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AllQuestion and Answers: Page 635

Question Number 155182 Answers: 0 Comments: 0

Question Number 155180 Answers: 0 Comments: 0

Question Number 155174 Answers: 2 Comments: 0

Find n if: 133^5 +110^5 +84^5 +27^5 =n^5

$${Find}\:{n}\:{if}: \\ $$$$\mathrm{133}^{\mathrm{5}} +\mathrm{110}^{\mathrm{5}} +\mathrm{84}^{\mathrm{5}} +\mathrm{27}^{\mathrm{5}} ={n}^{\mathrm{5}} \\ $$

Question Number 155165 Answers: 1 Comments: 0

Question Number 155164 Answers: 1 Comments: 0

solve.. ⌊ (( x)/(2+ (√x))) ⌋ = 3 ( x∈ Z )

$$\:\:\:{solve}.. \\ $$$$\:\:\:\:\:\:\:\:\:\lfloor\:\frac{\:{x}}{\mathrm{2}+\:\sqrt{{x}}}\:\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\left(\:{x}\in\:\mathbb{Z}\:\right) \\ $$$$ \\ $$

Question Number 155161 Answers: 0 Comments: 0

Question Number 155159 Answers: 0 Comments: 0

∫_0 ^1 ((ln^n (x)Li_(n+1) (−x))/(1+x^2 ))dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{ln}}^{\boldsymbol{{n}}} \left({x}\right)\boldsymbol{{Li}}_{\boldsymbol{{n}}+\mathrm{1}} \left(−{x}\right)}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=? \\ $$

Question Number 155154 Answers: 1 Comments: 0

let n∈N^+ solve for real numbers: x^(3n) - y^(2n) = y^(3n) - x^(2n) = 4

$$\mathrm{let}\:\:\mathrm{n}\in\mathbb{N}^{+} \:\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{y}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{y}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{4} \\ $$

Question Number 155146 Answers: 1 Comments: 0

L=∫_0 ^1 ∫_0 ^1 ∫_0 ^1 ({(x/y)}{(y/z)}{(z/x)})^n dxdydz=?

$$\mathscr{L}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \left(\left\{\frac{{x}}{{y}}\right\}\left\{\frac{{y}}{{z}}\right\}\left\{\frac{{z}}{{x}}\right\}\right)^{{n}} {dxdydz}=? \\ $$

Question Number 155144 Answers: 0 Comments: 3

how many integer solutions are there : ⌊ (1/(2+(√x)))⌋ = 3 ■

$$ \\ $$$$\:\:{how}\:{many}\:{integer}\:{solutions}\: \\ $$$$\:\:\:\:{are}\:{there}\:: \\ $$$$\:\:\:\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}+\sqrt{{x}}}\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\:\blacksquare \\ $$$$ \\ $$

Question Number 155264 Answers: 1 Comments: 0

en utilisant l′integrale de cauchy schwarz l′integrale ∫_o ^1 ((f(x))/(x+1))dx est majoree par?

$${en}\:{utilisant}\:{l}'{integrale}\:{de}\:{cauchy}\:{schwarz} \\ $$$${l}'{integrale}\:\int_{{o}} ^{\mathrm{1}} \frac{{f}\left({x}\right)}{{x}+\mathrm{1}}{dx}\:\:\:\:{est}\:{majoree}\:{par}? \\ $$$$ \\ $$

Question Number 155140 Answers: 0 Comments: 0

Question Number 155136 Answers: 0 Comments: 0

prove that ((log^2 (2))/2)Σ_(n=1) ^∞ ((𝛟(n))/((n+1)^2 2^n ))+log(2)Σ_(n=1) ^∞ ((𝛟(n))/((n+1)^3 2^n ))+Σ_(n=1) ^∞ ((𝛟(n))/((n+1)^4 2^n ))= =((23)/8)𝛇(6)−2𝛇^2 (3)−(1/(18))log^6 (2) m.A

$$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\frac{\boldsymbol{\mathrm{log}}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}}\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left(\boldsymbol{{n}}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{2}} \mathrm{2}^{\boldsymbol{{n}}} }+\boldsymbol{\mathrm{log}}\left(\mathrm{2}\right)\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left({n}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{3}} \mathrm{2}^{\boldsymbol{{n}}} }+\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left({n}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{4}} \mathrm{2}^{\boldsymbol{{n}}} }= \\ $$$$=\frac{\mathrm{23}}{\mathrm{8}}\boldsymbol{\zeta}\left(\mathrm{6}\right)−\mathrm{2}\boldsymbol{\zeta}^{\mathrm{2}} \left(\mathrm{3}\right)−\frac{\mathrm{1}}{\mathrm{18}}\boldsymbol{\mathrm{log}}^{\mathrm{6}} \left(\mathrm{2}\right) \\ $$$$\boldsymbol{{m}}.\boldsymbol{{A}} \\ $$

Question Number 155135 Answers: 0 Comments: 0

∫_0 ^1 ∫_0 ^1 (((log((1/x))−log((1/y)))/(log(log((1/x)))−log(log((1/y))))))^2 dxdy=?

Question Number 155134 Answers: 1 Comments: 0

∫_0 ^(π/2) sin^(2n) (x)dx=?

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{sin}}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \left({x}\right){dx}=? \\ $$

Question Number 155133 Answers: 2 Comments: 0

Σ_(n=0) ^∞ (((−1)^n )/((2n+1)^3 ))=?

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} }=? \\ $$

Question Number 155132 Answers: 0 Comments: 0

Question Number 155130 Answers: 1 Comments: 0

Question Number 155126 Answers: 0 Comments: 0

∫_0 ^( ∞) e^(− β (2x+b)^(1/a) ) dx

$$\int_{\mathrm{0}} ^{\:\infty} \:{e}^{−\:\beta\:\left(\mathrm{2}{x}+{b}\right)^{\frac{\mathrm{1}}{\boldsymbol{{a}}}} } \:{dx} \\ $$

Question Number 155122 Answers: 0 Comments: 2

Question Number 155120 Answers: 1 Comments: 0

lim_( x →0) ((1/x^( 2) ) − cot^( 2) (x))=?

$$ \\ $$$$\:\:\:{lim}_{\:{x}\:\rightarrow\mathrm{0}} \left(\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }\:−\:{cot}^{\:\mathrm{2}} \left({x}\right)\right)=? \\ $$$$ \\ $$

Question Number 155153 Answers: 1 Comments: 0

Solve the equation in R (√(2(x^2 - x + 1))) = 1 + (√x) - x

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{in}\:\mathbb{R} \\ $$$$\sqrt{\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:+\:\mathrm{1}\right)}\:=\:\mathrm{1}\:+\:\sqrt{\mathrm{x}}\:-\:\mathrm{x} \\ $$

Question Number 155109 Answers: 1 Comments: 0

how many terms contain “ ab^2 c^3 ” in (a+2b+3c+4d^2 +5e^3 )^(10) ?

$$\mathrm{how}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{contain}\:``\:\mathrm{ab}^{\mathrm{2}} \mathrm{c}^{\mathrm{3}} \:''\:\mathrm{in}\:\left(\mathrm{a}+\mathrm{2b}+\mathrm{3c}+\mathrm{4d}^{\mathrm{2}} +\mathrm{5e}^{\mathrm{3}} \right)^{\mathrm{10}} \:? \\ $$

Question Number 155106 Answers: 1 Comments: 3

Solve for real numbers: { (((√(x+y)) - (√(x-y)) + (√(x^2 -y^2 )) = 5)),((2x + 3(√(x^2 -y^2 )) = 19)) :}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}+\mathrm{y}}\:-\:\sqrt{\mathrm{x}-\mathrm{y}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{5}}\\{\mathrm{2x}\:+\:\mathrm{3}\sqrt{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{19}}\end{cases} \\ $$

Question Number 155101 Answers: 1 Comments: 3

soit: y y′+xy^2 +x=0 ,avec f(0)=1 f′′(0)=?

$${soit}:\:{y}\:{y}'+{xy}^{\mathrm{2}} +{x}=\mathrm{0}\:,{avec}\:{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${f}''\left(\mathrm{0}\right)=? \\ $$

Question Number 155100 Answers: 1 Comments: 2

Determine all triangle with: 1.The lengths of sides positive integers and at least one is prime number. 2.The semiperimetr is positive integer and area is equal with perimetr.

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{triangle}\:\mathrm{with}: \\ $$$$\mathrm{1}.\mathrm{The}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{is}\:\mathrm{prime}\:\mathrm{number}. \\ $$$$\mathrm{2}.\mathrm{The}\:\mathrm{semiperimetr}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{area}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{with}\:\mathrm{perimetr}. \\ $$

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