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Question Number 47581    Answers: 1   Comments: 1

The root of the equation (2/(x−1)) + (1/(x+2)) + ((3x(x+1))/((x−1)(x+2))) = 0 among the following is

$$\mathrm{The}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\frac{\mathrm{2}}{{x}−\mathrm{1}}\:+\:\frac{\mathrm{1}}{{x}+\mathrm{2}}\:+\:\frac{\mathrm{3}{x}\left({x}+\mathrm{1}\right)}{\left({x}−\mathrm{1}\right)\left({x}+\mathrm{2}\right)}\:=\:\mathrm{0}\:\: \\ $$$$\mathrm{among}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is} \\ $$

Question Number 47565    Answers: 0   Comments: 0

Question Number 47561    Answers: 0   Comments: 0

thanks sir

$$\mathrm{thanks}\:\mathrm{sir} \\ $$

Question Number 47559    Answers: 1   Comments: 1

Question Number 47556    Answers: 1   Comments: 1

Question Number 47566    Answers: 2   Comments: 0

∫sin51x(sinx)^(49) dx

$$\int{sin}\mathrm{51}{x}\left({sinx}\right)^{\mathrm{49}} {dx} \\ $$

Question Number 47543    Answers: 2   Comments: 0

solve (1+ix)^n =n with x unknown real and n integr natural .

$${solve}\:\left(\mathrm{1}+{ix}\right)^{{n}} ={n}\:\:\:{with}\:{x}\:{unknown}\:{real}\:{and}\:{n}\:{integr}\:{natural}\:. \\ $$

Question Number 47552    Answers: 3   Comments: 1

((5(x−2))/4)=((6x−9)/5) plz help me

$$\frac{\mathrm{5}\left(\mathrm{x}−\mathrm{2}\right)}{\mathrm{4}}=\frac{\mathrm{6x}−\mathrm{9}}{\mathrm{5}}\:\:\:\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 47532    Answers: 2   Comments: 0

(√(400^2 +100^(2=) ))

$$\sqrt{\mathrm{400}^{\mathrm{2}} +\mathrm{100}^{\mathrm{2}=} } \\ $$

Question Number 47531    Answers: 1   Comments: 2

Question Number 47527    Answers: 0   Comments: 0

Question Number 47526    Answers: 0   Comments: 0

Question Number 47523    Answers: 0   Comments: 3

I have a question, Can we consider as a complex number a number if its real part or his imaginary part is null ? For example : a + b i where a=0 xor b=0. for example, a=7 and b=0 7 + 0i = 7 So, is a whole number for example may be considered as a complex number ?

$$\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{question}, \\ $$$$\mathrm{Can}\:\mathrm{we}\:\mathrm{consider}\:\mathrm{as}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{a} \\ $$$$\mathrm{number}\:\mathrm{if}\:\mathrm{its}\:\mathrm{real}\:\mathrm{part}\:\mathrm{or}\:\mathrm{his}\:\mathrm{imaginary} \\ $$$$\mathrm{part}\:\mathrm{is}\:\mathrm{null}\:? \\ $$$$\mathrm{For}\:\mathrm{example}\:: \\ $$$${a}\:+\:{b}\:{i} \\ $$$$\mathrm{where}\:\mathrm{a}=\mathrm{0}\:\mathrm{xor}\:\mathrm{b}=\mathrm{0}. \\ $$$$\mathrm{for}\:\mathrm{example}, \\ $$$$\mathrm{a}=\mathrm{7}\:\mathrm{and}\:\mathrm{b}=\mathrm{0} \\ $$$$\mathrm{7}\:+\:\mathrm{0}{i}\:=\:\mathrm{7} \\ $$$$\mathrm{So},\:\mathrm{is}\:\mathrm{a}\:\mathrm{whole}\:\mathrm{number}\:\mathrm{for}\:\mathrm{example}\:\mathrm{may}\:\mathrm{be} \\ $$$$\mathrm{considered}\:\mathrm{as}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:? \\ $$

Question Number 47540    Answers: 1   Comments: 1

find ∫ arctan((√x))dx.

$${find}\:\int\:{arctan}\left(\sqrt{{x}}\right){dx}. \\ $$

Question Number 47519    Answers: 1   Comments: 1

Question Number 47515    Answers: 1   Comments: 1

Question Number 47513    Answers: 1   Comments: 1

Question Number 47510    Answers: 0   Comments: 1

the curve y = 3x^2 +4 (x=2 and x=3) is rotated about the x.axis.find the volume of the solid generated.Leave your answer in terms of π.

$${the}\:{curve}\:{y}\:=\:\mathrm{3}{x}^{\mathrm{2}} \:+\mathrm{4}\:\left({x}=\mathrm{2}\:{and}\:{x}=\mathrm{3}\right)\:{is}\:{rotated}\:{about}\:{the}\: \\ $$$${x}.{axis}.{find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{generated}.{Leave}\:{your} \\ $$$${answer}\:{in}\:{terms}\:{of}\:\pi. \\ $$

Question Number 47508    Answers: 0   Comments: 1

Question Number 47500    Answers: 0   Comments: 0

Question Number 47497    Answers: 1   Comments: 1

Question Number 47481    Answers: 1   Comments: 0

Three six−faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is k (3≤ k ≤ 8) is

$$\mathrm{Three}\:\mathrm{six}−\mathrm{faced}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{thrown} \\ $$$$\mathrm{together}.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{appearing}\:\mathrm{on}\:\mathrm{the}\:\mathrm{dice} \\ $$$$\mathrm{is}\:\:{k}\:\left(\mathrm{3}\leqslant\:{k}\:\leqslant\:\mathrm{8}\right)\:\mathrm{is} \\ $$

Question Number 47480    Answers: 1   Comments: 0

Question Number 47477    Answers: 1   Comments: 0

Let n ∈ Z^+ f(1) = 1 f(2n) = f(n) f(2n+1) = (f(n))^2 − 2 f(1) + f(2) + f(3) + …+ f(100) = ...

$${Let}\:\:{n}\:\:\in\:\:\mathbb{Z}^{+} \\ $$$${f}\left(\mathrm{1}\right)\:\:=\:\:\mathrm{1} \\ $$$${f}\left(\mathrm{2}{n}\right)\:\:=\:\:{f}\left({n}\right) \\ $$$${f}\left(\mathrm{2}{n}+\mathrm{1}\right)\:\:=\:\:\left({f}\left({n}\right)\right)^{\mathrm{2}} \:−\:\mathrm{2} \\ $$$${f}\left(\mathrm{1}\right)\:+\:{f}\left(\mathrm{2}\right)\:+\:{f}\left(\mathrm{3}\right)\:+\:\ldots+\:{f}\left(\mathrm{100}\right)\:\:=\:\:... \\ $$

Question Number 47476    Answers: 2   Comments: 1

How may I prove the following theorem ? ((a + b)/2) ≥ (√( ab )) Thank you

$$\mathrm{How}\:\mathrm{may}\:\mathrm{I}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{theorem}\:? \\ $$$$ \\ $$$$\:\:\:\frac{\boldsymbol{{a}}\:+\:\boldsymbol{{b}}}{\mathrm{2}}\:\:\:\geqslant\:\:\sqrt{\:\boldsymbol{{ab}}\:\:} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 47471    Answers: 1   Comments: 2

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