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Question Number 151954 Answers: 1 Comments: 0

nice...calculus 𝛗 := ∫_0 ^( (π/2)) x^( 3) . cot (x )dx =(a/(16)) a :=? m.n...

$$ \\ $$$$\:\:\:\:{nice}...{calculus} \\ $$$$\: \\ $$$$\:\:\:\:\:\boldsymbol{\phi}\::=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {x}^{\:\mathrm{3}} .\:{cot}\:\left({x}\:\right){dx}\:=\frac{{a}}{\mathrm{16}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}\::=? \\ $$$${m}.{n}... \\ $$

Question Number 151951 Answers: 4 Comments: 1

nice ... mathematics S:= Σ_(n=1) ^∞ (( ζ (2n ))/(n . 16^( n) )) = ? ......■

$$ \\ $$$$\:\:\:\:\:{nice}\:...\:{mathematics} \\ $$$$\:\:\:\:\:\:\mathrm{S}:=\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\:\left(\mathrm{2}{n}\:\right)}{{n}\:.\:\mathrm{16}^{\:{n}} }\:=\:?\:......\blacksquare \\ $$$$ \\ $$

Question Number 151948 Answers: 0 Comments: 0

Question Number 151943 Answers: 1 Comments: 1

Prove arctan1+arctan2+arctan3=π

$$\mathrm{Prove}\:\mathrm{arctan1}+\mathrm{arctan2}+\mathrm{arctan3}=\pi \\ $$

Question Number 151942 Answers: 0 Comments: 0

If x , y > 1 : Min ( (( x^( 4) )/((y −1 )^( 2) )) + (( y^( 4) )/(( x − 1 )^( 2) )) ) = ? ......■ ? m.n...

$$ \\ $$$$\:\:\:\mathrm{If}\:\:{x}\:,\:{y}\:>\:\mathrm{1}\:\:\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\:\left(\:\frac{\:{x}^{\:\mathrm{4}} }{\left({y}\:−\mathrm{1}\:\right)^{\:\mathrm{2}} }\:+\:\frac{\:{y}^{\:\mathrm{4}} }{\left(\:{x}\:−\:\mathrm{1}\:\right)^{\:\mathrm{2}} }\:\right)\:=\:?\:......\blacksquare\:\:?\:\: \\ $$$$\:\:\:\:{m}.{n}... \\ $$$$ \\ $$

Question Number 151941 Answers: 1 Comments: 0

Find solution set of equation 6cos x−8sin x=5(√3) 0°≤x≤360°

$$\mathrm{Find}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\:\mathrm{6cos}\:\mathrm{x}−\mathrm{8sin}\:\mathrm{x}=\mathrm{5}\sqrt{\mathrm{3}} \\ $$$$\:\mathrm{0}°\leqslant\mathrm{x}\leqslant\mathrm{360}° \\ $$

Question Number 151940 Answers: 1 Comments: 0

Question Number 151934 Answers: 1 Comments: 0

Question Number 151922 Answers: 0 Comments: 0

((cos ((2π)/9)))^(1/3) +((cos ((4π)/9)))^(1/3) −((cos (π/9)))^(1/3) =?

$$\:\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\:+\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}}−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\pi}{\mathrm{9}}}\:=? \\ $$$$ \\ $$

Question Number 151921 Answers: 0 Comments: 0

Question Number 152980 Answers: 2 Comments: 10

Question Number 151911 Answers: 0 Comments: 10

Determine the digit a and prime numbers x;y;z such that x<y, z<1000 and x + y^(2a) = z

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{digit}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\mathrm{prime} \\ $$$$\mathrm{numbers}\:\boldsymbol{\mathrm{x}};\boldsymbol{\mathrm{y}};\boldsymbol{\mathrm{z}}\:\mathrm{such}\:\mathrm{that}\:\boldsymbol{\mathrm{x}}<\boldsymbol{\mathrm{y}},\:\boldsymbol{\mathrm{z}}<\mathrm{1000} \\ $$$$\mathrm{and}\:\:\mathrm{x}\:+\:\mathrm{y}^{\mathrm{2}\boldsymbol{\mathrm{a}}} \:=\:\mathrm{z} \\ $$

Question Number 151907 Answers: 1 Comments: 2

If the area of a convex quadrilateral is 2k^2 and the sum of its diagonals is 4k^2 , then show that this quadrilateral is an orthodiagonal one.

$$\mathrm{If}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral} \\ $$$$\mathrm{is}\:\mathrm{2}\boldsymbol{\mathrm{k}}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its}\:\mathrm{diagonals} \\ $$$$\mathrm{is}\:\mathrm{4}\boldsymbol{\mathrm{k}}^{\mathrm{2}} ,\:\mathrm{then}\:\mathrm{show}\:\mathrm{that}\:\mathrm{this}\:\mathrm{quadrilateral} \\ $$$$\mathrm{is}\:\mathrm{an}\:\mathrm{orthodiagonal}\:\mathrm{one}. \\ $$

Question Number 151905 Answers: 1 Comments: 0

Question Number 151899 Answers: 1 Comments: 0

Question Number 151897 Answers: 1 Comments: 0

Question Number 151895 Answers: 0 Comments: 0

Question Number 151894 Answers: 1 Comments: 1

∫_0 ^a x (√((a^2 −x^2 )/(a^2 +x^2 )))

$$\int_{\mathrm{0}} ^{\mathrm{a}} \:\:\:\mathrm{x}\:\sqrt{\frac{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} }} \\ $$

Question Number 151893 Answers: 1 Comments: 0

∫x(x^3 +a^3 )dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\int\mathrm{x}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{a}^{\mathrm{3}} \right)\mathrm{dx} \\ $$

Question Number 151890 Answers: 1 Comments: 0

Question Number 151889 Answers: 1 Comments: 0

Compare: (((2020!)^3 ))^(1/(2020)) and 505∙2021^2

$$\mathrm{Compare}: \\ $$$$\sqrt[{\mathrm{2020}}]{\left(\mathrm{2020}!\right)^{\mathrm{3}} }\:\:\:\mathrm{and}\:\:\:\mathrm{505}\centerdot\mathrm{2021}^{\mathrm{2}} \\ $$

Question Number 151884 Answers: 2 Comments: 0

f(x)=(x-1)(x-2)...(x-2021) f^′ (2021) = ?

$$\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{x}-\mathrm{1}\right)\left(\mathrm{x}-\mathrm{2}\right)...\left(\mathrm{x}-\mathrm{2021}\right) \\ $$$$\mathrm{f}\:^{'} \left(\mathrm{2021}\right)\:=\:? \\ $$

Question Number 151876 Answers: 1 Comments: 0

Question Number 151874 Answers: 0 Comments: 0

Question Number 151863 Answers: 2 Comments: 0

lim_(x−0) ((1−Π_(k=1) ^n cos(kx))/x^2 )=????

$$\: \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{x}}−\mathrm{0}} {\boldsymbol{{m}}}\frac{\mathrm{1}−\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\prod}}\boldsymbol{{cos}}\left(\boldsymbol{{kx}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} }=???? \\ $$$$ \\ $$

Question Number 151851 Answers: 1 Comments: 0

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