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Question Number 226914 Answers: 2 Comments: 0

Question Number 226919 Answers: 3 Comments: 0

Question Number 226912 Answers: 1 Comments: 0

Question Number 226910 Answers: 2 Comments: 0

Question Number 226908 Answers: 1 Comments: 1

Question Number 226907 Answers: 0 Comments: 0

two small balls are hung from a point (same mass, same charge and rope length are same) the two strings make an angle 30^0 when immersed in a liquid of ρ=0.8g/cc the angle remains same.ρ_(ball) =1.6g/cc what is the value of κ(dielectric const.)of the liquid

$${two}\:{small}\:{balls}\:{are}\:{hung}\:{from}\:{a}\:{point} \\ $$$$\left({same}\:{mass},\:{same}\:{charge}\:{and}\:{rope}\:{length}\:{are}\:{same}\right) \\ $$$${the}\:{two}\:{strings}\:{make}\:{an}\:{angle}\:\mathrm{30}^{\mathrm{0}} \\ $$$${when}\:{immersed}\:{in}\:{a}\:{liquid}\:{of}\:\rho=\mathrm{0}.\mathrm{8}{g}/{cc} \\ $$$${the}\:{angle}\:{remains}\:{same}.\rho_{{ball}} =\mathrm{1}.\mathrm{6}{g}/{cc} \\ $$$${what}\:{is}\:{the}\:{value}\:{of}\:\kappa\left({dielectric}\:{const}.\right){of} \\ $$$${the}\:{liquid} \\ $$

Question Number 226898 Answers: 0 Comments: 0

Reduce to canonical form: sin^2 (x)(∂^2 u/∂x^2 )+sin^2 (2x)(∂^2 u/(∂x∂y))+cos^2 (x)(∂^2 u/∂y^2 )=0

$$\mathrm{Reduce}\:\mathrm{to}\:\mathrm{canonical}\:\mathrm{form}: \\ $$$$\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{x}^{\mathrm{2}} }+\mathrm{sin}^{\mathrm{2}} \left(\mathrm{2x}\right)\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{x}\partial\mathrm{y}}+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{y}^{\mathrm{2}} }=\mathrm{0} \\ $$

Question Number 226882 Answers: 1 Comments: 0

Question Number 226880 Answers: 1 Comments: 0

Question Number 226879 Answers: 2 Comments: 0

Question Number 226878 Answers: 1 Comments: 0

Question Number 226877 Answers: 0 Comments: 0

Question Number 226901 Answers: 2 Comments: 1

if x+y=2 with x, y >0, find the minimum of x+(√(x^2 +3y^2 )).

$${if}\:{x}+{y}=\mathrm{2}\:{with}\:{x},\:{y}\:>\mathrm{0},\:{find}\:{the} \\ $$$${minimum}\:{of}\:{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} }. \\ $$

Question Number 226855 Answers: 2 Comments: 0

Question Number 226850 Answers: 4 Comments: 0

Question Number 226830 Answers: 1 Comments: 0

Question Number 226829 Answers: 3 Comments: 0

Question Number 226828 Answers: 0 Comments: 0

(d^π /dx^π )(x^π )=?

$$\frac{{d}^{\pi} }{{dx}^{\pi} }\left({x}^{\pi} \right)=? \\ $$

Question Number 226821 Answers: 1 Comments: 0

Differentiate 20sin (x+3)cos (x^2 /2)

$${Differentiate}\:\: \\ $$$$\mathrm{20sin}\:\left({x}+\mathrm{3}\right)\mathrm{cos}\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\ $$

Question Number 226820 Answers: 1 Comments: 0

Differentiate x^x^x

$$ \\ $$$$\:\:\:\:\:{Differentiate}\:\:\:\:{x}^{{x}^{{x}} } \\ $$$$ \\ $$

Question Number 226819 Answers: 1 Comments: 0

Evaluate ∫_0 ^∞ (dx/(1+x^2 ))

$${Evaluate} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$

Question Number 226818 Answers: 1 Comments: 0

Evaluate ∫((x^2 +2x−1)/(2x^3 +3x^2 −2x))dx

$${Evaluate} \\ $$$$\int\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}{\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}}{dx} \\ $$

Question Number 226815 Answers: 1 Comments: 0

lim_(x→0) (lim_(n→∞) (cos (x/2) cos (x/2^2 ) ... cos (x/2^n ))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{cos}\:\frac{{x}}{\mathrm{2}}\:\mathrm{cos}\:\frac{{x}}{\mathrm{2}^{\mathrm{2}} }\:...\:\mathrm{cos}\:\frac{{x}}{\mathrm{2}^{{n}} }\right)\right)\:=\:? \\ $$

Question Number 226812 Answers: 2 Comments: 1

if 28x+30y+31z=360 with x, y, z being positive integers, find x+y+z=?

$${if}\:\mathrm{28}{x}+\mathrm{30}{y}+\mathrm{31}{z}=\mathrm{360}\:{with}\:{x},\:{y},\:{z} \\ $$$${being}\:{positive}\:{integers},\:{find} \\ $$$${x}+{y}+{z}=? \\ $$

Question Number 226809 Answers: 0 Comments: 0

φ_E =∮_S (q/(4πε)) dω

$$\phi_{{E}} =\oint_{{S}} \frac{{q}}{\mathrm{4}\pi\epsilon}\:{d}\omega \\ $$

Question Number 226799 Answers: 2 Comments: 0

∫_0 ^1 ((ln(1+x^2 ))/(1+x)) dx = ?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}\:\mathrm{d}{x}\:=\:? \\ $$

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