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Question Number 145136    Answers: 1   Comments: 0

Soit X une variable aleatoire de loi geometrique de parametre p∈]0.1[ calculer P({X≥4})

$${Soit}\:{X}\:{une}\:{variable}\:{aleatoire}\:{de}\:{loi} \\ $$$$\left.{geometrique}\:{de}\:{parametre}\:{p}\in\right]\mathrm{0}.\mathrm{1}\left[\right. \\ $$$${calculer}\:{P}\left(\left\{{X}\geqslant\mathrm{4}\right\}\right) \\ $$

Question Number 145134    Answers: 0   Comments: 1

On dispose de N+1 urnes.l′urne U_k contient k boules blanches et N−k boules noires.on tire successivement sans remise n boules de l′urne et on note An l′evenement ′′choisir n boules noires lors des n premiers tirages′′. Determiner P(An). on notera U_k =′′choisir l′urne k′′

$${On}\:{dispose}\:{de}\:{N}+\mathrm{1}\:{urnes}.{l}'{urne}\:{U}_{{k}} \\ $$$${contient}\:{k}\:{boules}\:{blanches}\:{et}\:{N}−{k}\:{boules} \\ $$$${noires}.{on}\:{tire}\:{successivement}\:{sans}\: \\ $$$${remise}\:{n}\:{boules}\:{de}\:{l}'{urne}\:{et}\:{on}\:{note}\: \\ $$$${An}\:{l}'{evenement}\:''{choisir}\:{n}\:{boules}\:{noires} \\ $$$${lors}\:{des}\:{n}\:{premiers}\:{tirages}''.\:{Determiner} \\ $$$${P}\left({An}\right).\:{on}\:{notera}\:{U}_{{k}} =''{choisir}\:{l}'{urne}\:{k}'' \\ $$

Question Number 145137    Answers: 2   Comments: 3

Let a≥b≥c≥0 and a^2 +b^2 +c^2 = 3. Prove that a^3 +(b+c)^3 ≤ 9

$$\mathrm{Let}\:{a}\geqslant{b}\geqslant{c}\geqslant\mathrm{0}\:\mathrm{and}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \:=\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\mathrm{3}} +\left({b}+{c}\right)^{\mathrm{3}} \:\leqslant\:\mathrm{9} \\ $$

Question Number 145129    Answers: 1   Comments: 0

Question Number 145119    Answers: 3   Comments: 0

(5^(log _(5/3) (5)) /3^(log _(5/3) (3)) ) =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}^{\mathrm{log}\:_{\frac{\mathrm{5}}{\mathrm{3}}} \left(\mathrm{5}\right)} }{\mathrm{3}^{\mathrm{log}\:_{\frac{\mathrm{5}}{\mathrm{3}}} \left(\mathrm{3}\right)} }\:=?\: \\ $$

Question Number 145114    Answers: 2   Comments: 4

Question Number 145113    Answers: 1   Comments: 0

Question Number 145109    Answers: 1   Comments: 0

Solve the equation: cos(6x)−cos(4x)=4y^2 +4y+3

$${Solve}\:{the}\:{equation}: \\ $$$${cos}\left(\mathrm{6}{x}\right)−{cos}\left(\mathrm{4}{x}\right)=\mathrm{4}{y}^{\mathrm{2}} +\mathrm{4}{y}+\mathrm{3} \\ $$

Question Number 145108    Answers: 1   Comments: 0

Question Number 145104    Answers: 1   Comments: 0

If ((!6)/x) −!4 = !x then x =?

$$\:\mathrm{If}\:\frac{!\mathrm{6}}{\mathrm{x}}\:−!\mathrm{4}\:=\:!\mathrm{x}\:\mathrm{then}\:\mathrm{x}\:=? \\ $$

Question Number 145101    Answers: 0   Comments: 1

Question Number 145093    Answers: 1   Comments: 0

if f(ax+2b)=x and f(2a)=(b/a) find f(5b)=?

$${if}\:\:{f}\left({ax}+\mathrm{2}{b}\right)={x}\:\:{and}\:\:{f}\left(\mathrm{2}{a}\right)=\frac{{b}}{{a}} \\ $$$${find}\:\:{f}\left(\mathrm{5}{b}\right)=? \\ $$

Question Number 145082    Answers: 4   Comments: 0

Σ_(n=2) ^∞ ((1/(2n^2 −2)))=?

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

Question Number 145081    Answers: 1   Comments: 0

∫_0 ^∞ (x−(x^3 /2)+(x^5 /(2∙4))−(x^7 /(2∙4∙6))+...)∙(1+(x^2 /2^2 )+(x^4 /(2^2 ∙4^2 ))+(x^6 /(2^2 ∙4^2 ∙6^2 ))+...)dx=(√e)

$$\int_{\mathrm{0}} ^{\infty} \left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{5}} }{\mathrm{2}\centerdot\mathrm{4}}−\frac{\mathrm{x}^{\mathrm{7}} }{\mathrm{2}\centerdot\mathrm{4}\centerdot\mathrm{6}}+...\right)\centerdot\left(\mathrm{1}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{x}^{\mathrm{6}} }{\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{4}^{\mathrm{2}} \centerdot\mathrm{6}^{\mathrm{2}} }+...\right)\mathrm{dx}=\sqrt{\mathrm{e}} \\ $$

Question Number 145074    Answers: 1   Comments: 0

ab+bc+ax+cx=?

$${ab}+{bc}+{ax}+{cx}=? \\ $$

Question Number 145073    Answers: 1   Comments: 2

let a_1 ,a_2 ,...,a_n be positive real numbers such that a_1 +a_2 +...+a_n =1 then find maximum value of a_1 ^a_1 .a_2 ^a_2 ....a_n ^a_n ?

$$\mathrm{let}\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,...,\mathrm{a}_{\mathrm{n}} \:\mathrm{be}\:\mathrm{positive} \\ $$$$\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{a}_{\mathrm{1}} +\mathrm{a}_{\mathrm{2}} +...+\mathrm{a}_{\mathrm{n}} =\mathrm{1}\:\mathrm{then}\:\mathrm{find}\: \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{a}_{\mathrm{1}} ^{\mathrm{a}_{\mathrm{1}} } .\mathrm{a}_{\mathrm{2}} ^{\mathrm{a}_{\mathrm{2}} } ....\mathrm{a}_{\mathrm{n}} ^{\mathrm{a}_{\mathrm{n}} } \:? \\ $$

Question Number 145071    Answers: 1   Comments: 0

log _(((x/2))) (x+2) = 1+ log _x (4−x) x=?

$$\mathrm{log}\:_{\left(\frac{\mathrm{x}}{\mathrm{2}}\right)} \left(\mathrm{x}+\mathrm{2}\right)\:=\:\mathrm{1}+\:\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{4}−\mathrm{x}\right) \\ $$$$\:\mathrm{x}=? \\ $$

Question Number 145067    Answers: 1   Comments: 0

log _3 (x+1) =log _4 (x+8) x=?

$$\:\mathrm{log}\:_{\mathrm{3}} \left({x}+\mathrm{1}\right)\:=\mathrm{log}\:_{\mathrm{4}} \left({x}+\mathrm{8}\right) \\ $$$$\:{x}=? \\ $$

Question Number 145065    Answers: 0   Comments: 0

(1/( (√(1+x))))=1+Σ_(k=1) ^n [(((−1)^k )/2^(2k) )C_(2k) ^k ]x^k +o(x^n )

$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{x}}}=\mathrm{1}+\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{2}^{\mathrm{2k}} }\mathrm{C}_{\mathrm{2k}} ^{\mathrm{k}} \right]\mathrm{x}^{\mathrm{k}} +\mathrm{o}\left(\mathrm{x}^{\mathrm{n}} \right) \\ $$

Question Number 145064    Answers: 1   Comments: 0

∫cos 2xln (1+tan x)dx

$$\:\:\:\:\:\:\int\mathrm{cos}\:\mathrm{2xln}\:\left(\mathrm{1}+\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 145057    Answers: 0   Comments: 3

find k if y^2 +y+k is a perfect square

$$\boldsymbol{{find}}\:\:\boldsymbol{{k}}\:\:\boldsymbol{{if}}\:\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{y}}+\boldsymbol{{k}}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{perfect}} \\ $$$$\boldsymbol{{square}} \\ $$

Question Number 145052    Answers: 0   Comments: 2

find laurant series at f(z)=(1/(lnz))????

$${find}\:{laurant}\:{series}\:{at}\:{f}\left({z}\right)=\frac{\mathrm{1}}{{lnz}}???? \\ $$

Question Number 145047    Answers: 3   Comments: 1

Question Number 145046    Answers: 0   Comments: 0

find ∫_0 ^∞ ∣cosx +sinx∣e^(−x) dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\mid\mathrm{cosx}\:+\mathrm{sinx}\mid\mathrm{e}^{−\mathrm{x}} \:\mathrm{dx} \\ $$

Question Number 145044    Answers: 3   Comments: 0

calculate ∫_0 ^∞ e^(−2x) (√(1+sinx))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\mathrm{e}^{−\mathrm{2x}} \sqrt{\mathrm{1}+\mathrm{sinx}}\mathrm{dx} \\ $$

Question Number 145025    Answers: 2   Comments: 0

Σ_(n=1) ^∞ (1/((n+1)(√n)+n(√(n+1)))) = ?

$$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\sqrt{{n}}+{n}\sqrt{{n}+\mathrm{1}}}\:=\:? \\ $$

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