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Question Number 210593 Answers: 1 Comments: 0

∫ ((sin x cos x)/( ((cos 2x))^(1/3) + (√(cos 2x)))) dx =? ∫ (dx/(sec x ((sin x))^(1/2) + cos x ((cosec^5 x))^(1/3) )) =?

$$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{2x}}\:+\:\sqrt{\mathrm{cos}\:\mathrm{2x}}}\:\mathrm{dx}\:=? \\ $$$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}\:\sqrt[{\mathrm{2}}]{\mathrm{sin}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}\:\sqrt[{\mathrm{3}}]{\mathrm{cosec}\:^{\mathrm{5}} \mathrm{x}}}\:=? \\ $$

Question Number 210591 Answers: 3 Comments: 0

If a + b = 1 a^2 + b^2 = 2 then, a^(11) + b^(11) = ??

$$\mathrm{If} \\ $$$$\:\:\:\:\mathrm{a}\:\:+\:\:\mathrm{b}\:\:=\:\:\mathrm{1} \\ $$$$\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{b}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\mathrm{then},\:\:\:\:\:\mathrm{a}^{\mathrm{11}} \:\:+\:\:\mathrm{b}^{\mathrm{11}} \:\:=\:\:?? \\ $$

Question Number 210590 Answers: 0 Comments: 0

Question Number 210587 Answers: 0 Comments: 3

f(x)= (√( 13 −12(√x) )) + (√(25 −24(√(1−x)) )) find : Min ( f )=?

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mathrm{13}\:−\mathrm{12}\sqrt{{x}}\:\:}\:+\:\sqrt{\mathrm{25}\:−\mathrm{24}\sqrt{\mathrm{1}−{x}}\:} \\ $$$$ \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\:\mathrm{M}{in}\:\left(\:{f}\:\right)=? \\ $$$$ \\ $$$$ \\ $$

Question Number 210581 Answers: 1 Comments: 0

{ ((x^2 +3x−(√(x^2 +3x−1 = 7)))),((2(√2) sin y = x)) :} x=? and y=?

$$\:\:\begin{cases}{{x}^{\mathrm{2}} +\mathrm{3}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}\:=\:\mathrm{7}}}\\{\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{sin}\:{y}\:=\:{x}}\end{cases} \\ $$$$\:\:\:{x}=?\:\:\:\:{and}\:\:\:\:{y}=? \\ $$

Question Number 210579 Answers: 0 Comments: 4

Please... Can anyone help me.. Find the value(s) of x, if (x−2)^((x^2 −2x+4)) =3

$${Please}...\:{Can}\:{anyone}\:{help}\:{me}.. \\ $$$$ \\ $$$$\:{Find}\:{the}\:{value}\left({s}\right)\:{of}\:{x},\:{if} \\ $$$$\:\:\:\left({x}−\mathrm{2}\right)^{\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}\right)} =\mathrm{3} \\ $$$$ \\ $$

Question Number 210574 Answers: 3 Comments: 0

if the roots of the equation x^2 +(k+1)x+k=0 are α and β, find the value of the real constant k for which α=2β

$${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$${x}^{\mathrm{2}} +\left({k}+\mathrm{1}\right){x}+{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta, \\ $$$$\:{find}\:{the}\:{value}\:{of}\:{the} \\ $$$$\:{real}\:{constant}\:{k}\:{for} \\ $$$${which}\:\alpha=\mathrm{2}\beta \\ $$

Question Number 210573 Answers: 1 Comments: 0

Question Number 210572 Answers: 1 Comments: 0

Question Number 210571 Answers: 1 Comments: 0

If x,y,z∈R^+ and x^2 +y^2 +z^2 =3 Prove that (1/(4−x)) + (1/(4−y)) + (1/(4−z)) ≤ 1

$$\mathrm{If}\:\:\mathrm{x},\mathrm{y},\mathrm{z}\in\mathrm{R}^{+} \:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}−\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{y}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{z}}\:\:\leqslant\:\:\mathrm{1} \\ $$

Question Number 210566 Answers: 1 Comments: 0

Prove that: if (x∈]−(π/2),(π/2)[ y =∫^( x) _( 0) (dt/(cos(t))) ) ⇒ (y∈IR x =∫^( y) _( 0) (dt/(cosh(t))) )

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{if}\:\left(\mathrm{x}\in\right]−\frac{\pi}{\mathrm{2}},\frac{\pi}{\mathrm{2}}\left[\:\:\mathrm{y}\:=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{x}} \frac{\mathrm{dt}}{\mathrm{cos}\left(\mathrm{t}\right)}\:\right)\:\Rightarrow\:\:\left(\mathrm{y}\in\mathrm{IR}\:\:\:\mathrm{x}\:=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{y}} \frac{\mathrm{dt}}{\mathrm{cosh}\left(\mathrm{t}\right)}\:\right) \\ $$

Question Number 210565 Answers: 1 Comments: 0

Question Number 210559 Answers: 1 Comments: 0

deg [p(x^2 )∙q(x)]=20 deg[((p(x)^3 )/(q(x)^2 ))]=2 then deg q(x)=?

$${deg}\:\left[{p}\left({x}^{\mathrm{2}} \right)\centerdot{q}\left({x}\right)\right]=\mathrm{20} \\ $$$${deg}\left[\frac{{p}\left({x}\right)^{\mathrm{3}} }{{q}\left({x}\right)^{\mathrm{2}} }\right]=\mathrm{2} \\ $$$${then}\:{deg}\:\:{q}\left({x}\right)=? \\ $$

Question Number 210554 Answers: 1 Comments: 0

Question Number 210549 Answers: 1 Comments: 0

let a sequence be difined as a_n = a_(n−1) + ((2cos ((a_(n−1) /2)))/(2sin ((a_(n−1) /2))−1)) , a_(0 ) = 0 find lim_(n→∞) a_(n ) = ?

$$\mathrm{let}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{be}\:\mathrm{difined}\:\mathrm{as} \\ $$$$\:\mathrm{a}_{\mathrm{n}} =\:\mathrm{a}_{\mathrm{n}−\mathrm{1}} \:+\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{a}_{\mathrm{n}−\mathrm{1}} }{\mathrm{2}}\right)}{\mathrm{2sin}\:\left(\frac{\mathrm{a}_{\mathrm{n}−\mathrm{1}} }{\mathrm{2}}\right)−\mathrm{1}}\:\:,\:\mathrm{a}_{\mathrm{0}\:} =\:\mathrm{0} \\ $$$$\mathrm{find}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\mathrm{n}\:} \:=\:? \\ $$

Question Number 210542 Answers: 1 Comments: 2

Question Number 210533 Answers: 1 Comments: 1

Question Number 210524 Answers: 1 Comments: 1

Question Number 210517 Answers: 3 Comments: 2

∫(1/(sinx−cos2x))dx

$$\int\frac{\mathrm{1}}{\mathrm{sin}{x}−\mathrm{cos2}{x}}{dx} \\ $$

Question Number 210516 Answers: 3 Comments: 0

Find: x = ? 1 + 3x + 5x^2 + 7x^3 + 9x^4 + 11x^5 + ... = 15

$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\mathrm{1}\:+\:\mathrm{3x}\:+\:\mathrm{5x}^{\mathrm{2}} \:+\:\mathrm{7x}^{\mathrm{3}} \:+\:\mathrm{9x}^{\mathrm{4}} \:+\:\mathrm{11x}^{\mathrm{5}} \:+\:...\:=\:\mathrm{15} \\ $$

Question Number 210515 Answers: 0 Comments: 13

Find: (1/7^2 ) + (1/(11^2 )) + (1/(13^2 )) + (1/(17^2 )) + (1/(19^2 )) + (1/(23^2 )) + (1/(29^2 )) + ... = ?

$$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{11}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{13}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{17}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{19}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{23}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{29}^{\mathrm{2}} }\:+\:...\:=\:? \\ $$

Question Number 210508 Answers: 1 Comments: 0

Question Number 210496 Answers: 1 Comments: 4

Question Number 210492 Answers: 0 Comments: 2

un objet C situe a une hsuteur h est lache sans vitesse initiale (v_0 =0) par un un petit avion volant a basse altitue cet objet est capte par une prrsonne entraine le long de la couronne a vitesse constante(v) −1) Determiner l instant de recuperariion de l objet −2) l altitude y ainsi que la vitesse de shute en ce point M −3)on supose que la couronne continue son mouvement apres coupure de courant et s arrete ensuite apres un instat t que l on definera Donnes: masse de la personne + banc =98kg g=10m/s^2 R=20m 𝛂=30° m_C =2kg

$$\mathrm{un}\:\mathrm{objet}\:\boldsymbol{\mathrm{C}}\:\mathrm{situe}\:\mathrm{a}\:\mathrm{une}\:\mathrm{hsuteur}\:\boldsymbol{\mathrm{h}} \\ $$$$\mathrm{est}\:\mathrm{lache}\:\mathrm{sans}\:\mathrm{vitesse}\:\:\mathrm{initiale}\:\left(\boldsymbol{\mathrm{v}}_{\mathrm{0}} =\mathrm{0}\right) \\ $$$$\mathrm{par}\:\mathrm{un}\:\mathrm{un}\:\mathrm{petit}\:\mathrm{avion}\:\mathrm{volant}\:\mathrm{a}\:\mathrm{basse} \\ $$$$\mathrm{altitue}\:\mathrm{cet}\:\mathrm{objet}\:\mathrm{est}\:\mathrm{capte}\:\mathrm{par}\:\mathrm{une}\: \\ $$$$\mathrm{prrsonne}\:\:\mathrm{entraine}\:\mathrm{le}\:\mathrm{long}\:\mathrm{de}\:\mathrm{la}\:\:\mathrm{couronne}\: \\ $$$$\mathrm{a}\:\mathrm{vitesse}\:\mathrm{const}\boldsymbol{\mathrm{a}}\mathrm{nte}\left(\boldsymbol{\mathrm{v}}\right)\: \\ $$$$\left.−\mathrm{1}\right)\:\mathrm{Determiner}\:\mathrm{l}\:\mathrm{instant}\:\mathrm{de}\:\mathrm{recuperariion} \\ $$$$\mathrm{de}\:\mathrm{l}\:\mathrm{objet}\: \\ $$$$\left.−\mathrm{2}\right)\:\mathrm{l}\:\mathrm{altitude}\:\boldsymbol{\mathrm{y}}\:\mathrm{ainsi}\:\mathrm{que}\:\mathrm{la}\:\mathrm{vitesse}\: \\ $$$$\mathrm{de}\:\mathrm{shute}\:\mathrm{en}\:\mathrm{ce}\:\mathrm{point}\:\boldsymbol{\mathrm{M}} \\ $$$$\left.−\mathrm{3}\right)\mathrm{on}\:\mathrm{supose}\:\mathrm{que}\:\mathrm{la}\:\mathrm{couronne}\:\mathrm{continue} \\ $$$$\mathrm{son}\:\mathrm{mouvement}\:\:\mathrm{apres}\:\mathrm{coupure}\:\mathrm{de}\: \\ $$$$\mathrm{courant}\:\mathrm{et}\:\mathrm{s}\:\mathrm{arrete}\:\mathrm{ensuite}\:\mathrm{apres}\:\mathrm{un}\: \\ $$$$\mathrm{instat}\:\boldsymbol{\mathrm{t}}\:\:\mathrm{que}\:\mathrm{l}\:\mathrm{on}\:\mathrm{definera} \\ $$$$ \\ $$$${Donnes}: \\ $$$$\:\:\mathrm{masse}\:\mathrm{de}\:\mathrm{la}\:\mathrm{personne}\:+\:\mathrm{banc}\:=\mathrm{98kg} \\ $$$$\mathrm{g}=\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \:\:\:\:\boldsymbol{\mathrm{R}}=\mathrm{20}\boldsymbol{\mathrm{m}}\:\:\:\:\:\:\:\:\boldsymbol{\alpha}=\mathrm{30}°\:\:\mathrm{m}_{\mathrm{C}} =\mathrm{2kg} \\ $$$$\: \\ $$

Question Number 210473 Answers: 5 Comments: 0

Question Number 210467 Answers: 3 Comments: 0

1+(√2)+(√3)+...+(√n) irrational ???

$$\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+...+\sqrt{\mathrm{n}}\:\:\:\mathrm{irrational}\:??? \\ $$

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