{\mathrm{2}} −\left(−\mathrm{4}+\mathrm{4}{i}\right){z}+\mathrm{2}{i}\mathrm{cos}\left(\frac{\pi}{\mathrm{5}}\right)−\mathrm{2sin}\left(\frac{\pi}{\mathrm{5}}\right) \\ $$$$\mathrm{Let}\:{S}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{P}\left({z}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Express}\:{S}\:\mathrm{in}\:\mathrm{algebraic}\:\mathrm{form}\:\mathrm{then}\:\mathrm{in}\:\mathrm{exponential}\:\mathrm{form}. \\ $$$$\mathrm{b}.\:\mathrm{Deduce}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{values}\:\mathrm{of}\:\mathrm{cos}\left(\frac{\mathrm{5}\pi}{\mathrm{12}}\right)\:\mathrm{and}\:\mathrm{sin}\left(\frac{\mathrm{5}\pi}{\mathrm{12}}\right). \\ $$

Question Number 159319 Answers: 1 Comments: 0

(dy/dx)+((x−y−2)/(x−2y−3))=0 Pls... solve the differential equation.

$$\:\:\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}+\frac{\mathrm{x}−\mathrm{y}−\mathrm{2}}{\mathrm{x}−\mathrm{2y}−\mathrm{3}}=\mathrm{0} \\ $$$$\mathrm{Pls}...\:\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}. \\ $$

Question Number 159318 Answers: 1 Comments: 1

lim_(x→1) (((√(x+1))+(√(x^2 −1))−(√(x^3 +1)))/( (√(x−1))+(√(x^2 +1)) −(√(x^4 +1)))) =?

$$\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}−\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:−\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}\:=? \\ $$

Question Number 159315 Answers: 0 Comments: 1

∫ (dx/( (((x−1)^3 (x+2)^5 ))^(1/4) )) ?

$$\:\int\:\frac{{dx}}{\:\sqrt[{\mathrm{4}}]{\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}+\mathrm{2}\right)^{\mathrm{5}} }\:}\:? \\ $$

Question Number 159309 Answers: 1 Comments: 0

Resolve I_n =∫_(−1) ^1 (1−x^2 )^n dx

$${Resolve}\:{I}_{{n}} =\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{{n}} {dx} \\ $$

Question Number 159297 Answers: 1 Comments: 1

Question Number 159293 Answers: 1 Comments: 1

Question Number 159345 Answers: 2 Comments: 0

Question Number 159436 Answers: 0 Comments: 1

Question Number 159435 Answers: 0 Comments: 0

Question Number 159434 Answers: 0 Comments: 0

Question Number 159433 Answers: 0 Comments: 2

((5x^2 −15x−11)/((x+1)(x−2)^2 )) fractio partil

$$\frac{\mathrm{5x}^{\mathrm{2}} −\mathrm{15x}−\mathrm{11}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} }\:\mathrm{fractio}\:\mathrm{partil} \\ $$$$ \\ $$

Question Number 159431 Answers: 1 Comments: 0

Question Number 159268 Answers: 1 Comments: 0

Find: Ω =∫_( 0) ^( 1) ∫_( 0) ^( 1) Li_3 (1 - xy)dxdy

$$\mathrm{Find}: \\ $$$$\Omega\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{Li}_{\mathrm{3}} \left(\mathrm{1}\:-\:{xy}\right){dxdy} \\ $$$$ \\ $$

Question Number 159278 Answers: 1 Comments: 1

Question Number 159281 Answers: 0 Comments: 2

Question Number 159280 Answers: 1 Comments: 0

Solve in R : (√x) = ((x^2 - 244x + 736)/(1008))

$$\boldsymbol{\mathrm{S}}\mathrm{olve}\:\mathrm{in}\:\mathbb{R}\::\:\:\sqrt{\mathrm{x}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{244x}\:+\:\mathrm{736}}{\mathrm{1008}} \\ $$$$ \\ $$

Question Number 159276 Answers: 1 Comments: 0

lim_(x→∞) ((1/(x^2 +1))+(1/(x^2 +4))+(1/(x^2 +9))+…)=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{4}}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{9}}+\ldots\right)=? \\ $$

Question Number 159259 Answers: 1 Comments: 0

montre que Σ_(k=0) ^n C_(2n) ^(2k) =2^(2n−1)

$$\boldsymbol{{montre}}\:\boldsymbol{{que}}\: \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{C}}_{\mathrm{2}\boldsymbol{{n}}} ^{\mathrm{2}\boldsymbol{{k}}} =\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} \\ $$

Question Number 159249 Answers: 1 Comments: 0

hi ! solve in IN×IN this one : (x+1)(y+2)=2xy. thanks.

$$\boldsymbol{\mathrm{hi}}\:! \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{IN}}×\boldsymbol{\mathrm{IN}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{one}}\::\:\left(\boldsymbol{{x}}+\mathrm{1}\right)\left(\boldsymbol{{y}}+\mathrm{2}\right)=\mathrm{2}\boldsymbol{{xy}}. \\ $$$$\boldsymbol{\mathrm{thanks}}. \\ $$

Question Number 159248 Answers: 0 Comments: 0

find the angle of intersection between the followng curves: y^2 = ax, x^3 +y^3 = 3axy

$${find}\:{the}\:{angle}\:{of}\:{intersection}\:{between} \\ $$$${the}\:{followng}\:{curves}: \\ $$$${y}^{\mathrm{2}} \:=\:{ax},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} \:=\:\mathrm{3}{axy} \\ $$

Question Number 159240 Answers: 0 Comments: 2

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Question Number 159233 Answers: 1 Comments: 0

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