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Question Number 224358 Answers: 2 Comments: 1

Question Number 224360 Answers: 1 Comments: 1

Find the equation of the circle which touches the circles x² + y² - 2x + 4y = 1, x² + y² - 12x + 2y = 4 and x² + y² + 2x - 12y + 12 = 0.

Question Number 224342 Answers: 3 Comments: 0

Question Number 224337 Answers: 1 Comments: 0

Question Number 224336 Answers: 2 Comments: 0

Question Number 224335 Answers: 1 Comments: 0

Question Number 224331 Answers: 0 Comments: 0

a,b,c > 0 prove that Σ a^2 ≥ Σ ab + (1/8) Σ (∣a−c∣ + ∣b−c∣)^2

$$\mathrm{a},\mathrm{b},\mathrm{c}\:>\:\mathrm{0} \\ $$$$\mathrm{prove}\:\mathrm{that} \\ $$$$\Sigma\:\mathrm{a}^{\mathrm{2}} \:\geqslant\:\Sigma\:\mathrm{ab}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:\Sigma\:\left(\mid\mathrm{a}−\mathrm{c}\mid\:+\:\mid\mathrm{b}−\mathrm{c}\mid\right)^{\mathrm{2}} \\ $$

Question Number 224330 Answers: 0 Comments: 0

recently I read a nice proof to the following problem I know everybody can look it up but if you′re interested in learning something try it by yourself first don′t post the answer you found on the www but post your thoughts instead randomly choose m, n ∈N then what is the probability for gcd (m, n) =1

$$\mathrm{recently}\:\mathrm{I}\:\mathrm{read}\:\mathrm{a}\:\mathrm{nice}\:\mathrm{proof}\:\mathrm{to}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{problem} \\ $$$$\mathrm{I}\:\mathrm{know}\:\mathrm{everybody}\:\mathrm{can}\:\mathrm{look}\:\mathrm{it}\:\mathrm{up}\:\mathrm{but}\:\mathrm{if}\:\mathrm{you}'\mathrm{re} \\ $$$$\mathrm{interested}\:\mathrm{in}\:\mathrm{learning}\:\mathrm{something}\:\mathrm{try}\:\mathrm{it}\:\mathrm{by} \\ $$$$\mathrm{yourself}\:\mathrm{first} \\ $$$$\mathrm{don}'\mathrm{t}\:\mathrm{post}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{you}\:\mathrm{found}\:\mathrm{on}\:\mathrm{the} \\ $$$${www}\:\mathrm{but}\:\mathrm{post}\:\mathrm{your}\:\mathrm{thoughts}\:\mathrm{instead} \\ $$$$ \\ $$$$\mathrm{randomly}\:\mathrm{choose}\:{m},\:{n}\:\in\mathbb{N} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{for} \\ $$$$\mathrm{gcd}\:\left({m},\:{n}\right)\:=\mathrm{1} \\ $$

Question Number 224327 Answers: 1 Comments: 1

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$$\:\:\:\rightleftharpoons \\ $$

Question Number 224325 Answers: 0 Comments: 4

Question Number 224324 Answers: 1 Comments: 0

Question Number 224320 Answers: 1 Comments: 0

Question Number 224316 Answers: 0 Comments: 1

Question Number 224314 Answers: 0 Comments: 1

solve ((1−(√x)))^(1/3) =2

$${solve}\:\sqrt[{\mathrm{3}}]{\mathrm{1}−\sqrt{{x}}}=\mathrm{2} \\ $$

Question Number 224312 Answers: 1 Comments: 0

Question Number 224305 Answers: 1 Comments: 0

Question Number 224302 Answers: 1 Comments: 1

Question Number 224293 Answers: 2 Comments: 1

Question Number 224288 Answers: 1 Comments: 2

P= Π_(k=1) ^∞ (1/( (√(1+(1/k))) (1−(1/(2k))))) =?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{P}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{k}}}\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right)}\:=?\:\:\:\: \\ $$$$ \\ $$

Question Number 224282 Answers: 2 Comments: 1

Question Number 224261 Answers: 0 Comments: 7

If I have 10 people and I want to create pairings, so that every person is matched with every other person at least once, how many unique pairings will there be in total?

Question Number 224255 Answers: 3 Comments: 2

Question Number 224249 Answers: 2 Comments: 3

Question Number 224248 Answers: 0 Comments: 0

∫_0 ^1 ((ln(1−x)Li_2 (1−(√x)))/x) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{Li}_{\mathrm{2}} \left(\mathrm{1}−\sqrt{\mathrm{x}}\right)}{\mathrm{x}}\:\:\mathrm{dx} \\ $$$$ \\ $$

Question Number 224246 Answers: 2 Comments: 1

Question Number 224234 Answers: 3 Comments: 0

(√x)+(√y)=7 (√(x+y))=5 Find (x,y).

$$\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=\mathrm{7} \\ $$$$\sqrt{\mathrm{x}+\mathrm{y}}=\mathrm{5} \\ $$$$\mathrm{Find}\:\left(\mathrm{x},\mathrm{y}\right). \\ $$

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