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Question Number 227055 Answers: 0 Comments: 0

A parabolic refector is formed by revolving the arc of the parabala y^2 =4ax from x=0 to x=h about the axis.If the diameter of the reflector is 2l.Show that the area of the reflecting surface is ((πl)/(6h^2 )){(l^2 +4h^2 )^(3/2) −l^3 }

$${A}\:{parabolic}\:{refector}\:{is}\:{formed}\:{by} \\ $$$${revolving}\:{the}\:{arc}\:{of}\:{the}\:{parabala} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{ax}\:\:{from}\:{x}=\mathrm{0}\:\:\:\:{to}\:\:{x}={h} \\ $$$${about}\:{the}\:{axis}.{If}\:{the}\:\:{diameter} \\ $$$${of}\:{the}\:{reflector}\:{is}\:\mathrm{2}{l}.{Show}\:{that} \\ $$$${the}\:{area}\:{of}\:{the}\:{reflecting}\:{surface}\:{is} \\ $$$$\frac{\pi{l}}{\mathrm{6}{h}^{\mathrm{2}} }\left\{\left({l}^{\mathrm{2}} +\mathrm{4}{h}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} −{l}^{\mathrm{3}} \right\} \\ $$$$ \\ $$

Question Number 227054 Answers: 0 Comments: 0

A Segment of a sphere has radius r and maximum height h.Prove that its volume ((𝛑h)/6)(h^2 +3r^2 )

$${A}\:{Segment}\:{of}\:{a}\:{sphere}\:{has}\:{radius}\:{r} \\ $$$${and}\:{maximum}\:{height}\:{h}.{Prove}\:{that} \\ $$$${its}\:{volume}\:\frac{\boldsymbol{\pi{h}}}{\mathrm{6}}\left(\boldsymbol{{h}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{{r}}^{\mathrm{2}} \right) \\ $$

Question Number 227051 Answers: 1 Comments: 1

Σ_(n∈N∪{0}) tan^(−1) ((1/(n^2 +3n + 2)) )=? ■

$$ \\ $$$$\:\:\:\:\:\underset{{n}\in\mathbb{N}\cup\left\{\mathrm{0}\right\}} {\sum}{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{3}{n}\:+\:\mathrm{2}}\:\right)=?\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 227047 Answers: 0 Comments: 0

Question Number 227032 Answers: 1 Comments: 1

Question Number 227011 Answers: 1 Comments: 3

in a cup filled with a liquid of density ρ,a bubble rests in the liquid in h deepness. radius initial of the bubble=r_i initial density of the bubble=σ_i ( mass&temparature is constant) a small jerk is given to the cup and the bubble starts to go upwards. find: 1)velocity & acceleration of the bubble at time t after it starts moving 2)force acting on the bubble at time t after it starts moving

$${in}\:{a}\:{cup}\:{filled}\:{with}\:{a}\:{liquid}\:{of}\:{density}\:\rho,{a} \\ $$$${bubble}\:{rests}\:{in}\:{the}\:{liquid}\:{in}\:{h}\:{deepness}. \\ $$$${radius}\:{initial}\:{of}\:{the}\:{bubble}={r}_{{i}} \\ $$$$\:{initial}\:{density}\:{of}\:{the}\:{bubble}=\sigma_{{i}} \\ $$$$\left(\:{mass\&temparature}\:{is}\:{constant}\right) \\ $$$${a}\:{small}\:{jerk}\:{is}\:{given}\:{to}\:{the}\:{cup}\:{and}\:{the} \\ $$$${bubble}\:{starts}\:{to}\:{go}\:{upwards}. \\ $$$${find}: \\ $$$$\left.\mathrm{1}\right){velocity}\:\&\:{acceleration}\:{of}\:{the}\:{bubble}\:{at}\:{time}\:{t}\:{after} \\ $$$${it}\:{starts}\:{moving} \\ $$$$\left.\mathrm{2}\right){force}\:{acting}\:{on}\:{the}\:{bubble}\:{at}\:{time}\:{t} \\ $$$${after}\:{it}\:{starts}\:{moving} \\ $$$$ \\ $$

Question Number 227002 Answers: 0 Comments: 2

merry christmas to all of you guys!

$${merry}\:{christmas}\:{to}\:{all}\:{of}\:{you}\:{guys}! \\ $$

Question Number 226995 Answers: 3 Comments: 0

Question Number 226994 Answers: 4 Comments: 0

Question Number 226983 Answers: 0 Comments: 0

Question Number 226981 Answers: 0 Comments: 0

Question Number 226991 Answers: 4 Comments: 0

Question Number 226975 Answers: 0 Comments: 0

Where are the sans serif letters?

$$ \\ $$Where are the sans serif letters?

Question Number 226973 Answers: 0 Comments: 0

lim_(n→+∞) (((sin (1/n))/(n+(1/1))) + ((sin (2/n))/(n+(1/2))) + ... + ((sin (n/n))/(n+(1/n))))=?

$$\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\frac{\mathrm{1}}{{n}}}{{n}+\frac{\mathrm{1}}{\mathrm{1}}}\:+\:\frac{\mathrm{sin}\:\frac{\mathrm{2}}{{n}}}{{n}+\frac{\mathrm{1}}{\mathrm{2}}}\:+\:...\:+\:\frac{\mathrm{sin}\:\frac{{n}}{{n}}}{{n}+\frac{\mathrm{1}}{{n}}}\right)=? \\ $$

Question Number 226953 Answers: 1 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: 4 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

Question Number 226910 Answers: 2 Comments: 0

Question Number 226908 Answers: 1 Comments: 1

Question Number 226907 Answers: 1 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

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