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Question Number 211563 Answers: 1 Comments: 0

1.x^3 −3x−2=0 2.e^x +x^2 −4=0

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}.\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{x}}−\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}.\boldsymbol{{e}}^{\boldsymbol{{x}}} +\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 211574 Answers: 1 Comments: 0

{ ((x^2 +y^2 =25)),((x+2y−3=0)) :}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{25}}\\{\boldsymbol{{x}}+\mathrm{2}\boldsymbol{\mathrm{y}}−\mathrm{3}=\mathrm{0}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$

Question Number 211562 Answers: 2 Comments: 0

{ ((x^2 +y^2 =1)),((x^3 −y=0)) :}

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{1}}\\{\boldsymbol{{x}}^{\mathrm{3}} −\boldsymbol{\mathrm{y}}=\mathrm{0}}\end{cases} \\ $$

Question Number 211560 Answers: 0 Comments: 0

certificate: I=∫_0 ^(𝛑/2) (√(√(x^2 +ln^2 cos(x)−lncos(x)dx)))=(𝛑/2)(√(2ln2))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \sqrt{\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \boldsymbol{\mathrm{cos}}\left(\boldsymbol{{x}}\right)−\boldsymbol{\mathrm{lncos}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}\sqrt{\mathrm{2}\boldsymbol{\mathrm{ln}}\mathrm{2}} \\ $$$$ \\ $$

Question Number 211548 Answers: 2 Comments: 0

{ ((2x^2 +3y^2 −6xy=12)),((x^2 −y^2 =4)) :}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{y}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{{x}\mathrm{y}}=\mathrm{12}}\\{\boldsymbol{{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{4}}\end{cases} \\ $$$$ \\ $$

Question Number 211546 Answers: 2 Comments: 0

∫(dx/( (√(x^2 −4x+13))))=?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{13}}}=? \\ $$

Question Number 211537 Answers: 3 Comments: 0

Question Number 211535 Answers: 1 Comments: 0

Question Number 211558 Answers: 1 Comments: 0

−−−−−−−−−−−− 𝛀= Σ_(n=0) ^∞ ((1/(3n+2)) −(1/(3n+1)) )= a𝛑 ⇒ a^2 = ? −−−−−−−−−−−−

$$ \\ $$$$ \\ $$$$\:\:\:\:\:−−−−−−−−−−−− \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\Omega}=\:\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{n}}+\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{n}}+\mathrm{1}}\:\right)=\:\boldsymbol{{a}\pi} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\boldsymbol{{a}}^{\mathrm{2}} =\:? \\ $$$$\:\:\:\:\:\:\:−−−−−−−−−−−− \\ $$

Question Number 211531 Answers: 1 Comments: 0

∫_0 ^∞ (x^2 /(sinh(x)^2 ))dx.

$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{{x}}\right)^{\mathrm{2}} }\boldsymbol{{dx}}. \\ $$

Question Number 211529 Answers: 1 Comments: 0

known:x+y=3,ask: min((√(x^2 +1))+(√(y2−4)))=?

$$\mathrm{known}:\boldsymbol{{x}}+\boldsymbol{\mathrm{y}}=\mathrm{3},\mathrm{ask}: \\ $$$$\boldsymbol{\mathrm{min}}\left(\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}+\sqrt{\boldsymbol{\mathrm{y}}\mathrm{2}−\mathrm{4}}\right)=? \\ $$

Question Number 211528 Answers: 0 Comments: 2

I = ∫_0 ^( 1) (( tanh^(−1) (x^2 ))/x^( 2) ) dx= ?

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{−\mathrm{1}} \:\left({x}^{\mathrm{2}} \:\right)}{{x}^{\:\mathrm{2}} }\:{dx}=\:?\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 211524 Answers: 1 Comments: 0

Solve for x: x^x = 4x

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:=\:\:\mathrm{4x} \\ $$

Question Number 211520 Answers: 2 Comments: 1

determiner les valeurs de pet q sachant que −2 et 3 sont les −2 et 3 sont les racines de l equation: 2pqz^2 −5z−4(p+q)=0

$$\mathrm{determiner}\:\mathrm{les}\:\mathrm{valeurs}\:\:\mathrm{de}\:\boldsymbol{\mathrm{p}}\mathrm{et}\:\boldsymbol{\mathrm{q}}\:\mathrm{sachant}\:\mathrm{que}\:−\mathrm{2}\:\mathrm{et}\:\mathrm{3}\:\mathrm{sont}\:\mathrm{les}\: \\ $$$$−\mathrm{2}\:\mathrm{et}\:\mathrm{3}\:\:\mathrm{sont}\:\mathrm{les}\:\mathrm{racines}\:\mathrm{de}\:\mathrm{l}\:\mathrm{equation}: \\ $$$$\mathrm{2}\boldsymbol{\mathrm{pqz}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{z}}−\mathrm{4}\left(\boldsymbol{\mathrm{p}}+\boldsymbol{\mathrm{q}}\right)=\mathrm{0} \\ $$$$ \\ $$

Question Number 211515 Answers: 0 Comments: 2

for example I say Bob is born in 1900s, there the symbol of (s) means century. what kind of word it taken from?

$${for}\:{example}\:{I}\:{say}\:{Bob}\:{is}\:{born}\:{in} \\ $$$$\mathrm{1900}{s},\:{there}\:{the}\:{symbol}\:{of}\:\left({s}\right)\:{means} \\ $$$${century}.\:{what}\:{kind}\:{of}\:{word}\:{it}\:{taken} \\ $$$${from}? \\ $$

Question Number 211513 Answers: 0 Comments: 1

why we use Ampier meter sequence with resistance in circuit?

$${why}\:{we}\:{use}\:{Ampier}\:{meter}\:{sequence} \\ $$$${with}\:{resistance}\:{in}\:{circuit}? \\ $$

Question Number 211509 Answers: 2 Comments: 0

Question Number 211508 Answers: 1 Comments: 3

If (√(1 − x^2 )) + (√(1 − y^2 )) = a(x − y) then prove that (dy/dx) = (√(((1 − y^2 )/(1 − x^2 )) )) .

$$\mathrm{If}\:\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{1}\:−\:{y}^{\mathrm{2}} }\:=\:{a}\left({x}\:−\:{y}\right)\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{dy}}{{dx}}\:=\:\sqrt{\frac{\mathrm{1}\:−\:{y}^{\mathrm{2}} }{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:}\:. \\ $$

Question Number 211502 Answers: 2 Comments: 0

If { ((f(x)=x^2 )),((g(x)=sin x)) :}, Then find (df/dg).

$$\mathrm{If}\:\begin{cases}{{f}\left({x}\right)={x}^{\mathrm{2}} }\\{{g}\left({x}\right)=\mathrm{sin}\:{x}}\end{cases}, \\ $$$$\mathrm{Then}\:\mathrm{find}\:\frac{{df}}{{dg}}. \\ $$

Question Number 211496 Answers: 1 Comments: 0

Question Number 211495 Answers: 2 Comments: 0

Question Number 211492 Answers: 1 Comments: 0

Question Number 211485 Answers: 1 Comments: 0

If ((a − b)/c) + ((b − c)/a) + ((c + a)/b) = 1 and a − b + c ≠ 0 then prove that (1/a) = (1/b) + (1/c) .

$$\mathrm{If}\:\frac{{a}\:−\:{b}}{{c}}\:+\:\frac{{b}\:−\:{c}}{{a}}\:+\:\frac{{c}\:+\:{a}}{{b}}\:=\:\mathrm{1}\:\mathrm{and}\: \\ $$$${a}\:−\:{b}\:+\:{c}\:\neq\:\mathrm{0}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}}\:=\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:. \\ $$

Question Number 211708 Answers: 2 Comments: 0

Question Number 211486 Answers: 0 Comments: 0

Mathematical Analysis... f:R → R is diffrentiable function, f and f ′ , has no common zero on R . prove that the following set is finite. X = { x ∈ [0 , 1 ] ∣ f(x)=0 } −−−−−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:{Mathematical}\:\:\:\:\:{Analysis}... \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:{f}:\mathbb{R}\:\rightarrow\:\mathbb{R}\:{is}\:{diffrentiable}\:{function}, \\ $$$$\:\:\:\:\:{f}\:\:{and}\:\:{f}\:'\:,\:{has}\:{no}\:{common}\:{zero} \\ $$$$\:\:\:\:\:{on}\:\:\mathbb{R}\:. \\ $$$$\:\:\:\:\:\:{prove}\:{that}\:{the}\:{following}\:{set}\:{is}\:{finite}. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{X}\:=\:\left\{\:{x}\:\in\:\left[\mathrm{0}\:,\:\mathrm{1}\:\right]\:\mid\:{f}\left({x}\right)=\mathrm{0}\:\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−−−−− \\ $$

Question Number 211482 Answers: 0 Comments: 0

25^(((1/2) + log_(1/2) 27 + log_(25) 27)) =?

$$\:\mathrm{25}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\:+\:{log}_{\frac{\mathrm{1}}{\mathrm{2}}} \mathrm{27}\:+\:{log}_{\mathrm{25}} \mathrm{27}\right)} =? \\ $$

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