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Question Number 158899    Answers: 1   Comments: 0

(1/2)+(3/4)=

$$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{4}}= \\ $$

Question Number 158894    Answers: 0   Comments: 1

Question Number 158893    Answers: 1   Comments: 0

Question Number 158884    Answers: 1   Comments: 0

Question Number 158883    Answers: 1   Comments: 4

Question Number 158886    Answers: 0   Comments: 1

Question Number 158878    Answers: 0   Comments: 0

Question Number 158874    Answers: 2   Comments: 1

Question Number 158873    Answers: 0   Comments: 0

Question Number 158870    Answers: 0   Comments: 1

Question Number 158869    Answers: 0   Comments: 2

The roots of the equation 2x^2 +px+p=0 are 2α+β and α+2β. Calculate the value of p

$$\:{The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\:\mathrm{2}{x}^{\mathrm{2}} +{px}+{p}=\mathrm{0}\:{are}\:\mathrm{2}\alpha+\beta\:{and} \\ $$$$\:\alpha+\mathrm{2}\beta.\:{Calculate}\:{the}\:{value}\:{of}\:{p} \\ $$

Question Number 158862    Answers: 1   Comments: 0

Question Number 158863    Answers: 0   Comments: 0

Question Number 158858    Answers: 0   Comments: 0

I_n =∫_(−1) ^1 (1−x^2 )^n cos ((a/(2b))x)dx to integrating by piece for n≥2 proven (a^2 /(4b^2 ))I_(n ) =2n(2n−1)I_(n−1) −4(n−1)I_(n−2) proven by rearring that ((a/(2b)))^(2n+1) I_n =n![p((q/(2b)))sin ((a/(2b)))+Q((a/(2b)))cos ((a/(2b)))]

$${I}_{{n}} =\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{{n}} \mathrm{cos}\:\left(\frac{{a}}{\mathrm{2}{b}}{x}\right){dx} \\ $$$${to}\:{integrating}\:{by}\:{piece}\:{for}\:{n}\geqslant\mathrm{2}\: \\ $$$${proven}\: \\ $$$$\frac{{a}^{\mathrm{2}} }{\mathrm{4}{b}^{\mathrm{2}} }{I}_{{n}\:} =\mathrm{2}{n}\left(\mathrm{2}{n}−\mathrm{1}\right){I}_{{n}−\mathrm{1}} −\mathrm{4}\left({n}−\mathrm{1}\right){I}_{{n}−\mathrm{2}} \\ $$$${proven}\:{by}\:{rearring}\:{that}\: \\ $$$$\left(\frac{{a}}{\mathrm{2}{b}}\right)^{\mathrm{2}{n}+\mathrm{1}} {I}_{{n}} ={n}!\left[{p}\left(\frac{{q}}{\mathrm{2}{b}}\right)\mathrm{sin}\:\left(\frac{{a}}{\mathrm{2}{b}}\right)+{Q}\left(\frac{{a}}{\mathrm{2}{b}}\right)\mathrm{cos}\:\left(\frac{{a}}{\mathrm{2}{b}}\right)\right] \\ $$

Question Number 158855    Answers: 1   Comments: 0

Resolve the system d′ unknow (x, y,z) ∈ ⊂^3 x+y+z=1 x^2 +y^2 +z^2 =1 x^3 +y^3 +z^3 =−5

$${Resolve}\:{the}\:{system}\:{d}'\:{unknow}\:\:\left({x},\:{y},{z}\right)\:\in\:\subset^{\mathrm{3}} \\ $$$${x}+{y}+{z}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{1} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =−\mathrm{5} \\ $$

Question Number 158847    Answers: 1   Comments: 0

Question Number 158843    Answers: 2   Comments: 2

Question Number 158839    Answers: 2   Comments: 0

Evaluate the following integrals using integration By Parts 1. ∫_((π )/4) ^(π/2) xcsc^2 xdx 2. ∫_1 ^(√3) arctan((1/x))dx

$$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integrals}\:\mathrm{using} \\ $$$$\mathrm{integration}\:\boldsymbol{\mathrm{By}}\:\boldsymbol{\mathrm{Parts}} \\ $$$$\mathrm{1}.\:\int_{\frac{\pi\:}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} {xcsc}^{\mathrm{2}} {xdx} \\ $$$$ \\ $$$$\mathrm{2}.\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} {arctan}\left(\frac{\mathrm{1}}{{x}}\right){dx} \\ $$

Question Number 158823    Answers: 0   Comments: 0

Question Number 158822    Answers: 1   Comments: 0

Σ_(n=0) ^∞ arctan (((−1)^n )/(2n+1))=?

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

Question Number 158833    Answers: 1   Comments: 0

what is 1(1/2)%

$${what}\:{is}\:\mathrm{1}\frac{\mathrm{1}}{\mathrm{2}}\% \\ $$

Question Number 158829    Answers: 1   Comments: 2

The roots of the equation 2x^2 +px+q=0 are 2α+β and α+2β. Calculate the values of p and q

$$\:{The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\:\mathrm{2}{x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\:{are}\:\mathrm{2}\alpha+\beta\:{and} \\ $$$$\:\alpha+\mathrm{2}\beta.\:{Calculate}\:{the}\:{values}\:{of} \\ $$$$\:{p}\:{and}\:{q} \\ $$

Question Number 158827    Answers: 1   Comments: 0

resolve ∫ln (cos x)dx

$${resolve}\:\int\mathrm{ln}\:\left(\mathrm{cos}\:{x}\right){dx} \\ $$

Question Number 158816    Answers: 0   Comments: 0

Prove that 2017^(2017) and 2017^(2018) can be written as the sum of two perfect squares.

$$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{2017}^{\mathrm{2017}} \:\:\mathrm{and}\:\:\:\mathrm{2017}^{\mathrm{2018}} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{perfect}\:\mathrm{squares}. \\ $$$$ \\ $$

Question Number 158814    Answers: 2   Comments: 0

Compare it: (log_4 20)^2 and log_4 320

$$\mathrm{Compare}\:\mathrm{it}: \\ $$$$\left(\mathrm{log}_{\mathrm{4}} \mathrm{20}\right)^{\mathrm{2}} \:\:\:\mathrm{and}\:\:\:\mathrm{log}_{\mathrm{4}} \mathrm{320} \\ $$$$ \\ $$

Question Number 158813    Answers: 0   Comments: 0

Find all value 𝛃>0 such that: ∫_( 0) ^( +∞) (dx/(x^(2021𝛃) + ln∙(1 + βx))) dx < +∞

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{value}\:\:\boldsymbol{\beta}>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:+\infty} {\int}}\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2021}\boldsymbol{\beta}} \:+\:\mathrm{ln}\centerdot\left(\mathrm{1}\:+\:\beta\mathrm{x}\right)}\:\mathrm{dx}\:<\:+\infty \\ $$

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