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Question Number 227108 Answers: 1 Comments: 0

∫_0 ^π ((sin 2x)/3)(√(cos x+1)) dx =?

$$\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{3}}\sqrt{\mathrm{cos}\:{x}+\mathrm{1}}\:{dx}\:=? \\ $$

Question Number 227111 Answers: 0 Comments: 0

Happy new year guys!

$${Happy}\:{new}\:{year}\:{guys}! \\ $$$$ \\ $$

Question Number 227102 Answers: 1 Comments: 0

(m/n)

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\frac{{m}}{{n}}\: \\ $$$$ \\ $$

Question Number 227098 Answers: 1 Comments: 0

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 227096 Answers: 0 Comments: 0

Question Number 227085 Answers: 0 Comments: 3

Question Number 227080 Answers: 1 Comments: 0

Question Number 227073 Answers: 1 Comments: 0

Question Number 227075 Answers: 0 Comments: 0

Question Number 227074 Answers: 0 Comments: 0

Question Number 227067 Answers: 6 Comments: 0

Question Number 227063 Answers: 1 Comments: 0

is (−e)^π real number?

$${is}\:\left(−{e}\right)^{\pi} \:\:{real}\:{number}? \\ $$

Question Number 227055 Answers: 1 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: 1 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: 2

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