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Question Number 66842 Answers: 0 Comments: 2

Question Number 66845 Answers: 0 Comments: 1

A cylindrical tank of radius 2m and height 1.5m initially contains water to a depth of 50cm. Water is added to the tank at the rate of 62.84l per minute for 15 minutes. Find the new height of water in the tank.

$${A}\:{cylindrical}\:{tank}\:{of}\:{radius}\:\mathrm{2}{m}\: \\ $$$${and}\:{height}\:\mathrm{1}.\mathrm{5}{m}\:{initially}\:{contains} \\ $$$${water}\:{to}\:{a}\:{depth}\:{of}\:\mathrm{50}{cm}.\:{Water} \\ $$$${is}\:{added}\:{to}\:{the}\:{tank}\:{at}\:{the}\:{rate}\:{of}\: \\ $$$$\mathrm{62}.\mathrm{84}{l}\:{per}\:{minute}\:{for}\:\mathrm{15}\:{minutes}. \\ $$$${Find}\:{the}\:{new}\:{height}\:{of}\:{water}\:{in} \\ $$$${the}\:{tank}. \\ $$

Question Number 66833 Answers: 0 Comments: 0

Somewhere , there are scorpio, snake and mouse. We ascertain that : Every morning , each snake eats a mouse . Every afternoon ,each scorpio kills a snake. And every night , each mouse eats a scorpio. Two weeks passed and we find that there was remaining only one animal . 1) If that animal is a snake , how many snake were there two week ago? 2)If that animal is a scorpio , how many scorpio were there two weeks ago? 3)If that animal is a mouse ,how many mouse were there two weeks ago? 4)If there are remaining one animal of each breed , How many were they for each breed.

$${Somewhere}\:,\:{there}\:{are}\:{scorpio},\:{snake}\:{and}\:{mouse}. \\ $$$${We}\:{ascertain}\:{that}\:: \\ $$$${Every}\:{morning}\:,\:{each}\:{snake}\:{eats}\:{a}\:{mouse}\:. \\ $$$${Every}\:{afternoon}\:,{each}\:{scorpio}\:\:{kills}\:{a}\:{snake}. \\ $$$${And}\:{every}\:{night}\:,\:{each}\:{mouse}\:{eats}\:{a}\:{scorpio}. \\ $$$${Two}\:{weeks}\:{passed}\:{and}\:{we}\:{find}\:{that}\:{there}\:{was}\:{remaining}\:{only}\:{one}\:{animal}\:. \\ $$$$\left.\mathrm{1}\right)\:{If}\:{that}\:{animal}\:{is}\:{a}\:{snake}\:,\:{how}\:{many}\:{snake}\:{were}\:{there}\:{two}\:{week}\:{ago}? \\ $$$$\left.\mathrm{2}\right){If}\:{that}\:{animal}\:{is}\:{a}\:{scorpio}\:,\:{how}\:{many}\:{scorpio}\:{were}\:{there}\:{two}\:{weeks}\:{ago}? \\ $$$$\left.\mathrm{3}\right){If}\:{that}\:{animal}\:{is}\:{a}\:{mouse}\:,{how}\:{many}\:{mouse}\:{were}\:{there}\:\:{two}\:{weeks}\:{ago}? \\ $$$$\left.\mathrm{4}\right){If}\:{there}\:{are}\:{remaining}\:{one}\:{animal}\:{of}\:{each}\:{breed}\:,\:{How}\:{many}\:{were}\:{they}\:{for}\:{each}\:{breed}. \\ $$

Question Number 66832 Answers: 2 Comments: 0

solve the system of congruence {: ((x≡ 1 (mod 5))),((x ≡ 2 (mod 7))),((x≡ 3(mod 9))),((x ≡ 4( mod 11))) }

$${solve}\:{the}\:{system}\:{of}\:{congruence} \\ $$$$\:\:\:\left.\begin{matrix}{{x}\equiv\:\mathrm{1}\:\left({mod}\:\mathrm{5}\right)}\\{{x}\:\equiv\:\mathrm{2}\:\left({mod}\:\mathrm{7}\right)}\\{{x}\equiv\:\:\mathrm{3}\left({mod}\:\mathrm{9}\right)}\\{{x}\:\equiv\:\mathrm{4}\left(\:{mod}\:\mathrm{11}\right)}\end{matrix}\right\} \\ $$

Question Number 66830 Answers: 0 Comments: 4

evaluate. ∫_1 ^( ∞) (1/x^(2 ) ) dx. can i assume lim_(t→0) ∫_1 ^( t) (1/x^(2 ) ) dx ????

$${evaluate}. \\ $$$$\:\int_{\mathrm{1}} ^{\:\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{2}\:} }\:{dx}. \\ $$$$ \\ $$$${can}\:{i}\:{assume}\:\underset{{t}\rightarrow\mathrm{0}} {\:\mathrm{lim}}\:\int_{\mathrm{1}} ^{\:\:{t}} \frac{\mathrm{1}}{{x}^{\mathrm{2}\:} }\:{dx}\:???? \\ $$

Question Number 66827 Answers: 0 Comments: 3

Question Number 66814 Answers: 0 Comments: 0

Let consider an integer serie {a_n x^n } given by a_n = H_n =Σ_(k=1) ^n (1/k) 1) Find out the largest domain D of convergence of that integer serie 2) ∀ x∈D , explicit the sum S(x) of the {a_n x^n } 3) Calculate ∫_(−1) ^1 S(1−x)S(x) dx .

$${Let}\:{consider}\:{an}\:{integer}\:{serie}\:\left\{{a}_{{n}} {x}^{{n}} \right\}\:{given}\:{by}\:\:{a}_{{n}} \:=\:{H}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\: \\ $$$$\left.\mathrm{1}\right)\:{Find}\:{out}\:{the}\:{largest}\:{domain}\:{D}\:{of}\:{convergence}\:{of}\:{that}\:{integer}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:\forall\:{x}\in{D}\:\:,\:{explicit}\:{the}\:{sum}\:{S}\left({x}\right)\:{of}\:{the}\:\left\{{a}_{{n}} {x}^{{n}} \right\}\: \\ $$$$\left.\mathrm{3}\right)\:{Calculate}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:{S}\left(\mathrm{1}−{x}\right){S}\left({x}\right)\:{dx}\:. \\ $$$$ \\ $$$$\:\:\:\: \\ $$

Question Number 66803 Answers: 1 Comments: 3

prove that Σ_(r=k) ^n r = (1/2)n(n+1) show with a diagram that the volume of a parallepipe is a.(b×c)

$$\:{prove}\:{that} \\ $$$$\underset{{r}={k}} {\overset{{n}} {\sum}}\:{r}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{n}\left({n}+\mathrm{1}\right) \\ $$$$ \\ $$$${show}\:{with}\:{a}\:{diagram}\:{that}\:{the}\:{volume}\:{of}\:{a}\:{parallepipe}\:{is}\:\:\:{a}.\left({b}×{c}\right) \\ $$

Question Number 66802 Answers: 0 Comments: 6

given that f(x) = 3x^3 − 2x^2 + 5x + 7 find a) α + β + γ b) αβγ c) α^2 + β^2 + γ^2 d) α^3 + β^3 + γ^3 any solutions directly?

$${given}\:{that}\: \\ $$$${f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:−\:\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\:\mathrm{7}\:\:{find} \\ $$$$\left.{a}\right)\:\:\alpha\:+\:\beta\:+\:\gamma \\ $$$$\left.{b}\right)\:\alpha\beta\gamma\:\: \\ $$$$\left.{c}\right)\:\alpha^{\mathrm{2}} \:+\:\beta^{\mathrm{2}} \:+\:\gamma^{\mathrm{2}} \\ $$$$\left.{d}\right)\:\alpha^{\mathrm{3}} \:+\:\beta^{\mathrm{3}} \:+\:\gamma^{\mathrm{3}} \\ $$$${any}\:\:{solutions}\:\:{directly}? \\ $$

Question Number 66801 Answers: 0 Comments: 3

let f(x) =∫_0 ^2 (√(x+t^2 ))dt with x≥0 1) calculate f(x) 2)calculate g(x) =∫_0 ^2 (dt/(√(x+t^2 ))) 3)find the value[of ∫_0 ^2 (√(4+t^2 ))dt and ∫_0 ^2 (dt/(√(3+t^2 ))) 4) give g^′ (x) at form of integral.

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}} \sqrt{{x}+{t}^{\mathrm{2}} }{dt}\:\:\:{with}\:{x}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}} \:\frac{{dt}}{\sqrt{{x}+{t}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\left[{of}\:\int_{\mathrm{0}} ^{\mathrm{2}} \sqrt{\mathrm{4}+{t}^{\mathrm{2}} }{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{2}} \frac{{dt}}{\sqrt{\mathrm{3}+{t}^{\mathrm{2}} }}\right. \\ $$$$\left.\mathrm{4}\right)\:{give}\:{g}^{'} \left({x}\right)\:{at}\:{form}\:{of}\:{integral}. \\ $$

Question Number 66800 Answers: 0 Comments: 1

calculate U_n =∫_(1/n) ^n ((arctan(x))/(1+x^2 ))dx and determine lim_(n→+∞) U_n 2)find nature of Σ U_n

$${calculate}\:{U}_{{n}} =\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\:\:\frac{{arctan}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$${and}\:{determine}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 66799 Answers: 0 Comments: 0

let S_n =Σ_(k=1) ^n (((−1)^k )/(√k)) find a equivalent of S_n when n→+∞

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\sqrt{{k}}}\:\:{find}\:{a}\:{equivalent}\:{of}\:{S}_{{n}} \:{when}\:{n}\rightarrow+\infty \\ $$

Question Number 66798 Answers: 0 Comments: 0

find S_n =Σ_(k=0) ^n k^2 (C_n ^k )^2

$${find}\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:\left({C}_{{n}} ^{{k}} \right)^{\mathrm{2}} \\ $$

Question Number 66797 Answers: 0 Comments: 0

find S_n =Σ_(k=0) ^n (C_n ^k )^3