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Question Number 45746    Answers: 0   Comments: 1

Question Number 45783    Answers: 0   Comments: 1

sec(π/7)=((48−(√(3a)))/(36))

$${sec}\frac{\pi}{\mathrm{7}}=\frac{\mathrm{48}−\sqrt{\mathrm{3}{a}}}{\mathrm{36}} \\ $$

Question Number 45735    Answers: 2   Comments: 1

∫_α ^β (1/((x−α)(β−x)))dx =? β>α

$$\int_{\alpha} ^{\beta} \frac{\mathrm{1}}{\left({x}−\alpha\right)\left(\beta−{x}\right)}{dx}\:\:=?\:\:\:\beta>\alpha \\ $$

Question Number 45730    Answers: 2   Comments: 3

Question Number 45753    Answers: 1   Comments: 0

Question Number 45721    Answers: 0   Comments: 3

Integrate sin (x^2 )dx

$$\:{Integrate}\:\mathrm{sin}\:\left({x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 45719    Answers: 1   Comments: 0

Question Number 45720    Answers: 2   Comments: 5

𝚺_(r = 1) ^n (r + 1)^3

$$\underset{\boldsymbol{\mathrm{r}}\:=\:\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\boldsymbol{\sum}}}\:\:\left(\boldsymbol{\mathrm{r}}\:+\:\mathrm{1}\right)^{\mathrm{3}} \\ $$

Question Number 45712    Answers: 0   Comments: 3

prove that : (√2) is irrationl number

$$\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\sqrt{\mathrm{2}}\:\mathrm{is}\:\mathrm{irrationl}\:\mathrm{number} \\ $$

Question Number 45707    Answers: 0   Comments: 0

Question Number 45706    Answers: 1   Comments: 0

Question Number 45705    Answers: 0   Comments: 3

Question Number 45690    Answers: 1   Comments: 1

Question Number 45688    Answers: 1   Comments: 2

∫(1/(sinxcos^2 x))dx=?

$$\int\frac{\mathrm{1}}{{sinxcos}^{\mathrm{2}} {x}}{dx}=? \\ $$

Question Number 45681    Answers: 1   Comments: 0

Question Number 45673    Answers: 1   Comments: 1

Question Number 45670    Answers: 1   Comments: 1

∫cos^(−1) (sinx)dx=?

$$\int{cos}^{−\mathrm{1}} \left({sinx}\right){dx}=? \\ $$

Question Number 45669    Answers: 2   Comments: 0

∫tan^(−1) (√((1−sinx)/(1+sinx))) dx=?

$$\int{tan}^{−\mathrm{1}} \sqrt{\frac{\mathrm{1}−{sinx}}{\mathrm{1}+{sinx}}}\:{dx}=? \\ $$

Question Number 45654    Answers: 0   Comments: 1

Question Number 45649    Answers: 1   Comments: 1

Let consider A(3,5), B(6,4) and C(3,−2), d : x−5y+7=0 Consider a dot D such as ABCD is a trapezium and (AD) and (BC) are parallel lines. Q1) Give the equation of the line which contains the point D. Q2) Considering that the trapezium should be convex, are all the points D of the lines correct for the Trapezium ? Which ones are ? Give a proof. I have some difficulties to anzwer the question n°2, could someone please, help me. Thank you. H.T.

$$\mathrm{Let}\:\mathrm{consider}\:\mathrm{A}\left(\mathrm{3},\mathrm{5}\right),\:\mathrm{B}\left(\mathrm{6},\mathrm{4}\right)\:\mathrm{and}\:\mathrm{C}\left(\mathrm{3},−\mathrm{2}\right), \\ $$$$\mathrm{d}\::\:{x}−\mathrm{5}{y}+\mathrm{7}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Consider}\:\mathrm{a}\:\mathrm{dot}\:\mathrm{D}\:\mathrm{such}\:\mathrm{as}\:\mathrm{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{trapezium} \\ $$$$\mathrm{and}\:\left(\mathrm{AD}\right)\:\mathrm{and}\:\left(\mathrm{BC}\right)\:\mathrm{are}\:\mathrm{parallel}\:\mathrm{lines}. \\ $$$$ \\ $$$$\left.\mathrm{Q1}\right)\:\:\:\mathrm{Give}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{which} \\ $$$$\mathrm{contains}\:\mathrm{the}\:\mathrm{point}\:\mathrm{D}. \\ $$$$ \\ $$$$\left.\mathrm{Q2}\right)\:\:\:\mathrm{Considering}\:\mathrm{that}\:\mathrm{the}\:\mathrm{trapezium} \\ $$$$\mathrm{should}\:\mathrm{be}\:\mathrm{convex},\:\mathrm{are}\:\mathrm{all}\:\mathrm{the}\:\mathrm{points}\:\mathrm{D}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{lines}\:\mathrm{correct}\:\mathrm{for}\:\mathrm{the}\:\mathrm{Trapezium}\:? \\ $$$$\mathrm{Which}\:\mathrm{ones}\:\mathrm{are}\:? \\ $$$$\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{some}\:\mathrm{difficulties}\:\mathrm{to}\:\mathrm{anzwer}\:\mathrm{the} \\ $$$$\mathrm{question}\:\mathrm{n}°\mathrm{2},\:\mathrm{could}\:\mathrm{someone}\:\mathrm{please}, \\ $$$$\mathrm{help}\:\mathrm{me}. \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}. \\ $$$$ \\ $$$$\mathrm{H}.\mathrm{T}. \\ $$

Question Number 45646    Answers: 0   Comments: 2

According to relativistic theory, E^2 = p^2 c^2 +m_0 ^2 c^4 where m_0 is rest mass. For photon E= pc... (m_0 =0 for photon) For electron E=mc^2 ... Unlike photon ,Why p^2 c^2 is neglected in case of electron ?

$${According}\:{to}\:{relativistic}\:{theory}, \\ $$$${E}^{\mathrm{2}} =\:{p}^{\mathrm{2}} {c}^{\mathrm{2}} +{m}_{\mathrm{0}} ^{\mathrm{2}} {c}^{\mathrm{4}} \:{where}\:{m}_{\mathrm{0}} \:{is}\:{rest}\:{mass}. \\ $$$${For}\:{photon}\:{E}=\:{pc}... \\ $$$$\left({m}_{\mathrm{0}} =\mathrm{0}\:{for}\:{photon}\right) \\ $$$${For}\:{electron}\:{E}={mc}^{\mathrm{2}} ... \\ $$$${Unlike}\:{photon}\:,{Why}\:{p}^{\mathrm{2}} {c}^{\mathrm{2}} \:{is}\:{neglected}\:\: \\ $$$${in}\:{case}\:{of}\:{electron}\:? \\ $$

Question Number 45645    Answers: 1   Comments: 0

Question Number 45641    Answers: 2   Comments: 1

Question Number 45639    Answers: 3   Comments: 0

Question Number 45638    Answers: 1   Comments: 0

Question Number 45635    Answers: 0   Comments: 2

1)find f(x)=∫_0 ^1 ln(1+xt^3 )dt with ∣x∣<1 2) calculate ∫_0 ^1 ln(2+t^3 )dt .

$$\left.\mathrm{1}\right){find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{3}} \right){dt}\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{2}+{t}^{\mathrm{3}} \right){dt}\:. \\ $$

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