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Question Number 119956 Answers: 2 Comments: 0

Given a = 1+3+3^2 +3^3 +3^4 +...+3^(100) Find the remainder of dividing the number by 5 . (a) 2 (b) 0 (c)4 (d)1 (e) 3

$${Given}\:{a}\:=\:\mathrm{1}+\mathrm{3}+\mathrm{3}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +\mathrm{3}^{\mathrm{4}} +...+\mathrm{3}^{\mathrm{100}} \\ $$$${Find}\:{the}\:{remainder}\:{of}\:{dividing}\:{the}\:{number} \\ $$$${by}\:\mathrm{5}\:. \\ $$$$\left({a}\right)\:\mathrm{2}\:\:\:\:\:\left({b}\right)\:\mathrm{0}\:\:\:\:\:\:\:\left({c}\right)\mathrm{4}\:\:\:\:\:\:\left({d}\right)\mathrm{1}\:\:\:\:\:\:\left({e}\right)\:\mathrm{3} \\ $$

Question Number 119939 Answers: 3 Comments: 0

Question Number 119937 Answers: 3 Comments: 0

(i)((1/2)−cos (π/7))((1/2)−cos ((3π)/7))((1/2)−cos ((9π)/7))? (ii) ((√3)+tan 1°)((√3)+tan 2°)((√3)+tan 3°)×...×((√3)+tan 29°)?

$$\:\left({i}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\pi}{\mathrm{7}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{7}}\right)? \\ $$$$\left({ii}\right)\:\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{1}°\right)\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{2}°\right)\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{3}°\right)×...×\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{29}°\right)? \\ $$

Question Number 119934 Answers: 2 Comments: 0

∫ ((sin^8 x−cos^8 x)/(1−(1/2)sin^2 2x)) dx

$$\:\:\:\int\:\frac{\mathrm{sin}\:^{\mathrm{8}} {x}−\mathrm{cos}\:^{\mathrm{8}} {x}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}\:{dx}\: \\ $$

Question Number 119933 Answers: 4 Comments: 0

(dx/dy) −y = xy^2

$$\:\frac{{dx}}{{dy}}\:−{y}\:=\:{xy}^{\mathrm{2}} \\ $$

Question Number 119930 Answers: 1 Comments: 0

Question Number 119928 Answers: 2 Comments: 0

Question Number 119922 Answers: 0 Comments: 0

Question Number 119921 Answers: 2 Comments: 0

solving the following system of equations { ((((3x−y)/(x−3y))=x^2 )),((((3y−z)/(y−3z))=y^2 )),((((3z−x)/(z−3x))=z^2 )) :}

$${solving}\:{the}\:{following}\:{system}\:{of}\:{equations} \\ $$$$\begin{cases}{\frac{\mathrm{3}{x}−{y}}{{x}−\mathrm{3}{y}}={x}^{\mathrm{2}} }\\{\frac{\mathrm{3}{y}−{z}}{{y}−\mathrm{3}{z}}={y}^{\mathrm{2}} }\\{\frac{\mathrm{3}{z}−{x}}{{z}−\mathrm{3}{x}}={z}^{\mathrm{2}} }\end{cases} \\ $$

Question Number 119920 Answers: 5 Comments: 0

∫ (√((1−x)/(1+x))) dx = ? , xε(−1,1)

$$\:\int\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:{dx}\:=\:?\:,\:{x}\epsilon\left(−\mathrm{1},\mathrm{1}\right) \\ $$

Question Number 119919 Answers: 1 Comments: 0

sin 70° cos 50° + sin 260° cos 280° =?

$$\:\mathrm{sin}\:\mathrm{70}°\:\mathrm{cos}\:\mathrm{50}°\:+\:\mathrm{sin}\:\mathrm{260}°\:\mathrm{cos}\:\mathrm{280}°\:=? \\ $$

Question Number 119915 Answers: 1 Comments: 0

Question Number 119914 Answers: 0 Comments: 0

Question Number 119909 Answers: 2 Comments: 0

Given f(x)=((px+q)/(x+2)) , q≠ 0 f^(−1) (q) = −1 then f^(−1) (2q)=?

$${Given}\:{f}\left({x}\right)=\frac{{px}+{q}}{{x}+\mathrm{2}}\:,\:{q}\neq\:\mathrm{0} \\ $$$${f}^{−\mathrm{1}} \:\left({q}\right)\:=\:−\mathrm{1}\:{then}\:{f}^{−\mathrm{1}} \left(\mathrm{2}{q}\right)=? \\ $$

Question Number 119902 Answers: 3 Comments: 0

lim_(x→0) (cos x)^(1/(sin^2 x)) ?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} {x}}} \:? \\ $$

Question Number 119896 Answers: 2 Comments: 1

Question Number 119894 Answers: 2 Comments: 0

Question Number 119893 Answers: 2 Comments: 0

Question Number 119892 Answers: 1 Comments: 0

Question Number 119891 Answers: 0 Comments: 0

show that (d/dx) Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) lnt dt

$${show}\:{that}\: \\ $$$$\frac{{d}}{{dx}}\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {t}^{{x}−\mathrm{1}} {e}^{−{t}} {lnt}\:{dt} \\ $$

Question Number 119876 Answers: 0 Comments: 0

Question Number 119875 Answers: 3 Comments: 1

Question Number 119866 Answers: 1 Comments: 4

Question Number 119867 Answers: 1 Comments: 2

lim_(x→∞) (((1+(1/(2n)))^n −(√e))/((1+(2/n))^n −e^2 ))=???

$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}{n}}\right)^{{n}} −\sqrt{{e}}}{\left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)^{{n}} −{e}^{\mathrm{2}} }=??? \\ $$

Question Number 119856 Answers: 0 Comments: 4

i have forgotten my password. how may i retrieve it? please help me or forward me to one of the developers please

$$\mathrm{i}\:\mathrm{have}\:\mathrm{forgotten}\:\mathrm{my}\:\mathrm{password}. \\ $$$$\mathrm{how}\:\mathrm{may}\:\mathrm{i}\:\mathrm{retrieve}\:\mathrm{it}? \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{or}\:\mathrm{forward}\:\mathrm{me}\:\mathrm{to} \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{developers}\:\mathrm{please} \\ $$

Question Number 119852 Answers: 1 Comments: 0

lim_(n→∞) n^2 ∫ _0 ^(1/n) x^(x+1) dx =?

$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int\:\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{{n}}} {\:}}{x}^{{x}+\mathrm{1}} \:{dx}\:=? \\ $$

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