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Question Number 137014    Answers: 0   Comments: 2

Question Number 137035    Answers: 1   Comments: 1

Given a 10−digit number X = 1345789026 How many 10−digit number that can be made using every digit from X, with condition: If a number n is located in k^(th) position of X, then the new created number must not contain number n in k^(th) position Example: • Number 1 is located in 1^(st) position of X, hence 1234567890 is not valid, but 2134567890 is valid • Number 5 and 0 are located in 4^(th) and 8^(th) position of X, hence 9435162087 is not valid, but 9431506287 is valid. • 1345026789 is not valid • and so on...

$$\mathrm{Given}\:\mathrm{a}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:{X}\:=\:\mathrm{1345789026} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{using}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{from}\:{X},\:\mathrm{with}\:\mathrm{condition}: \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:{n}\:\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{new}\:\mathrm{created}\:\mathrm{number}\:\mathrm{must}\:\mathrm{not}\:\mathrm{contain} \\ $$$$\mathrm{number}\:{n}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position} \\ $$$$ \\ $$$$\mathrm{Example}: \\ $$$$\bullet\:\mathrm{Number}\:\mathrm{1}\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:\mathrm{1}^{{st}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{hence} \\ $$$$\mathrm{1234567890}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid},\:\mathrm{but}\:\mathrm{2134567890} \\ $$$$\mathrm{is}\:\mathrm{valid} \\ $$$$\bullet\:\mathrm{Number}\:\mathrm{5}\:\mathrm{and}\:\mathrm{0}\:\mathrm{are}\:\mathrm{located}\:\mathrm{in}\:\mathrm{4}^{{th}} \:\mathrm{and}\:\mathrm{8}^{{th}} \:\mathrm{position} \\ $$$$\mathrm{of}\:{X},\:\mathrm{hence}\:\mathrm{9435162087}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid},\:\mathrm{but} \\ $$$$\mathrm{9431506287}\:\mathrm{is}\:\mathrm{valid}. \\ $$$$\bullet\:\mathrm{1345026789}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid} \\ $$$$\bullet\:\mathrm{and}\:\mathrm{so}\:\mathrm{on}... \\ $$

Question Number 137011    Answers: 4   Comments: 2

Question Number 137010    Answers: 0   Comments: 1

if f(x,y)=(xy)^3 +e^(xy) +sec((y/x)) find f_(xx) , f_(yy) , f_(xy) , f_(yx)

$${if}\:{f}\left({x},{y}\right)=\left({xy}\right)^{\mathrm{3}} +{e}^{{xy}} +{sec}\left(\frac{{y}}{{x}}\right)\:{find} \\ $$$${f}_{{xx}} \:\:,\:{f}_{{yy}} \:,\:{f}_{{xy}} \:\:,\:\:{f}_{{yx}} \\ $$

Question Number 137007    Answers: 0   Comments: 3

Question Number 137005    Answers: 0   Comments: 1

Hi, guyz ! For R = (1/2)×(3/4)×(5/6)×...×((223)/(224)) and S = (2/3)×(4/5)×(6/7)×...×((224)/(225)) . Prove that : R < (1/(15)) < S.

$$\boldsymbol{\mathrm{Hi}},\:\boldsymbol{\mathrm{guyz}}\:! \\ $$$$\boldsymbol{\mathrm{For}}\:\boldsymbol{\mathrm{R}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{5}}{\mathrm{6}}×...×\frac{\mathrm{223}}{\mathrm{224}}\:\:\:\boldsymbol{\mathrm{and}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{S}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{4}}{\mathrm{5}}×\frac{\mathrm{6}}{\mathrm{7}}×...×\frac{\mathrm{224}}{\mathrm{225}}\:. \\ $$$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\::\:\:\boldsymbol{\mathrm{R}}\:<\:\frac{\mathrm{1}}{\mathrm{15}}\:<\:\boldsymbol{\mathrm{S}}. \\ $$

Question Number 137004    Answers: 3   Comments: 0

find ∫ ((√x)/( (√(x−1))+(√(x+1))))dx

$${find}\:\int\:\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}{dx} \\ $$

Question Number 137003    Answers: 1   Comments: 0

find ∫_0 ^(π/4) ((cos^5 t)/(cos(5t)))dt

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{cos}^{\mathrm{5}} {t}}{{cos}\left(\mathrm{5}{t}\right)}{dt} \\ $$

Question Number 137001    Answers: 0   Comments: 0

calculate ∫_3 ^∞ (dx/((x^2 −4)^5 (x+1)^3 ))

$${calculate}\:\:\int_{\mathrm{3}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{5}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 136999    Answers: 2   Comments: 0

......advanced ...... calculus.... 𝛗=∫_0 ^( ∞) ln(x).sin(x).e^(−x) dx=?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:......{advanced}\:\:......\:\:\:{calculus}.... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} {ln}\left({x}\right).{sin}\left({x}\right).{e}^{−{x}} {dx}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 136996    Answers: 0   Comments: 0

Given a,b and c is real number satisfy a+b+c = 4 and ab+ac+bc = 3 . The value of ⌈ 3c+2 ⌉ = ?

$$\mathrm{Given}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{is}\:\mathrm{real}\:\mathrm{number}\:\mathrm{satisfy} \\ $$$$\mathrm{a}+\mathrm{b}+\mathrm{c}\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{ab}+\mathrm{ac}+\mathrm{bc}\:=\:\mathrm{3}\:.\:\mathrm{The}\:\mathrm{value} \\ $$$$\mathrm{of}\:\lceil\:\mathrm{3c}+\mathrm{2}\:\rceil\:=\:? \\ $$

Question Number 136995    Answers: 0   Comments: 0

1−(((1.1.3)/(2.3.4)))(1/(1!))+(((3.3.7)/(2^2 .3^2 .4^2 )))(1/(2!))−(((5.7.10)/(2^3 .3^3 .4^3 )))(1/(3!))−....

$$\mathrm{1}−\left(\frac{\mathrm{1}.\mathrm{1}.\mathrm{3}}{\mathrm{2}.\mathrm{3}.\mathrm{4}}\right)\frac{\mathrm{1}}{\mathrm{1}!}+\left(\frac{\mathrm{3}.\mathrm{3}.\mathrm{7}}{\mathrm{2}^{\mathrm{2}} .\mathrm{3}^{\mathrm{2}} .\mathrm{4}^{\mathrm{2}} }\right)\frac{\mathrm{1}}{\mathrm{2}!}−\left(\frac{\mathrm{5}.\mathrm{7}.\mathrm{10}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}^{\mathrm{3}} .\mathrm{4}^{\mathrm{3}} }\right)\frac{\mathrm{1}}{\mathrm{3}!}−.... \\ $$

Question Number 136992    Answers: 2   Comments: 0

ℓ = ∫ ((cos 7x−cos 8x)/(1+2cos 5x)) dx =?

$$\ell\:=\:\int\:\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$

Question Number 136990    Answers: 0   Comments: 0

Given a cube ABCD.EFGH where point Z is the midpoint of AE, point R on the edge of BC such that BR: CR = 3: 1, point U on the CG edge so that CG = 2GU. where x is the angle of the BR line to the BUZ plane. the value of sin x is equal to

$$ \\ $$Given a cube ABCD.EFGH where point Z is the midpoint of AE, point R on the edge of BC such that BR: CR = 3: 1, point U on the CG edge so that CG = 2GU. where x is the angle of the BR line to the BUZ plane. the value of sin x is equal to

Question Number 136988    Answers: 2   Comments: 0

whats the intersiction of the curves r=(1/(1−cosθ)) and r=(1/(1+cosθ)) ?

$${whats}\:{the}\:{intersiction}\:{of}\:{the}\:{curves}\:{r}=\frac{\mathrm{1}}{\mathrm{1}−{cos}\theta} \\ $$$$ \\ $$$${and}\:{r}=\frac{\mathrm{1}}{\mathrm{1}+{cos}\theta}\:? \\ $$

Question Number 136987    Answers: 0   Comments: 0

⇒2x

$$\Rightarrow\mathrm{2}{x} \\ $$

Question Number 136984    Answers: 0   Comments: 4

Question Number 136983    Answers: 0   Comments: 0

Question Number 137016    Answers: 1   Comments: 0

Question Number 136971    Answers: 1   Comments: 0

∫csc^4 (x) cot^2 (x) dx

$$\int{csc}^{\mathrm{4}} \left({x}\right)\:{cot}^{\mathrm{2}} \left({x}\right)\:{dx} \\ $$

Question Number 136969    Answers: 1   Comments: 0

∫_0 ^( π/2) (((1+sec^2 t) (√(sec t)))/((1+sec t)^2 −2)) dt =?

$$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \frac{\left(\mathrm{1}+\mathrm{sec}\:^{\mathrm{2}} \mathrm{t}\right)\:\sqrt{\mathrm{sec}\:\mathrm{t}}}{\left(\mathrm{1}+\mathrm{sec}\:\mathrm{t}\right)^{\mathrm{2}} −\mathrm{2}}\:\mathrm{dt}\:=?\: \\ $$

Question Number 136968    Answers: 3   Comments: 0

1)∫(8/(x^2 (√(4−x^2 ))))dx 2)∫((x−6 )/(2x^2 −5x+3))

$$\left.\mathrm{1}\right)\int\frac{\mathrm{8}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}−{x}^{\mathrm{2}} }}{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{{x}−\mathrm{6}\:}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{3}} \\ $$

Question Number 136966    Answers: 1   Comments: 0

unsolved question....... ∫_0 ^∞ (cos (x^2 )−cos x)(dx/x)=(γ/2)

$${unsolved}\:{question}....... \\ $$$$\int_{\mathrm{0}} ^{\infty} \left(\mathrm{cos}\:\left({x}^{\mathrm{2}} \right)−\mathrm{cos}\:{x}\right)\frac{{dx}}{{x}}=\frac{\gamma}{\mathrm{2}} \\ $$

Question Number 136953    Answers: 0   Comments: 0

Q136005

$${Q}\mathrm{136005} \\ $$

Question Number 136950    Answers: 2   Comments: 0

Question Number 136948    Answers: 3   Comments: 0

∫((√(4+x^2 ))/x)dx

$$\int\frac{\sqrt{\mathrm{4}+{x}^{\mathrm{2}} }}{{x}}{dx} \\ $$

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