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Question Number 200137    Answers: 1   Comments: 5

Question Number 200134    Answers: 0   Comments: 0

Question Number 200133    Answers: 1   Comments: 0

Question Number 200129    Answers: 0   Comments: 0

Question Number 200130    Answers: 2   Comments: 0

solve by contour integrstion ∫_0 ^(2π) (dx/(1+acosx))

$$\:\:{solve}\:{by}\:{contour}\:{integrstion} \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{\mathrm{1}+{a}\mathrm{cos}{x}}\: \\ $$

Question Number 200125    Answers: 0   Comments: 0

NO_2 (g) ⇒ 2NO (g)+O_2 (g) at 300°C The initial concentration of NO_2 is 0.01 mol/L and its concentration after 150 s is .0055 mol/L. What are the average rates of the above reaction during the first 150 s and during the second 150 s?

$$\mathrm{NO}_{\mathrm{2}} \left(\mathrm{g}\right)\:\Rightarrow\:\mathrm{2NO}\:\left(\mathrm{g}\right)+\mathrm{O}_{\mathrm{2}} \:\left(\mathrm{g}\right)\:\mathrm{at}\:\mathrm{300}°\mathrm{C} \\ $$$$\mathrm{The}\:\mathrm{initial}\:\mathrm{concentration}\:\mathrm{of}\:\mathrm{NO}_{\mathrm{2}} \:\mathrm{is}\: \\ $$$$\mathrm{0}.\mathrm{01}\:\mathrm{mol}/\mathrm{L}\:\mathrm{and}\:\mathrm{its}\:\mathrm{concentration}\: \\ $$$$\mathrm{after}\:\mathrm{150}\:\mathrm{s}\:\mathrm{is}\:.\mathrm{0055}\:\mathrm{mol}/\mathrm{L}.\:\mathrm{What}\:\mathrm{are} \\ $$$$\:\mathrm{the}\:\mathrm{average}\:\mathrm{rates}\:\mathrm{of}\:\mathrm{the}\:\mathrm{above} \\ $$$$\:\mathrm{reaction}\:\mathrm{during}\:\mathrm{the}\:\mathrm{first}\:\mathrm{150}\:\mathrm{s}\:\mathrm{and} \\ $$$$\:\mathrm{during}\:\mathrm{the}\:\mathrm{second}\:\mathrm{150}\:\mathrm{s}? \\ $$

Question Number 200122    Answers: 0   Comments: 0

Question Number 200121    Answers: 0   Comments: 0

Question Number 200120    Answers: 1   Comments: 0

Question Number 200110    Answers: 1   Comments: 0

Question Number 200109    Answers: 1   Comments: 0

Question Number 200104    Answers: 0   Comments: 0

Question Number 200103    Answers: 1   Comments: 0

lim_(x→∞) sin (√(x+1))−sin (√x) =?

$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{\mathrm{x}}\:=? \\ $$

Question Number 200102    Answers: 1   Comments: 0

Question Number 200092    Answers: 1   Comments: 1

Question Number 200087    Answers: 1   Comments: 2

if ω ≠ 1 is a root of unity aand z is a complex number such that ∣z∣ = 1 then ∣((2+3ω+4zω^2 )/(4ω+3ω^2 z+2z))∣= ?

$$\:\:\mathrm{if}\:\omega\:\neq\:\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{aand}\:\mathrm{z}\:\mathrm{is}\:\mathrm{a}\: \\ $$$$\mathrm{complex}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that}\:\mid{z}\mid\:=\:\mathrm{1}\:\mathrm{then} \\ $$$$\:\:\mid\frac{\mathrm{2}+\mathrm{3}\omega+\mathrm{4}{z}\omega^{\mathrm{2}} }{\mathrm{4}\omega+\mathrm{3}\omega^{\mathrm{2}} {z}+\mathrm{2}{z}}\mid=\:? \\ $$

Question Number 200085    Answers: 1   Comments: 2

perimetre of White triangle?

$$\mathrm{perimetre}\:\mathrm{of}\:\:\mathrm{White}\:\mathrm{triangle}? \\ $$

Question Number 200105    Answers: 1   Comments: 2

Question Number 200075    Answers: 1   Comments: 0

Question Number 200066    Answers: 1   Comments: 0

If ((1 + x)/( (√3))) = 3 find x + (1/x) − 1 = ?

$$\mathrm{If}\:\:\:\frac{\mathrm{1}\:+\:\mathrm{x}}{\:\sqrt{\mathrm{3}}}\:=\:\mathrm{3}\:\:\:\mathrm{find}\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:−\:\mathrm{1}\:=\:? \\ $$

Question Number 200051    Answers: 2   Comments: 2

There are many ways to arrange 3 red balls and 9 black balls in a circle so that there are a minimum of 2 black balls between 2 adjacent red balls. (a) 180×8! (b) 240×7! (c) 364×6! (d) 282×4! (e) 144×5!

$$ \\ $$$$\mathrm{There}\:\mathrm{are}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{arrange}\:\mathrm{3}\:\mathrm{red} \\ $$$$\:\mathrm{balls}\:\mathrm{and}\:\mathrm{9}\:\mathrm{black}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{2} \\ $$$$\mathrm{black}\:\mathrm{balls}\:\mathrm{between}\:\mathrm{2}\:\mathrm{adjacent}\:\mathrm{red} \\ $$$$\mathrm{balls}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{180}×\mathrm{8}!\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{240}×\mathrm{7}!\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{364}×\mathrm{6}! \\ $$$$\:\left(\mathrm{d}\right)\:\mathrm{282}×\mathrm{4}!\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{144}×\mathrm{5}!\: \\ $$

Question Number 200048    Answers: 0   Comments: 2

Question Number 200041    Answers: 3   Comments: 0

By strong induction prove that any natural number equal to or bigger than 8 can be written as 3a+5b where a and b are non−negative integers.

$${By}\:{strong}\:{induction}\:{prove}\:{that}\:{any} \\ $$$${natural}\:{number}\:{equal}\:{to}\:{or}\:{bigger}\:{than} \\ $$$$\mathrm{8}\:{can}\:{be}\:{written}\:{as}\:\mathrm{3}{a}+\mathrm{5}{b}\:{where}\:{a}\:{and}\:{b} \\ $$$${are}\:{non}−{negative}\:{integers}. \\ $$

Question Number 200040    Answers: 2   Comments: 0

Q: If , tan((π/4) −α )= (1/2) ⇒Find the value of , tan(4α)=?

$$ \\ $$$$\:\:\:\:\:{Q}:\:\:{If}\:\:,\:\:{tan}\left(\frac{\pi}{\mathrm{4}}\:−\alpha\:\right)=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\Rightarrow{Find}\:{the}\:{value}\:{of}\:,\:{tan}\left(\mathrm{4}\alpha\right)=? \\ $$$$ \\ $$

Question Number 200035    Answers: 1   Comments: 2

Question Number 200025    Answers: 3   Comments: 0

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