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Question Number 151174    Answers: 2   Comments: 0

((a+(√(3∙((a+(√(3∙((a+(√(3∙...))))^(1/3) ))))^(1/3) ))))^(1/3) = 3 find a=?

$$\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot...}}}}}}\:\:=\:\mathrm{3}\: \\ $$$$\mathrm{find}\:\:{a}=? \\ $$

Question Number 151191    Answers: 0   Comments: 0

Question Number 151197    Answers: 1   Comments: 0

etude de la monotonie? svp u_n =Σ_(k=1) ^n (1/k)−ln(n)

$${etude}\:{de}\:{la}\:{monotonie}?\:{svp} \\ $$$${u}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}−{ln}\left({n}\right) \\ $$

Question Number 151196    Answers: 0   Comments: 0

Question Number 151164    Answers: 1   Comments: 1

Question Number 151162    Answers: 1   Comments: 2

Question Number 151157    Answers: 0   Comments: 0

x

$${x} \\ $$

Question Number 151142    Answers: 0   Comments: 0

if x;y;z∈R^+ and (1/x^2 ) + (1/y^2 ) + (1/z^2 ) = ((27)/4) prove that: ((x^3 + y^2 )/(x^2 + y^2 )) + ((y^3 + z^2 )/(y^2 + z^2 )) + ((z^3 + x^2 )/(z^2 + x^2 )) ≥ (5/2)

$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\in\mathbb{R}^{+} \:\:\mathrm{and}\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} }\:=\:\frac{\mathrm{27}}{\mathrm{4}} \\ $$$$\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} }\:+\:\frac{\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{2}} }{\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{2}} }\:\geqslant\:\frac{\mathrm{5}}{\mathrm{2}} \\ $$

Question Number 151132    Answers: 0   Comments: 1

Find the minimum value of x , if α<82^o .

$$ \\ $$$${Find}\:{the}\:{minimum}\:{value}\:{of}\:\:{x}\:,\:{if}\:\:\:\alpha<\mathrm{82}^{{o}} \:. \\ $$

Question Number 151118    Answers: 1   Comments: 0

∫_0 ^( ∞) (( arctan((x/2))+arctan(2x))/(x^( 2) +1))=^? (π^( 2) /4)

$$\:\: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{arctan}\left(\frac{{x}}{\mathrm{2}}\right)+{arctan}\left(\mathrm{2}{x}\right)}{{x}^{\:\mathrm{2}} +\mathrm{1}}\overset{?} {=}\frac{\pi^{\:\mathrm{2}} }{\mathrm{4}} \\ $$$$ \\ $$

Question Number 151117    Answers: 0   Comments: 0

Question Number 151115    Answers: 3   Comments: 0

Solve the system: { ((x^2 y^2 + xy^2 + x + y = 0)),((x^2 y + xy + 1 = 0)) :}

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} \:+\:\mathrm{xy}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{y}\:=\:\mathrm{0}}\\{\mathrm{x}^{\mathrm{2}} \mathrm{y}\:+\:\mathrm{xy}\:+\:\mathrm{1}\:=\:\mathrm{0}}\end{cases} \\ $$

Question Number 151114    Answers: 1   Comments: 0

solve.... Q := ∫_0 ^( 1) ln (x ). ln ( 2− x )dx =? ...........■ m.n.1970...

$$ \\ $$$$\:\:\:\:\:{solve}.... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Q}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\:\left({x}\:\right).\:{ln}\:\left(\:\mathrm{2}−\:{x}\:\right){dx}\:=?\:...........\blacksquare \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970}... \\ $$$$ \\ $$

Question Number 151111    Answers: 1   Comments: 0

Question Number 151104    Answers: 1   Comments: 1

Question Number 151101    Answers: 1   Comments: 0

Solve for real numbers the equation [(x/2)] + [((3x)/5)] = [(x/(10))] + x , where we denoting by [x] the great integer part of x.

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left[\frac{\mathrm{x}}{\mathrm{2}}\right]\:+\:\left[\frac{\mathrm{3x}}{\mathrm{5}}\right]\:=\:\left[\frac{\mathrm{x}}{\mathrm{10}}\right]\:+\:\mathrm{x}\:,\:\:\mathrm{where}\:\mathrm{we} \\ $$$$\mathrm{denoting}\:\mathrm{by}\:\left[\boldsymbol{\mathrm{x}}\right]\:\mathrm{the}\:\mathrm{great}\:\mathrm{integer}\:\mathrm{part} \\ $$$$\mathrm{of}\:\boldsymbol{\mathrm{x}}. \\ $$

Question Number 151100    Answers: 1   Comments: 0

if 0≤x;y;z≤k and k>0 then: y(x - z) - z(x - k) ≤ k^2

$$\mathrm{if}\:\:\mathrm{0}\leqslant\mathrm{x};\mathrm{y};\mathrm{z}\leqslant\mathrm{k}\:\:\mathrm{and}\:\:\mathrm{k}>\mathrm{0}\:\:\mathrm{then}: \\ $$$$\mathrm{y}\left(\mathrm{x}\:-\:\mathrm{z}\right)\:-\:\mathrm{z}\left(\mathrm{x}\:-\:\mathrm{k}\right)\:\leqslant\:\mathrm{k}^{\mathrm{2}} \\ $$

Question Number 151097    Answers: 2   Comments: 0

Find sum of this expression . ((n),(1) ) + 2 ((n),(2) ) + 3 ((n),(3) ) + 4 ((n),(4) ) + … + n ((n),(n) ) Please show your workings. Thank you .

$${Find}\:\:{sum}\:\:{of}\:\:{this}\:\:{expression}\:. \\ $$$$\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\:+\:\mathrm{2}\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\:+\:\mathrm{3}\begin{pmatrix}{{n}}\\{\mathrm{3}}\end{pmatrix}\:+\:\mathrm{4}\begin{pmatrix}{{n}}\\{\mathrm{4}}\end{pmatrix}\:+\:\ldots\:+\:{n}\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix} \\ $$$${Please}\:\:{show}\:\:{your}\:\:{workings}.\:{Thank}\:\:{you}\:. \\ $$

Question Number 151096    Answers: 0   Comments: 4

find the center of gravity with respect to point O

$$ \\ $$find the center of gravity with respect to point O

Question Number 151085    Answers: 1   Comments: 0

Question Number 151082    Answers: 0   Comments: 1

Question Number 151081    Answers: 3   Comments: 0

if f(x)=ax^2 +bx+c and f(x+3)=7x^2 +2x+5 find 1) a+b+c 2) a−b+c

$${if}\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:{f}\left({x}+\mathrm{3}\right)=\mathrm{7}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}\:{find} \\ $$$$\left.\mathrm{1}\left.\right)\:{a}+{b}+{c}\:\:\:\:\:\mathrm{2}\right)\:{a}−{b}+{c} \\ $$

Question Number 151080    Answers: 2   Comments: 0

if (f○f○f○f)(x)=16x+15 find f(x)

$${if}\:\left({f}\circ{f}\circ{f}\circ{f}\right)\left({x}\right)=\mathrm{16}{x}+\mathrm{15} \\ $$$${find}\:{f}\left({x}\right) \\ $$

Question Number 151079    Answers: 1   Comments: 0

Question Number 151078    Answers: 0   Comments: 0

Ω_k =lim_(n→∞) (1/n) ∙Σ_(p=0) ^n ( ((n),(p) )/ (((n+k)),((n+p)) )) ; k∈N^∗ -fixed find Ω=lim_(n→∞) (1/Ω_(n-1) ) ∙Σ_(i=1) ^n ((i!))^(1/i^2 )

$$\Omega_{\boldsymbol{\mathrm{k}}} =\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\:\centerdot\underset{\boldsymbol{\mathrm{p}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\frac{\begin{pmatrix}{\mathrm{n}}\\{\mathrm{p}}\end{pmatrix}}{\begin{pmatrix}{\mathrm{n}+\mathrm{k}}\\{\mathrm{n}+\mathrm{p}}\end{pmatrix}}\:\:;\:\:\mathrm{k}\in\mathbb{N}^{\ast} -\mathrm{fixed} \\ $$$$\mathrm{find}\:\:\Omega=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\Omega_{\boldsymbol{\mathrm{n}}-\mathrm{1}} }\:\centerdot\underset{\boldsymbol{\mathrm{i}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\sqrt[{\boldsymbol{\mathrm{i}}^{\mathrm{2}} }]{\boldsymbol{\mathrm{i}}!}\: \\ $$

Question Number 151074    Answers: 1   Comments: 0

5+5+5

$$\mathrm{5}+\mathrm{5}+\mathrm{5} \\ $$

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