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Question Number 68349    Answers: 1   Comments: 0

Question Number 68346    Answers: 0   Comments: 0

Question Number 68342    Answers: 3   Comments: 1

Question Number 68336    Answers: 1   Comments: 1

A man gave $5,720.00 to be shared among his son and three daughters. If each of the daughter′s share is (3/4) of the son′s share, how much did the son receive?

$$\mathrm{A}\:\mathrm{man}\:\mathrm{gave}\:\$\mathrm{5},\mathrm{720}.\mathrm{00}\:\mathrm{to}\:\mathrm{be}\:\mathrm{shared}\:\mathrm{among} \\ $$$$\mathrm{his}\:\mathrm{son}\:\mathrm{and}\:\mathrm{three}\:\mathrm{daughters}.\:\mathrm{If}\:\mathrm{each}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{daughter}'\mathrm{s}\:\mathrm{share}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{son}'\mathrm{s}\:\mathrm{share}, \\ $$$$\mathrm{how}\:\mathrm{much}\:\mathrm{did}\:\mathrm{the}\:\mathrm{son}\:\mathrm{receive}? \\ $$

Question Number 68331    Answers: 2   Comments: 0

Differentiate y=ln tan^(−1) (3x^2 )_

$${Differentiate}\:{y}={ln}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{3}{x}^{\mathrm{2}} \underset{} {\right)} \\ $$

Question Number 68329    Answers: 0   Comments: 0

y=ln (sinx+x^2 )

$${y}=\mathrm{ln}\:\left({sinx}+{x}^{\mathrm{2}} \right) \\ $$

Question Number 68327    Answers: 1   Comments: 0

y=(1−2x^(−7) )^3

$${y}=\left(\mathrm{1}−\mathrm{2}{x}^{−\mathrm{7}} \right)^{\mathrm{3}} \\ $$

Question Number 68316    Answers: 0   Comments: 1

∫(4sin 3x+(e^(4x) /4))

$$\int\left(\mathrm{4sin}\:\mathrm{3}{x}+\frac{{e}^{\mathrm{4}{x}} }{\mathrm{4}}\right) \\ $$

Question Number 68315    Answers: 0   Comments: 1

∫(((x^(−3) +2x−4)/x))

$$\int\left(\frac{{x}^{−\mathrm{3}} +\mathrm{2}{x}−\mathrm{4}}{{x}}\right) \\ $$

Question Number 68309    Answers: 1   Comments: 3

Question Number 68313    Answers: 0   Comments: 1

∫(1−(6/x)+(2/x^2 )+(√x))

$$\int\left(\mathrm{1}−\frac{\mathrm{6}}{{x}}+\frac{\mathrm{2}}{{x}^{\mathrm{2}} }+\sqrt{{x}}\right) \\ $$

Question Number 68305    Answers: 1   Comments: 3

Question Number 68303    Answers: 0   Comments: 0

Question Number 68308    Answers: 1   Comments: 0

solve y′′′=y′′y′

$${solve}\:{y}'''={y}''{y}' \\ $$

Question Number 68294    Answers: 0   Comments: 0

Question Number 68285    Answers: 1   Comments: 2

two students ngum ebon gave their ages as 124_4 and 33_x respectively.if both of them are of thesame ages .find in what base ebon gave her age

$${two}\:{students}\:{ngum}\:{ebon}\:{gave}\:{their}\:{ages}\:{as}\:\mathrm{124}_{\mathrm{4}} {and}\:\mathrm{33}_{{x}} {respectively}.{if}\:{both}\:{of}\:{them}\:{are}\:{of}\:{thesame}\:{ages}\:.{find}\:{in}\:{what}\:{base}\:{ebon}\:{gave}\:{her}\:{age} \\ $$

Question Number 68280    Answers: 1   Comments: 1

given that 432_n −413_n =11_(10) .find the value of n

$${given}\:{that}\:\mathrm{432}_{{n}} −\mathrm{413}_{{n}} =\mathrm{11}_{\mathrm{10}} .{find}\:{the}\:{value}\:{of}\:{n} \\ $$

Question Number 68289    Answers: 1   Comments: 0

A circle is divided into two equal parts By An arc with center on the circle. Determine (a) The length of the arc (b)The ratio in which the arc divides the diameter meeting the center of the arc.

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{parts} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{By} \\ $$$$\:\mathrm{An}\:\mathrm{arc}\:\mathrm{with}\:\mathrm{center}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circle}. \\ $$$$\mathcal{D}{etermine} \\ $$$$\:\:\left({a}\right)\:{The}\:{length}\:{of}\:{the}\:{arc} \\ $$$$\:\:\left({b}\right){The}\:{ratio}\:{in}\:{which}\:{the}\:{arc} \\ $$$$\:\:\:\:\:\:\:\:{divides}\:{the}\:{diameter}\: \\ $$$$\:\:\:\:\:\:\:\:{meeting}\:{the}\:{center}\:{of}\:{the}\:{arc}. \\ $$

Question Number 68272    Answers: 1   Comments: 0

Question Number 68271    Answers: 0   Comments: 0

Find J=∫_0 ^1 ((W(−ulnu))/(ulnu)) du when W is the lambert function

$$\:\:{Find}\:\:{J}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{W}\left(−{ulnu}\right)}{{ulnu}}\:{du}\:\:\:\:{when}\:\:{W}\:{is}\:{the}\:{lambert}\:{function} \\ $$

Question Number 68270    Answers: 1   Comments: 3

Prove that if Li_2 (x)=Σ_(n=1) (x^n /n^2 ) then ∀ x Li_2 (x)+Li_2 (1−x) = (π^2 /6) −ln(x)ln(1−x) ∀ x∉[0:1] Li_2 (x)+Li_2 ((1/x)) = −(π^2 /6) −[ln(−x)]^2 Find A=Σ_(n=1) ^∞ (ϕ^n /n^2 ) and B=Σ_(n=1) ^∞ (2^n /n^2 )

$$\:{Prove}\:{that}\:\:{if}\:\:{Li}_{\mathrm{2}} \left({x}\right)=\underset{{n}=\mathrm{1}} {\sum}\:\frac{{x}^{{n}} }{{n}^{\mathrm{2}} }\:\:\:{then} \\ $$$$\forall\:{x}\:\:{Li}_{\mathrm{2}} \left({x}\right)+{Li}_{\mathrm{2}} \left(\mathrm{1}−{x}\right)\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:−{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)\:\: \\ $$$$\forall\:{x}\notin\left[\mathrm{0}:\mathrm{1}\right]\:{Li}_{\mathrm{2}} \left({x}\right)+{Li}_{\mathrm{2}} \left(\frac{\mathrm{1}}{{x}}\right)\:=\:−\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:−\left[{ln}\left(−{x}\right)\right]^{\mathrm{2}} \:\: \\ $$$${Find}\:\:{A}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\varphi^{{n}} }{{n}^{\mathrm{2}} }\:\:{and}\:\:{B}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{2}^{{n}} }{{n}^{\mathrm{2}} }\:\: \\ $$

Question Number 68260    Answers: 0   Comments: 1

find f(x) if f((1/x))+f(1−x)=x

$${find}\:{f}\left({x}\right)\:{if}\: \\ $$$${f}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left(\mathrm{1}−{x}\right)={x} \\ $$

Question Number 68278    Answers: 0   Comments: 2

Question Number 68257    Answers: 0   Comments: 0

Prove that (6/(673)) Σ_(n=1) ^∞ (1/(n^2 (((2n)),(n) ))) = (π^2 /(2019))

$$\:\:{Prove}\:{that}\:\:\frac{\mathrm{6}}{\mathrm{673}}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}}\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{2019}}\: \\ $$

Question Number 68244    Answers: 0   Comments: 1

find nature of the serie Σ_(n=1) ^∞ arctan(n+(1/n))

$${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{arctan}\left({n}+\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 68243    Answers: 0   Comments: 3

let f(x) =arctan(ax +1) with a real 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3) calculate ∫_(−∞) ^(+∞) ((f(x))/(x^2 +4))dx

$${let}\:{f}\left({x}\right)\:={arctan}\left({ax}\:+\mathrm{1}\right)\:\:{with}\:{a}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{f}\left({x}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$

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