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Question Number 76075    Answers: 1   Comments: 0

how i evaluate sin(π/7)×sin(2π/7)×sin(3π/7) please help me

$$\mathrm{how}\:\mathrm{i}\:\mathrm{evaluate}\:\mathrm{sin}\left(\pi/\mathrm{7}\right)×\mathrm{sin}\left(\mathrm{2}\pi/\mathrm{7}\right)×\mathrm{sin}\left(\mathrm{3}\pi/\mathrm{7}\right)\: \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 76061    Answers: 1   Comments: 0

What′s the minimum value of ((13a+13b+2c)/(2a+2b))+((24a−b+13c)/(2b+2c))+((−a+24b+13c)/(2a+2c))? (a,b,c are positive numbers.) I think nobody can solve this.

$$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{13}{a}+\mathrm{13}{b}+\mathrm{2}{c}}{\mathrm{2}{a}+\mathrm{2}{b}}+\frac{\mathrm{24}{a}−{b}+\mathrm{13}{c}}{\mathrm{2}{b}+\mathrm{2}{c}}+\frac{−{a}+\mathrm{24}{b}+\mathrm{13}{c}}{\mathrm{2}{a}+\mathrm{2}{c}}? \\ $$$$\left({a},{b},{c}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers}.\right) \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{nobody}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}. \\ $$

Question Number 76053    Answers: 1   Comments: 2

how I calculate ∫(1/(x^8 +x^2 ))dx ?

$${how}\:{I}\:{calculate}\:\int\frac{\mathrm{1}}{{x}^{\mathrm{8}} +{x}^{\mathrm{2}} }{dx}\:? \\ $$

Question Number 76052    Answers: 0   Comments: 1

Question Number 76048    Answers: 2   Comments: 0

∫e^x^2 dx

$$\int{e}^{{x}^{\mathrm{2}} } {dx} \\ $$

Question Number 76038    Answers: 1   Comments: 0

Question Number 76037    Answers: 1   Comments: 0

Prove That sin 3°sin 39°sin 75°=sin 9°sin 24°sin 30°

$${Prove}\:{That} \\ $$$$\mathrm{sin}\:\mathrm{3}°\mathrm{sin}\:\mathrm{39}°\mathrm{sin}\:\mathrm{75}°=\mathrm{sin}\:\mathrm{9}°\mathrm{sin}\:\mathrm{24}°\mathrm{sin}\:\mathrm{30}° \\ $$

Question Number 76034    Answers: 1   Comments: 0

53^(log_x (7)) = (√x) x = ?

$$\: \\ $$$$\:\mathrm{53}^{\boldsymbol{\mathrm{log}}_{\boldsymbol{\mathrm{x}}} \left(\mathrm{7}\right)} \:=\:\sqrt{\boldsymbol{\mathrm{x}}} \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\: \\ $$

Question Number 76032    Answers: 0   Comments: 0

Question Number 76015    Answers: 0   Comments: 0

Question Number 76014    Answers: 0   Comments: 0

Question Number 76013    Answers: 1   Comments: 0

Question Number 76012    Answers: 1   Comments: 0

show that 1−3sin^2 xcos^2 x=(5/8)+(3/8)cos4x

$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{1}−\mathrm{3sin}^{\mathrm{2}} {x}\mathrm{cos}^{\mathrm{2}} {x}=\frac{\mathrm{5}}{\mathrm{8}}+\frac{\mathrm{3}}{\mathrm{8}}\boldsymbol{\mathrm{cos}}\mathrm{4}\boldsymbol{{x}} \\ $$

Question Number 76009    Answers: 1   Comments: 0

hiw do i solve 2^x = 4x?

$${hiw}\:{do}\:{i}\:{solve} \\ $$$$\mathrm{2}^{{x}} \:=\:\mathrm{4}{x}? \\ $$

Question Number 76003    Answers: 1   Comments: 0

22+2

$$\mathrm{22}+\mathrm{2} \\ $$

Question Number 75991    Answers: 1   Comments: 1

Question Number 75990    Answers: 0   Comments: 0

Question Number 75989    Answers: 0   Comments: 0

Question Number 75988    Answers: 0   Comments: 3

Question Number 75987    Answers: 1   Comments: 0

Question Number 75986    Answers: 1   Comments: 1

Question Number 75985    Answers: 1   Comments: 0

Question Number 75984    Answers: 1   Comments: 0

Question Number 75983    Answers: 0   Comments: 2

show that cos^6 x+sin^6 x=(1/8)(5+3cos4x)

$$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{cos}^{\mathrm{6}} \mathrm{x}+\mathrm{sin}^{\mathrm{6}} \mathrm{x}=\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{5}+\mathrm{3cos4x}\right) \\ $$

Question Number 75976    Answers: 0   Comments: 3

hello solve it in ]−π;π] and place solutions in trigonometric circle. cos^6 x+sin^6 x=(3/8)((√3)sin4x+(8/3)) please help me...

$$\left.\mathrm{h}\left.\mathrm{ello}\:\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\right]−\pi;\pi\right]\:\mathrm{and}\:\mathrm{place}\:\mathrm{solutions} \\ $$$$\mathrm{in}\:\mathrm{trigonometric}\:\mathrm{circle}. \\ $$$$\mathrm{cos}^{\mathrm{6}} \mathrm{x}+\mathrm{sin}^{\mathrm{6}} \mathrm{x}=\frac{\mathrm{3}}{\mathrm{8}}\left(\sqrt{\mathrm{3}}\mathrm{sin4x}+\frac{\mathrm{8}}{\mathrm{3}}\right) \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}... \\ $$

Question Number 76077    Answers: 2   Comments: 3

Find the maximum area of an isosceles triangle inscribed in an ellipse (x^2 /a^2 ) + (y^2 /b^2 ) = 1with its vetrex at one end of the major axis ? ?

$$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{isosceles}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{inscribed}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{ellipse}}\:\frac{\boldsymbol{{x}}^{\mathrm{2}} }{\boldsymbol{{a}}^{\mathrm{2}} }\:+\:\frac{\boldsymbol{{y}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} }\:=\:\mathrm{1}\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{vetrex}}\: \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{end}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axis}}\:?\:? \\ $$

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