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Question Number 224432 Answers: 1 Comments: 4

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Question Number 224406 Answers: 1 Comments: 0

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Question Number 224393 Answers: 0 Comments: 2

there is a number when the digits of the number are suffled randomly a new number is generated which is double of the first number The question is what is the smallest number which satisfies the rules??

$${there}\:{is}\:{a}\:{number}\: \\ $$$${when}\:{the}\:{digits}\:{of}\:{the}\:{number} \\ $$$${are}\:{suffled}\:{randomly}\:{a}\:{new} \\ $$$${number}\:{is}\:{generated}\:{which} \\ $$$${is}\:{double}\:{of}\:{the}\:{first}\:{number} \\ $$$${The}\:{question}\:{is} \\ $$$${what}\:{is}\:{the}\:{smallest}\:{number} \\ $$$${which}\:{satisfies}\:{the}\:{rules}?? \\ $$

Question Number 224392 Answers: 2 Comments: 0

−∞<a<b<∞ and 0<λ<1 x_1 = a , x_2 = b x_(n+2) = λx_n + (1−λ)x_(n+1) ∀ n ∈ N find x_(n ) = ?

$$\:\:\:\:\:\:\:−\infty<{a}<{b}<\infty\:\:{and}\:\mathrm{0}<\lambda<\mathrm{1}\:\: \\ $$$$\:\:\:\:\:\:\:{x}_{\mathrm{1}} \:=\:{a}\:,\:{x}_{\mathrm{2}} \:=\:{b} \\ $$$$\:\:\:\:\:\:\:\:{x}_{{n}+\mathrm{2}} \:=\:\lambda{x}_{{n}} \:+\:\left(\mathrm{1}−\lambda\right){x}_{{n}+\mathrm{1}} \:\:\forall\:{n}\:\in\:\mathbb{N} \\ $$$$\:\:\mathrm{find}\:\:{x}_{{n}\:} \:=\:?\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 224382 Answers: 0 Comments: 7

Q224176. Sir can this be solved without using trigonometry?? If not can you please show me the way which uses trig.the least??

$${Q}\mathrm{224176}. \\ $$$${Sir}\:{can}\:{this}\:{be}\:{solved}\:{without} \\ $$$${using}\:{trigonometry}?? \\ $$$${If}\:{not}\:{can}\:{you}\:{please}\:{show}\:{me} \\ $$$${the}\:{way}\:{which}\:{uses}\:{trig}.{the}\:{least}?? \\ $$

Question Number 224381 Answers: 0 Comments: 0

Question Number 224380 Answers: 0 Comments: 2

Please some geometry Q Living an inactive live for several days...

$${Please}\:{some}\:{geometry}\:{Q} \\ $$$${Living}\:{an}\:{inactive}\:{live}\:{for} \\ $$$${several}\:{days}... \\ $$

Question Number 224373 Answers: 0 Comments: 0

Show that ; I = ∫_( 0) ^( 1) ∫_( 0) ^( 1) ((ln(1+(√(xy))) ln(1+ (√((1−x)/(1−y)))))/( (√(1−x)) (√(1−y)) (x+y))) dxdy I = ζ(3)−((70)/(351))−((280)/(351)) ln 2−((40)/(117)) ln^2 2 +((412)/(351)) ln^3 2 + ((167)/(2106)) π^2 ln 2

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}}\:; \\ $$$$\:\:\:\:\:\mathcal{I}\:=\:\underset{\:\:\mathrm{0}} {\overset{\:\:\mathrm{1}} {\int}}\underset{\:\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\:\frac{\mathrm{ln}\left(\mathrm{1}+\sqrt{{xy}}\right)\:\mathrm{ln}\left(\mathrm{1}+\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}−{y}}}\right)}{\:\sqrt{\mathrm{1}−{x}}\:\:\sqrt{\mathrm{1}−{y}}\:\:\left({x}+{y}\right)}\:\:{dxdy}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathcal{I}\:=\:\zeta\left(\mathrm{3}\right)−\frac{\mathrm{70}}{\mathrm{351}}−\frac{\mathrm{280}}{\mathrm{351}}\:\mathrm{ln}\:\mathrm{2}−\frac{\mathrm{40}}{\mathrm{117}}\:\mathrm{ln}^{\mathrm{2}} \:\mathrm{2}\:+\frac{\mathrm{412}}{\mathrm{351}}\:\mathrm{ln}^{\mathrm{3}} \:\mathrm{2}\:+\:\frac{\mathrm{167}}{\mathrm{2106}}\:\pi^{\mathrm{2}} \:\mathrm{ln}\:\mathrm{2}\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

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

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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

$$\:\: \\ $$$$ \\ $$$$ \\ $$$$ ? \\ $$

Question Number 224325 Answers: 0 Comments: 4

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Question Number 224314 Answers: 0 Comments: 1

solve ((1−(√x)))^(1/3) =2

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

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