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AllQuestion and Answers: Page 31

Question Number 214047 Answers: 1 Comments: 1

Question Number 214040 Answers: 1 Comments: 1

Question Number 214030 Answers: 1 Comments: 0

Question Number 214020 Answers: 2 Comments: 1

Question Number 214012 Answers: 1 Comments: 1

Question Number 214005 Answers: 1 Comments: 0

find all zero divisors of Z_(24)

$${find}\:{all}\:{zero}\:{divisors}\:{of}\:{Z}_{\mathrm{24}} \\ $$

Question Number 214002 Answers: 2 Comments: 0

find the integers x that satisfies a congruence 3x=4 (mod 11) .

$${find}\:{the}\:{integers}\:{x}\:{that}\:{satisfies}\:{a}\:{congruence}\:\mathrm{3}{x}=\mathrm{4}\:\left({mod}\:\mathrm{11}\right)\:. \\ $$

Question Number 214001 Answers: 2 Comments: 0

find all solutions of the equation x^2 =x in each of the rings Z_2 Z_3 and Z_6

$$\mathrm{find}\:\mathrm{all}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} ={x}\:\mathrm{in}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rings}\: \\ $$$${Z}_{\mathrm{2}} \: \\ $$$${Z}_{\mathrm{3}} \\ $$$$\mathrm{and}\:\mathrm{Z}_{\mathrm{6}} \\ $$

Question Number 214000 Answers: 0 Comments: 4

Let y(x) be the solution of diff eq. y ′= ((cos x+y)/(cos x)) , y(0)=0 Find y((π/6)).

$$\:\:\mathrm{Let}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{diff}\:\mathrm{eq}. \\ $$$$\:\:\mathrm{y}\:'=\:\frac{\mathrm{cos}\:\mathrm{x}+\mathrm{y}}{\mathrm{cos}\:\mathrm{x}}\:,\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\:\:\mathrm{Find}\:\mathrm{y}\left(\frac{\pi}{\mathrm{6}}\right). \\ $$

Question Number 213999 Answers: 1 Comments: 1

∫∫...∫_( D) e^(−(z_1 ^2 +z_2 ^2 ...+z_n ^2 )) da D=[0,∞)×[0,∞)......[0,∞)_(n times) ∫_0 ^( π) e^(−sin^2 (z)) dz help

$$\int\int...\int_{\:\mathcal{D}} \:\:{e}^{−\left({z}_{\mathrm{1}} ^{\mathrm{2}} +{z}_{\mathrm{2}} ^{\mathrm{2}} ...+{z}_{{n}} ^{\mathrm{2}} \right)} \mathrm{da} \\ $$$$\mathcal{D}=\underset{\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{times}}} {\left[\mathrm{0},\infty\right)×\left[\mathrm{0},\infty\right)......\left[\mathrm{0},\infty\right)} \\ $$$$\int_{\mathrm{0}} ^{\:\pi} \:{e}^{−\mathrm{sin}^{\mathrm{2}} \left({z}\right)} \mathrm{d}{z} \\ $$$$\mathrm{help} \\ $$

Question Number 213992 Answers: 0 Comments: 0

Question Number 213991 Answers: 0 Comments: 0

Question Number 213962 Answers: 1 Comments: 0

∫((x^4 −1)/(x(x^4 −5)(x^5 −5x+1)))dx

$$\int\frac{{x}^{\mathrm{4}} −\mathrm{1}}{{x}\left({x}^{\mathrm{4}} −\mathrm{5}\right)\left({x}^{\mathrm{5}} −\mathrm{5}{x}+\mathrm{1}\right)}{dx} \\ $$

Question Number 213960 Answers: 1 Comments: 1

Question Number 213956 Answers: 2 Comments: 0

Question Number 213953 Answers: 1 Comments: 0

Question Number 213948 Answers: 0 Comments: 0

evaluate. 1. (1/π)∫_0 ^( π) e^(−i(t−sin(t))) dt 2. ∫_0 ^( a) ∫_0 ^( a) (√(u^2 +v^2 −6u+9)) dudv 3. ∫_0 ^( π/2) e^(cos(t)) cos(2t+sin(t))dt 4. ∫_(−∞) ^( ∞) ((sin(3z))/(z^2 +2z+5)) dz 5.∫_0 ^( 2π) (1/(2+cos(θ))) dθ

$$\mathrm{evaluate}. \\ $$$$\mathrm{1}.\:\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\:\pi} \:\:{e}^{−\boldsymbol{{i}}\left({t}−\mathrm{sin}\left({t}\right)\right)} \mathrm{d}{t} \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\:\mathrm{a}} \int_{\mathrm{0}} ^{\:\mathrm{a}} \:\:\sqrt{{u}^{\mathrm{2}} +{v}^{\mathrm{2}} −\mathrm{6}{u}+\mathrm{9}}\:\mathrm{d}{u}\mathrm{d}{v} \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\:{e}^{\mathrm{cos}\left({t}\right)} \mathrm{cos}\left(\mathrm{2}{t}+\mathrm{sin}\left({t}\right)\right)\mathrm{d}{t} \\ $$$$\mathrm{4}.\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{sin}\left(\mathrm{3}{z}\right)}{{z}^{\mathrm{2}} +\mathrm{2}{z}+\mathrm{5}}\:\mathrm{d}{z} \\ $$$$\mathrm{5}.\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \:\:\frac{\mathrm{1}}{\mathrm{2}+\mathrm{cos}\left(\theta\right)}\:\mathrm{d}\theta \\ $$

Question Number 213945 Answers: 3 Comments: 0

Question Number 213944 Answers: 1 Comments: 0

Question Number 213939 Answers: 2 Comments: 1

Question Number 213923 Answers: 3 Comments: 0

Question Number 213920 Answers: 1 Comments: 1

Question Number 213934 Answers: 0 Comments: 3

∫_(−π/2) ^( π/2) ∫_0 ^( R) (((dθ)(dr)(a+rcos θ))/((r^2 +a^2 +2arcos θ)^(3/2) )) =f(a,R) Find f(a, R).

$$\int_{−\pi/\mathrm{2}} ^{\:\pi/\mathrm{2}} \int_{\mathrm{0}} ^{\:{R}} \frac{\left({d}\theta\right)\left({dr}\right)\left({a}+{r}\mathrm{cos}\:\theta\right)}{\left({r}^{\mathrm{2}} +{a}^{\mathrm{2}} +\mathrm{2}{ar}\mathrm{cos}\:\theta\right)^{\mathrm{3}/\mathrm{2}} }\:={f}\left({a},{R}\right) \\ $$$${Find}\:{f}\left({a},\:{R}\right). \\ $$

Question Number 213894 Answers: 0 Comments: 0

Question Number 213893 Answers: 1 Comments: 2

∫_( −π) ^( π) (dz/(1+3cos^2 (z)))=¿¿

$$\int_{\:−\pi} ^{\:\:\pi} \:\:\frac{\mathrm{d}{z}}{\mathrm{1}+\mathrm{3cos}^{\mathrm{2}} \left({z}\right)}=¿¿\:\:\: \\ $$

Question Number 213890 Answers: 2 Comments: 0

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