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Question Number 116226 Answers: 2 Comments: 1

(1/(2+(√2))) +(1/(3(√2)+2(√3))) +(1/(4(√3)+3(√4)))+...+(1/(100(√(99))+99(√(100))))

$$\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}+\mathrm{2}\sqrt{\mathrm{3}}}\:+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{3}\sqrt{\mathrm{4}}}+...+\frac{\mathrm{1}}{\mathrm{100}\sqrt{\mathrm{99}}+\mathrm{99}\sqrt{\mathrm{100}}} \\ $$

Question Number 116123 Answers: 0 Comments: 0

Study according to the values of the real α the convergence of the integral ∫_α ^(+∞) ((ln∣x∣)/( ((x(x+1)))^(1/3) ))dx

$$ \\ $$$$\mathrm{Study}\:\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{real}\:\alpha\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{integral}\:\:\int_{\alpha} ^{+\infty} \frac{{ln}\mid{x}\mid}{\:\sqrt[{\mathrm{3}}]{{x}\left({x}+\mathrm{1}\right)}}{dx} \\ $$

Question Number 116105 Answers: 2 Comments: 0

solve the Cauchy-Euler Differential Equation by substituting x=e^t x^3 (d^3 y/dx^3 ) + 2x^2 (d^2 y/dx^2 ) + 2y = 10x + ((10)/x)

$${solve}\:{the}\:{Cauchy}-{Euler}\: \\ $$$${Differential}\:{Equation}\:{by} \\ $$$${substituting}\:{x}={e}^{{t}} \\ $$$${x}^{\mathrm{3}} \:\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }\:+\:\mathrm{2}{x}^{\mathrm{2}} \:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{2}{y}\:=\:\mathrm{10}{x}\:+\:\frac{\mathrm{10}}{{x}} \\ $$$$ \\ $$

Question Number 116098 Answers: 0 Comments: 0

1)calculate f(x)=∫_0 ^(2π) (dθ/(x^2 −2x cosθ +1)) 0<θ<(π/2) 2)explicite ∫_0 ^(2π) ((cosθ)/((x^2 −2xcosθ +1)^2 ))dθ

$$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{d}\theta}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}\:\mathrm{cos}\theta\:+\mathrm{1}}\:\:\:\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$

Question Number 116097 Answers: 3 Comments: 0

calculate ∫_0 ^∞ ((lnx)/(x^4 +1))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{1}}\mathrm{dx}\: \\ $$

Question Number 116096 Answers: 1 Comments: 0

find ∫_0 ^∞ ((lnx)/(x^2 −i))dx (i=(√(−1)))

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{x}^{\mathrm{2}} −\mathrm{i}}\mathrm{dx}\:\:\:\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$

Question Number 116094 Answers: 1 Comments: 0

Question Number 116093 Answers: 2 Comments: 0

Find the equation of a circle which touches x−axis and the line y=x in the 1^(st) quadrant. Determine its centre and radius if it touches the line y+x=4.

$${Find}\:{the}\:{equation}\:{of}\:{a}\:{circle}\:{which}\:{touches} \\ $$$${x}−{axis}\:{and}\:{the}\:{line}\:{y}={x}\:{in}\:{the}\:\mathrm{1}^{{st}} \:{quadrant}. \\ $$$${Determine}\:{its}\:{centre}\:{and}\:{radius}\:{if}\:{it}\:{touches}\:{the}\:{line}\:{y}+{x}=\mathrm{4}. \\ $$

Question Number 116092 Answers: 1 Comments: 2

Solve for x and y if x^y =36

$${Solve}\:{for}\:{x}\:{and}\:{y}\:{if} \\ $$$${x}^{{y}} =\mathrm{36} \\ $$

Question Number 116091 Answers: 2 Comments: 0

Is there a formular to tell how many times a digit occur in an interval. e.g. How many times digits 2 occur between 1 − 100

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{formular}\:\mathrm{to}\:\mathrm{tell}\:\mathrm{how}\:\mathrm{many}\:\mathrm{times}\:\mathrm{a}\:\mathrm{digit}\:\mathrm{occur}\:\mathrm{in}\:\mathrm{an}\:\mathrm{interval}. \\ $$$$ \\ $$$$\mathrm{e}.\mathrm{g}.\:\:\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{digits}\:\:\mathrm{2}\:\:\mathrm{occur}\:\mathrm{between}\:\:\mathrm{1}\:−\:\mathrm{100} \\ $$

Question Number 116090 Answers: 1 Comments: 0

what is 3(7/8)hrs?

$${what}\:{is}\:\mathrm{3}\frac{\mathrm{7}}{\mathrm{8}}{hrs}? \\ $$

Question Number 116087 Answers: 0 Comments: 2

soit f la fonction de^ finie sur[0,2] par f(x)=3 si x∈[0,2]∩Q f(x)=1 si x∈[0,2]∩R\Q

$${soit}\:{f}\:{la}\:{fonction}\:{d}\acute {{e}finie}\:{sur}\left[\mathrm{0},\mathrm{2}\right]\:{par}\: \\ $$$${f}\left({x}\right)=\mathrm{3}\:\:\:{si}\:{x}\in\left[\mathrm{0},\mathrm{2}\right]\cap\mathbb{Q} \\ $$$${f}\left({x}\right)=\mathrm{1}\:\:\:{si}\:{x}\in\left[\mathrm{0},\mathrm{2}\right]\cap\mathbb{R}\backslash\mathbb{Q} \\ $$

Question Number 116083 Answers: 0 Comments: 0

Given X ∣ Θ=θ ∽ Uniform(0,θ) and Θ ∽ Uniform(20,40). Find the cdf of X, F_X (x) for x∈[0,20) and x∈[20,40)

$$\mathrm{Given}\:{X}\:\mid\:\Theta=\theta\:\backsim\:{Uniform}\left(\mathrm{0},\theta\right)\:\mathrm{and}\: \\ $$$$\Theta\:\backsim\:{Uniform}\left(\mathrm{20},\mathrm{40}\right). \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{cdf}\:\mathrm{of}\:{X},\:\:{F}_{{X}} \left({x}\right)\:\mathrm{for}\:{x}\in\left[\mathrm{0},\mathrm{20}\right)\:\mathrm{and}\:{x}\in\left[\mathrm{20},\mathrm{40}\right) \\ $$

Question Number 116085 Answers: 0 Comments: 1

6+log_(3/2) {(1/(3(√2)))(√(4−(1/(3(√2)))(√(4−(1/(3(√2)))(√(4−(1/(3(√2)))∙∙∙))))))}= ?

$$\mathrm{6}+\mathrm{log}_{\frac{\mathrm{3}}{\mathrm{2}}} \left\{\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\centerdot\centerdot\centerdot}}}\right\}=\:? \\ $$

Question Number 116079 Answers: 1 Comments: 0

prove that Re=((ρ∙v∙d)/μ) renulds number

$${prove}\:{that}\:{Re}=\frac{\rho\centerdot{v}\centerdot{d}}{\mu}\:\:\:\:\:{renulds}\:{number} \\ $$

Question Number 116078 Answers: 1 Comments: 0

prove that Fr=(v^2 /(gh)) froude numer

$${prove}\:{that}\:\:\:{Fr}=\frac{{v}^{\mathrm{2}} }{{gh}}\:\:\:\:{froude}\:{numer} \\ $$

Question Number 116061 Answers: 1 Comments: 0

Kent Mark is running for class president. Assume that there are a total of n ca− ndidates running, where n is a natu− ral number. After the votes are tallied, Kent Mark is told only the fraction of votes that he recieved. Suppose he recieved less than (1/n) of the votes. Show that he cannot have won the election.

$$\mathrm{Kent}\:\mathrm{Mark}\:\mathrm{is}\:\mathrm{running}\:\mathrm{for}\:\mathrm{class}\:\mathrm{president}. \\ $$$$\mathrm{Assume}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{a}\:\mathrm{total}\:\mathrm{of}\:\mathrm{n}\:\mathrm{ca}− \\ $$$$\mathrm{ndidates}\:\mathrm{running},\:\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{natu}− \\ $$$$\mathrm{ral}\:\mathrm{number}. \\ $$$$\mathrm{After}\:\mathrm{the}\:\mathrm{votes}\:\mathrm{are}\:\mathrm{tallied},\:\mathrm{Kent}\:\mathrm{Mark} \\ $$$$\mathrm{is}\:\mathrm{told}\:\mathrm{only}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{of}\:\mathrm{votes}\:\mathrm{that}\:\mathrm{he} \\ $$$$\mathrm{recieved}. \\ $$$$\mathrm{Suppose}\:\mathrm{he}\:\mathrm{recieved}\:\mathrm{less}\:\mathrm{than}\:\frac{\mathrm{1}}{\mathrm{n}}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{votes}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{he}\:\mathrm{cannot}\:\mathrm{have}\:\mathrm{won} \\ $$$$\mathrm{the}\:\mathrm{election}. \\ $$

Question Number 116059 Answers: 2 Comments: 0

Σ_(n=1) ^∞ ((n!)/3^(n+1) )

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!}{\mathrm{3}^{{n}+\mathrm{1}} } \\ $$

Question Number 116057 Answers: 2 Comments: 0

Σ_(n=2) ^∞ (3/(3n+1))=?

$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{3}}{\mathrm{3}{n}+\mathrm{1}}=? \\ $$

Question Number 116056 Answers: 2 Comments: 0

Σ_(n=1) ^∞ (5^n /(n!))=?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{5}^{{n}} }{{n}!}=? \\ $$

Question Number 116055 Answers: 1 Comments: 1

3(d^2 y/dx^2 )+4(dy/dx)+5y=0 y=?