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Question Number 164211 Answers: 1 Comments: 0

Question Number 164210 Answers: 1 Comments: 0

Question Number 164208 Answers: 0 Comments: 0

Question Number 164206 Answers: 2 Comments: 5

Question Number 164457 Answers: 1 Comments: 0

((20)/(10))=2(0/(10))=>((20)/(10))=0 why?

$$\frac{\mathrm{20}}{\mathrm{10}}=\mathrm{2}\frac{\mathrm{0}}{\mathrm{10}}=>\frac{\mathrm{20}}{\mathrm{10}}=\mathrm{0}\:\:\:\:\:{why}? \\ $$

Question Number 164196 Answers: 1 Comments: 0

Evalute the sum: Σ_(k=1) ^n k ((π/n))^2 arctan (((kπ)/n))^2

$$\mathrm{Evalute}\:\mathrm{the}\:\mathrm{sum}: \\ $$$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{k}\:\left(\frac{\pi}{\mathrm{n}}\right)^{\mathrm{2}} \mathrm{arctan}\:\left(\frac{\mathrm{k}\pi}{\mathrm{n}}\right)^{\mathrm{2}} \\ $$

Question Number 164193 Answers: 2 Comments: 2

Question Number 164191 Answers: 1 Comments: 0

Question Number 164189 Answers: 0 Comments: 1

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?

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

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