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Question Number 82647 Answers: 0 Comments: 2

In the rectangular region, −2<x<2, −3<y<3, the surface charge density is given as ρ_s =(x^2 +y^2 +1)^(3/2) . If no other charge is present, find E at P(0,0,1).

$${In}\:{the}\:{rectangular}\:{region},\:−\mathrm{2}<{x}<\mathrm{2}, \\ $$$$−\mathrm{3}<{y}<\mathrm{3},\:{the}\:{surface}\:{charge}\:{density} \\ $$$${is}\:{given}\:{as}\:\rho_{{s}} =\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} .\:{If}\:{no}\:{other} \\ $$$${charge}\:{is}\:{present},\:{find}\:{E}\:{at}\:{P}\left(\mathrm{0},\mathrm{0},\mathrm{1}\right). \\ $$

Question Number 82644 Answers: 1 Comments: 2

Question Number 82638 Answers: 0 Comments: 4

given x= cos^3 x what is x ?

$${given}\:{x}=\:\mathrm{cos}\:^{\mathrm{3}} {x} \\ $$$${what}\:{is}\:{x}\:? \\ $$

Question Number 82631 Answers: 0 Comments: 1

Eight point charges of 1nC each are located at corners of the cube in free space that is 1m on a side . Find ∣E∣ at the centre of an edge. (Assume origin to be centre of cube).

$${Eight}\:{point}\:{charges}\:{of}\:\mathrm{1}{nC}\:{each}\:{are} \\ $$$${located}\:{at}\:{corners}\:{of}\:{the}\:{cube}\:{in}\:{free} \\ $$$${space}\:{that}\:{is}\:\mathrm{1}{m}\:{on}\:{a}\:{side}\:.\:{Find}\:\:\mid\boldsymbol{{E}}\mid \\ $$$${at}\:{the}\:{centre}\:{of}\:{an}\:{edge}. \\ $$$$\left({Assume}\:{origin}\:{to}\:{be}\:{centre}\:{of}\:{cube}\right). \\ $$

Question Number 82628 Answers: 1 Comments: 1

If a,b, c are in Harmonic progression find the value of ((a+b)/(b−a)) + ((b+c)/(b−c)) . ?

$${If}\:{a},{b},\:{c}\:{are}\:{in}\:{Harmonic}\:{progression} \\ $$$${find}\:{the}\:{value}\:{of}\:\frac{{a}+{b}}{{b}−{a}}\:+\:\frac{{b}+{c}}{{b}−{c}}\:.\:? \\ $$

Question Number 82627 Answers: 0 Comments: 1

A 20nC point charge is located at P(2,4,−3) in free space. Find the locus of all points at which E_r =1V/m.

$${A}\:\mathrm{20}{nC}\:{point}\:{charge}\:{is}\:{located}\:{at} \\ $$$${P}\left(\mathrm{2},\mathrm{4},−\mathrm{3}\right)\:{in}\:{free}\:{space}.\:\boldsymbol{{F}}{ind}\:{the}\:{locus} \\ $$$${of}\:{all}\:{points}\:{at}\:{which}\:{E}_{{r}} =\mathrm{1}{V}/{m}. \\ $$

Question Number 82639 Answers: 0 Comments: 3

Question Number 82617 Answers: 1 Comments: 0

∫sin (101x)(sinx)^(99) dx

$$\int\mathrm{sin}\:\left(\mathrm{101}{x}\right)\left({sinx}\right)^{\mathrm{99}} {dx} \\ $$

Question Number 82616 Answers: 0 Comments: 0

Find the normalization constant ψ_((φ,θ)) =Ne^(iφ) sinθ

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{normalization}\:\mathrm{constant}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\psi_{\left(\phi,\theta\right)} =\mathrm{Ne}^{\mathrm{i}\phi} \mathrm{sin}\theta \\ $$

Question Number 82614 Answers: 1 Comments: 0

∫ ((sin 2x)/(sin 5x sin 3x)) dx ?

$$\int\:\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{sin}\:\mathrm{5}{x}\:\mathrm{sin}\:\mathrm{3}{x}}\:{dx}\:?\: \\ $$

Question Number 82609 Answers: 0 Comments: 1

Question Number 82608 Answers: 0 Comments: 1

Question Number 82607 Answers: 1 Comments: 5

Question Number 82685 Answers: 0 Comments: 0

∫_0 ^5 (((3x^3 −x^4 ))^(1/4) /(5−x))dx

$$\int_{\mathrm{0}} ^{\mathrm{5}} \:\frac{\sqrt[{\mathrm{4}}]{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{4}} }}{\mathrm{5}−{x}}{dx} \\ $$

Question Number 82604 Answers: 1 Comments: 0

∫ ((cos (5x)+cos (4x) dx)/(1−2cos (3x))) =

$$\int\:\frac{\mathrm{cos}\:\left(\mathrm{5}{x}\right)+\mathrm{cos}\:\left(\mathrm{4}{x}\right)\:{dx}}{\mathrm{1}−\mathrm{2cos}\:\left(\mathrm{3}{x}\right)}\:=\: \\ $$

Question Number 82596 Answers: 0 Comments: 4

Question Number 82593 Answers: 0 Comments: 3

Question Number 82591 Answers: 0 Comments: 12

A closed surface is defined in spherical coordinates by 3<r<5 , 0.1π<θ<0.3π, 1.2π<φ<1.6π. Find the total surface area.

$${A}\:{closed}\:{surface}\:{is}\:{defined}\:{in}\:{spherical} \\ $$$${coordinates}\:{by}\:\mathrm{3}<{r}<\mathrm{5}\:,\:\mathrm{0}.\mathrm{1}\pi<\theta<\mathrm{0}.\mathrm{3}\pi, \\ $$$$\mathrm{1}.\mathrm{2}\pi<\phi<\mathrm{1}.\mathrm{6}\pi.\:\boldsymbol{{F}}{ind}\:{the}\:{total}\:{surface} \\ $$$${area}. \\ $$

Question Number 82589 Answers: 0 Comments: 1

Question Number 82583 Answers: 0 Comments: 0

Question Number 82582 Answers: 0 Comments: 2

solve x^3 −3x+1=0

$${solve} \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 82579 Answers: 1 Comments: 0

if y=cos(ln(x))+sin(ln(x)) show that y′′+y^′ +y=0

$${if}\:{y}={cos}\left({ln}\left({x}\right)\right)+{sin}\left({ln}\left({x}\right)\right) \\ $$$${show}\:{that} \\ $$$${y}''+{y}^{'} +{y}=\mathrm{0} \\ $$

Question Number 82577 Answers: 0 Comments: 3

∫((2−(√(x+3)))/(2+(√(x−3)))) dx

$$\int\frac{\mathrm{2}−\sqrt{{x}+\mathrm{3}}}{\mathrm{2}+\sqrt{{x}−\mathrm{3}}}\:{dx} \\ $$

Question Number 82574 Answers: 0 Comments: 0

Question Number 82573 Answers: 0 Comments: 4

Question Number 82572 Answers: 0 Comments: 1

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