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Question Number 226962 Answers: 0 Comments: 0

Question Number 226953 Answers: 0 Comments: 0

If I_n =∫(x^2 +a^2 )^n dx Show that I_n =(1/(2n+1))x(x^2 +a^2 )^n +2na^2 I_(n−1)

$${If}\:{I}_{{n}} =\int\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{{n}} {dx}\: \\ $$$${Show}\:{that} \\ $$$${I}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}{x}\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{{n}} +\mathrm{2}{na}^{\mathrm{2}} {I}_{{n}−\mathrm{1}} \: \\ $$

Question Number 226952 Answers: 0 Comments: 0

Question Number 226958 Answers: 2 Comments: 0

3^x =x^9 x^2 = ..?

$$\:\:\:\mathrm{3}^{\mathrm{x}} =\mathrm{x}^{\mathrm{9}} \: \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{2}} =\:..? \\ $$

Question Number 226914 Answers: 2 Comments: 0

Question Number 226919 Answers: 4 Comments: 0

Question Number 226912 Answers: 1 Comments: 0

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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