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Question Number 164188 Answers: 0 Comments: 0

Question Number 164187 Answers: 0 Comments: 0

Question Number 164178 Answers: 2 Comments: 1

Question Number 164177 Answers: 1 Comments: 0

x+(1/x)=3 (x/( (√x)+1))=?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3} \\ $$$$\frac{{x}}{\:\sqrt{{x}}+\mathrm{1}}=? \\ $$

Question Number 164176 Answers: 2 Comments: 0

Question Number 164174 Answers: 1 Comments: 1

Question Number 164171 Answers: 1 Comments: 0

∫ (dx/(1+x^(10) ))

$$\int\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{10}} } \\ $$

Question Number 164163 Answers: 2 Comments: 0

Prove the; ∫_(−∞) ^∞ (1/(1 + x^2 )) dx = 𝛑 ^({Z.A})

$$\mathrm{Prove}\:\mathrm{the}; \\ $$$$\int_{−\infty} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{1}\:+\:\boldsymbol{{x}}^{\mathrm{2}} }\:\boldsymbol{{dx}}\:=\:\boldsymbol{\pi} \\ $$$$\:^{\left\{\mathrm{Z}.\mathrm{A}\right\}} \\ $$

Question Number 164162 Answers: 0 Comments: 5

Prove the; (tan 𝛂 + ((cos 𝛂)/(1 + sin 𝛂))) sin 𝛂 = 𝛂 ^([Z.A])

$$\mathrm{Prove}\:\mathrm{the}; \\ $$$$\left(\boldsymbol{{tan}}\:\boldsymbol{\alpha}\:+\:\frac{\boldsymbol{{cos}}\:\boldsymbol{\alpha}}{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\boldsymbol{\alpha}}\right)\:\boldsymbol{{sin}}\:\boldsymbol{\alpha}\:=\:\boldsymbol{\alpha} \\ $$$$\:^{\left[\mathrm{Z}.\mathrm{A}\right]} \\ $$

Question Number 164157 Answers: 0 Comments: 0

let a;b;c≥0 and ab+bc+ca+2abc≥1 find min - value of S S = (√(a + 1)) + (√(b + 1)) + (√(c + 1))

$$\mathrm{let}\:\:\mathrm{a};\mathrm{b};\mathrm{c}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}+\mathrm{2abc}\geqslant\mathrm{1} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{min}}\:-\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{S}} \\ $$$$\boldsymbol{\mathrm{S}}\:=\:\sqrt{\mathrm{a}\:+\:\mathrm{1}}\:+\:\sqrt{\mathrm{b}\:+\:\mathrm{1}}\:+\:\sqrt{\mathrm{c}\:+\:\mathrm{1}} \\ $$

Question Number 164156 Answers: 0 Comments: 0

if ABC is a triangle with usual notations, then prove the following inequality: (4R + r)^3 - 4r^2 (2R - r) - 3s^2 (2R + r) ≥ 0

$$\mathrm{if}\:\:\mathrm{ABC}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{usual} \\ $$$$\mathrm{notations},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{inequality}: \\ $$$$\left(\mathrm{4R}\:+\:\mathrm{r}\right)^{\mathrm{3}} \:-\:\mathrm{4r}^{\mathrm{2}} \left(\mathrm{2R}\:-\:\mathrm{r}\right)\:-\:\mathrm{3s}^{\mathrm{2}} \left(\mathrm{2R}\:+\:\mathrm{r}\right)\:\geqslant\:\mathrm{0} \\ $$

Question Number 164155 Answers: 1 Comments: 2

if the root of equation x^9 - 10x + 1 = 0 are x_1 and x_2 x_1 x_2 = 1 find: x_1 + x_2 = ?

$$\mathrm{if}\:\mathrm{the}\:\mathrm{root}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{9}} \:-\:\mathrm{10x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\:\mathrm{are}\:\:\mathrm{x}_{\mathrm{1}} \:\:\mathrm{and}\:\:\mathrm{x}_{\mathrm{2}} \\ $$$$\mathrm{x}_{\mathrm{1}} \mathrm{x}_{\mathrm{2}} \:=\:\mathrm{1} \\ $$$$\mathrm{find}:\:\:\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{x}_{\mathrm{2}} \:=\:? \\ $$

Question Number 164154 Answers: 1 Comments: 0

{ ((x^2 + xy + y^2 = 9)),((y^2 + yz + z^2 = 16)),((x^2 + xz + z^2 = 25)) :} Find: S = xy + yz + xz

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{xy}\:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{9}}\\{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{yz}\:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{16}}\\{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{xz}\:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{25}}\end{cases} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{S}\:=\:\mathrm{xy}\:+\:\mathrm{yz}\:+\:\mathrm{xz} \\ $$

Question Number 164149 Answers: 0 Comments: 0

Question Number 164148 Answers: 1 Comments: 0

ln((3^x /((27)/(81))))=0 then x=?

$${ln}\left(\frac{\mathrm{3}^{{x}} }{\frac{\mathrm{27}}{\mathrm{81}}}\right)=\mathrm{0}\:\:\:\:\:\:\:\:\:{then}\:\:\:\:{x}=? \\ $$

Question Number 164138 Answers: 1 Comments: 0

Question Number 164137 Answers: 0 Comments: 1

what is the triple point of water?

$${what}\:{is}\:{the}\:{triple}\:{point}\:{of}\:{water}? \\ $$

Question Number 164135 Answers: 1 Comments: 0

p(x)+xp(−x)=x^2 +1 faind p(2)=?

$${p}\left({x}\right)+{xp}\left(−{x}\right)={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${faind}\:\:\:{p}\left(\mathrm{2}\right)=? \\ $$

Question Number 164134 Answers: 1 Comments: 0

Question Number 164133 Answers: 1 Comments: 0

Question Number 164129 Answers: 1 Comments: 0

prove 𝛗= Re (∫_0 ^( 1) Li_( 2) ( (1/x) ) )dx = ζ (2) −−−m.n−−−

$$ \\ $$$$\:\:\:{prove} \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\:\mathscr{R}{e}\:\left(\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{Li}_{\:\mathrm{2}} \:\left(\:\frac{\mathrm{1}}{{x}}\:\right)\:\right){dx}\:=\:\zeta\:\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:−−−{m}.{n}−−− \\ $$

Question Number 164125 Answers: 1 Comments: 0

Prove that: ∫_( 0) ^( (𝛑/2)) ∫_( 0) ^( 1) arctan (((sinx)/(u + cosx))) dudx = (π^2 /(16)) + (3/2) ln(2) - (π/4)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{arctan}\:\left(\frac{\mathrm{sin}\boldsymbol{\mathrm{x}}}{\mathrm{u}\:+\:\mathrm{cos}\boldsymbol{\mathrm{x}}}\right)\:\mathrm{dudx}\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{16}}\:+\:\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{ln}\left(\mathrm{2}\right)\:-\:\frac{\pi}{\mathrm{4}} \\ $$

Question Number 164124 Answers: 1 Comments: 0

Solve for real numbers: ((16^x + 4^x + 1^x )/(4^x + 2^x + 1^x )) = ((8^x + 1)/(65))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{16}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{1}^{\boldsymbol{\mathrm{x}}} }{\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{1}^{\boldsymbol{\mathrm{x}}} }\:=\:\frac{\mathrm{8}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{1}}{\mathrm{65}} \\ $$

Question Number 164123 Answers: 0 Comments: 0

very nice to problem: find in closed form; ∫_0 ^1 log (1−x^2 ) log^(n ) (1−x) dx; n ∈ N^+ ^(z.)

$$\mathrm{very}\:\mathrm{nice}\:\mathrm{to}\:\mathrm{problem}: \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{in}}\:\boldsymbol{{closed}}\:\boldsymbol{{form}}; \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\boldsymbol{{log}}\:\left(\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} \right)\:\boldsymbol{{log}}\:^{\boldsymbol{{n}}\:} \:\left(\mathrm{1}−\boldsymbol{{x}}\right)\:\boldsymbol{{dx}}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{n}}\:\in\:\:\mathbb{N}^{+} \\ $$$$\:^{\mathrm{z}.} \\ $$

Question Number 164122 Answers: 1 Comments: 0

lim_(n→∞) Σ_(k=1) ^n sin (1/(n+k))=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{k}}=? \\ $$

Question Number 164121 Answers: 1 Comments: 3

if w = f(x,y) and x = r cosθ , y = rsinθ then prove that w_(rr) + w_(θθ) = 0?

$${if}\:{w}\:=\:{f}\left({x},{y}\right)\:{and}\:{x}\:=\:{r}\:{cos}\theta\:,\:{y}\:=\:{rsin}\theta \\ $$$$ \\ $$$${then}\:{prove}\:{that}\:{w}_{{rr}} \:+\:{w}_{\theta\theta} \:=\:\mathrm{0}? \\ $$

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