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Question Number 159281    Answers: 0   Comments: 2

Question Number 159280    Answers: 1   Comments: 0

Solve in R : (√x) = ((x^2 - 244x + 736)/(1008))

$$\boldsymbol{\mathrm{S}}\mathrm{olve}\:\mathrm{in}\:\mathbb{R}\::\:\:\sqrt{\mathrm{x}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{244x}\:+\:\mathrm{736}}{\mathrm{1008}} \\ $$$$ \\ $$

Question Number 159276    Answers: 1   Comments: 0

lim_(x→∞) ((1/(x^2 +1))+(1/(x^2 +4))+(1/(x^2 +9))+…)=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{4}}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{9}}+\ldots\right)=? \\ $$

Question Number 159259    Answers: 1   Comments: 0

montre que Σ_(k=0) ^n C_(2n) ^(2k) =2^(2n−1)

$$\boldsymbol{{montre}}\:\boldsymbol{{que}}\: \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{C}}_{\mathrm{2}\boldsymbol{{n}}} ^{\mathrm{2}\boldsymbol{{k}}} =\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} \\ $$

Question Number 159249    Answers: 1   Comments: 0

hi ! solve in IN×IN this one : (x+1)(y+2)=2xy. thanks.

$$\boldsymbol{\mathrm{hi}}\:! \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{IN}}×\boldsymbol{\mathrm{IN}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{one}}\::\:\left(\boldsymbol{{x}}+\mathrm{1}\right)\left(\boldsymbol{{y}}+\mathrm{2}\right)=\mathrm{2}\boldsymbol{{xy}}. \\ $$$$\boldsymbol{\mathrm{thanks}}. \\ $$

Question Number 159248    Answers: 0   Comments: 0

find the angle of intersection between the followng curves: y^2 = ax, x^3 +y^3 = 3axy

$${find}\:{the}\:{angle}\:{of}\:{intersection}\:{between} \\ $$$${the}\:{followng}\:{curves}: \\ $$$${y}^{\mathrm{2}} \:=\:{ax},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} \:=\:\mathrm{3}{axy} \\ $$

Question Number 159240    Answers: 0   Comments: 2

Question Number 159239    Answers: 0   Comments: 0

Question Number 159233    Answers: 1   Comments: 0

Question Number 159229    Answers: 2   Comments: 0

lim_(x→∞) x((√(x^2 +2x))+x−2(√(x^2 +x)) )=?

$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}}+{x}−\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{x}}\:\right)=? \\ $$

Question Number 159226    Answers: 1   Comments: 0

Ω = ∫_0 ^∞ (((x^5 )^(1/6) −(√x))/((1+x^2 ) ln x)) dx =?

$$\:\Omega\:=\:\int_{\mathrm{0}} ^{\infty} \frac{\sqrt[{\mathrm{6}}]{{x}^{\mathrm{5}} }−\sqrt{{x}}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\:\mathrm{ln}\:{x}}\:{dx}\:=? \\ $$

Question Number 159222    Answers: 1   Comments: 1

find an explicit formula for the sequence (2/3), (4/5), (8/9), ((16)/(17)), ((32)/(33)), ...

$$\mathrm{find}\:\mathrm{an}\:\mathrm{explicit}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{sequence} \\ $$$$\frac{\mathrm{2}}{\mathrm{3}},\:\frac{\mathrm{4}}{\mathrm{5}},\:\frac{\mathrm{8}}{\mathrm{9}},\:\frac{\mathrm{16}}{\mathrm{17}},\:\frac{\mathrm{32}}{\mathrm{33}},\:... \\ $$

Question Number 159221    Answers: 2   Comments: 4

find the general term of the sequence 3, 5 , 9, 17, 33, ...

$$\mathrm{find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{term}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sequence}\: \\ $$$$\mathrm{3},\:\mathrm{5}\:,\:\mathrm{9},\:\mathrm{17},\:\mathrm{33},\:... \\ $$

Question Number 159217    Answers: 1   Comments: 0

Question Number 159189    Answers: 1   Comments: 0

Question Number 159188    Answers: 3   Comments: 2

If α and β are the roots of equation (√(t/(1−t))) + (√((1−t)/t)) = ((13)/6) . Find 2α+3β .

$$\:{If}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{roots}\:{of} \\ $$$${equation}\:\sqrt{\frac{{t}}{\mathrm{1}−{t}}}\:+\:\sqrt{\frac{\mathrm{1}−{t}}{{t}}}\:=\:\frac{\mathrm{13}}{\mathrm{6}}\:. \\ $$$${Find}\:\mathrm{2}\alpha+\mathrm{3}\beta\:. \\ $$

Question Number 159180    Answers: 1   Comments: 0

Question Number 159179    Answers: 1   Comments: 0

X^3 −4X^2 −6X−24 = 0

$$\:\:\mathcal{X}^{\mathrm{3}} −\mathrm{4}\mathcal{X}^{\mathrm{2}} −\mathrm{6}\mathcal{X}−\mathrm{24}\:=\:\mathrm{0} \\ $$

Question Number 159173    Answers: 1   Comments: 0

Question Number 159172    Answers: 1   Comments: 0

Question Number 159171    Answers: 1   Comments: 0

Prove by absurd that log 2 is the number irrational

$${Prove}\:{by}\:{absurd}\:{that}\:\mathrm{log}\:\mathrm{2}\:{is}\:{the} \\ $$$${number}\:{irrational} \\ $$

Question Number 159170    Answers: 1   Comments: 1

Question Number 159300    Answers: 1   Comments: 0

Question Number 159163    Answers: 2   Comments: 1

Question Number 159159    Answers: 1   Comments: 0

Three students are runing for school SRC president, kada′s probability of winning is (1/8), Atiga′s probability of winnig (1/3) and kada is half as likely to win as Apio. i. what is the probability that both Atiga and Apio draw ii. what is the probability that only one wins the presidency.

$$\:\mathrm{Three}\:\mathrm{students}\:\mathrm{are}\:\mathrm{runing}\:\mathrm{for}\:\mathrm{school} \\ $$$$\:\mathrm{SRC}\:\mathrm{president},\:\mathrm{kada}'\mathrm{s}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{winning}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{8}},\:\mathrm{Atiga}'\mathrm{s}\:\mathrm{probability}\: \\ $$$$\mathrm{of}\:\mathrm{winnig}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\:\mathrm{kada}\:\mathrm{is}\:\mathrm{half}\:\mathrm{as}\:\mathrm{likely} \\ $$$$\mathrm{to}\:\mathrm{win}\:\mathrm{as}\:\mathrm{Apio}.\: \\ $$$$\mathrm{i}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{both}\: \\ $$$$\:\mathrm{Atiga}\:\mathrm{and}\:\mathrm{Apio}\:\mathrm{draw} \\ $$$$\mathrm{ii}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{only} \\ $$$$\mathrm{one}\:\mathrm{wins}\:\mathrm{the}\:\mathrm{presidency}. \\ $$

Question Number 159292    Answers: 1   Comments: 0

Find: 𝛀 =∫_( 0) ^( ∞) ((x arctan(x))/((x + 1)(x^2 + 1))) dx

$$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{x}\:\mathrm{arctan}\left(\mathrm{x}\right)}{\left(\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)}\:\mathrm{dx} \\ $$$$ \\ $$

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