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Question Number 217897 Answers: 1 Comments: 7

Question Number 217895 Answers: 1 Comments: 6

Question Number 217894 Answers: 0 Comments: 0

In △ABC holds: Σ ((cot A)/( (√(cot B + 3 cot C)))) ≥ (1/2) ((27))^(1/4)

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{holds}: \\ $$$$\Sigma\:\frac{\mathrm{cot}\:\mathrm{A}}{\:\sqrt{\mathrm{cot}\:\mathrm{B}\:\:+\:\:\mathrm{3}\:\mathrm{cot}\:\mathrm{C}}}\:\:\geqslant\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\sqrt[{\mathrm{4}}]{\mathrm{27}}\: \\ $$

Question Number 217888 Answers: 3 Comments: 0

Solve: ((x^2 −3x+2)/(x^2 −8x+15))=((x^2 −5x+6)/(x^2 −10x+24))

$${Solve}: \\ $$$$\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{15}}=\frac{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}}{{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{24}} \\ $$

Question Number 217887 Answers: 2 Comments: 0

Solve : ((x+1)/(x−2))+((x−1)/(x+2))=((2x+1)/(x−1))+((2x−1)/(x+1))

$${Solve}\:: \\ $$$$\frac{{x}+\mathrm{1}}{{x}−\mathrm{2}}+\frac{{x}−\mathrm{1}}{{x}+\mathrm{2}}=\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{1}}+\frac{\mathrm{2}{x}−\mathrm{1}}{{x}+\mathrm{1}} \\ $$

Question Number 217881 Answers: 2 Comments: 0

Question Number 217873 Answers: 1 Comments: 1

What is 5^(! ) = ?

$${What}\:{is}\:\mathrm{5}^{!\:} =\:? \\ $$

Question Number 217872 Answers: 0 Comments: 0

a , b , c > 0 ab + ac + bc = 1 Prove that: (√(a^3 + a)) + (√(b^3 + b)) + (√(c^3 + c)) ≥ 2 (√(a + b + c))

$$\mathrm{a}\:,\:\mathrm{b}\:,\:\mathrm{c}\:>\:\mathrm{0} \\ $$$$\mathrm{ab}\:+\:\mathrm{ac}\:+\:\mathrm{bc}\:=\:\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt{\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{a}}\:\:+\:\:\sqrt{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{b}}\:\:+\:\:\sqrt{\mathrm{c}^{\mathrm{3}} \:+\:\mathrm{c}}\:\:\geqslant\:\mathrm{2}\:\sqrt{\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}} \\ $$

Question Number 217871 Answers: 1 Comments: 0

n ≥ 2 Prove that: Π_(k=1) ^n tg [ (π/3) (1 + (3^k /(3^n − 1)))] = Π_(k=1) ^n ctg [ (π/3) (1 − (3^k /(3^n − 1)))]

Question Number 217858 Answers: 0 Comments: 0

Question Number 217857 Answers: 2 Comments: 0

Prove that: ((cos20°))^(1/3) + ((cos80°))^(1/3) + ((cos160°))^(1/3) = (((3 ∙ (9)^(1/3) − 6)/2))^(1/3)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{cos20}°}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{cos80}°}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{cos160}°}\:=\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{3}\:\centerdot\:\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\mathrm{6}}{\mathrm{2}}} \\ $$

Question Number 217855 Answers: 2 Comments: 0

i need help ∫_0 ^1 x^n (e^(−(x^2 /2)) )dx ,(n∈N)

$${i}\:{need}\:{help}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \left({e}^{−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}} \right){dx}\:\:,\left({n}\in\mathbb{N}\right) \\ $$

Question Number 217849 Answers: 0 Comments: 0

Question Number 217843 Answers: 0 Comments: 5

Question Number 217842 Answers: 2 Comments: 0

f(x)=(√(x^2 −6x+10)) f(3+2(√6))=?

$${f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{10}} \\ $$$${f}\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{6}}\right)=? \\ $$

Question Number 217837 Answers: 1 Comments: 0

do you guys know about Three Body problem?? when 2−Body problem we can solve equation of motions x_1 ^→ (t) , x_2 ^→ (t) but why we can′t solve 3−body problem? The reason why we can′t solve 3−Body problem is because this Equation isn′t Linear equation???

$$\mathrm{do}\:\mathrm{you}\:\mathrm{guys}\:\mathrm{know}\:\mathrm{about}\:\mathrm{Three}\:\mathrm{Body}\:\mathrm{problem}?? \\ $$$$\mathrm{when}\:\mathrm{2}−\mathrm{Body}\:\mathrm{problem}\: \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{motions}\:\overset{\rightarrow} {\boldsymbol{\mathrm{x}}}_{\mathrm{1}} \left({t}\right)\:,\:\overset{\rightarrow} {\boldsymbol{\mathrm{x}}}_{\mathrm{2}} \left({t}\right) \\ $$$$\mathrm{but}\:\mathrm{why}\:\mathrm{we}\:\mathrm{can}'\mathrm{t}\:\mathrm{solve}\:\mathrm{3}−\mathrm{body}\:\mathrm{problem}? \\ $$$$\mathrm{The}\:\mathrm{reason}\:\mathrm{why}\:\mathrm{we}\:\mathrm{can}'\mathrm{t}\:\mathrm{solve}\:\mathrm{3}−\mathrm{Body}\:\mathrm{problem} \\ $$$$\mathrm{is}\:\mathrm{because}\:\mathrm{this}\:\mathrm{Equation}\:\mathrm{isn}'\mathrm{t}\:\:\mathrm{Linear}\:\mathrm{equation}??? \\ $$

Question Number 217821 Answers: 0 Comments: 0