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Question Number 60313 Answers: 3 Comments: 1

Question Number 60311 Answers: 1 Comments: 2

∫(dx/(√(sec h^2 (x)+1))) dx

$$\int\frac{{dx}}{\sqrt{{sec}\:{h}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}}\:{dx} \\ $$

Question Number 60308 Answers: 0 Comments: 0

Question Number 60307 Answers: 0 Comments: 0

Question Number 60304 Answers: 0 Comments: 0

Question Number 60303 Answers: 1 Comments: 0

Question Number 60287 Answers: 2 Comments: 2

f(x) = x^3 + 3x − 7 f^(−1) (x) = ?

$${f}\left({x}\right)\:\:=\:\:{x}^{\mathrm{3}} \:+\:\mathrm{3}{x}\:−\:\mathrm{7} \\ $$$${f}\:^{−\mathrm{1}} \left({x}\right)\:\:=\:\:? \\ $$

Question Number 60283 Answers: 1 Comments: 1

Question Number 60269 Answers: 3 Comments: 3

if tan A − cot A = 0 prove that sin A + cos A=?

$${if} \\ $$$${tan}\:{A}\:−\:{cot}\:{A}\:=\:\mathrm{0} \\ $$$${prove}\:{that} \\ $$$${sin}\:{A}\:+\:{cos}\:{A}=? \\ $$

Question Number 60264 Answers: 0 Comments: 0

let f(t) =∫_0 ^∞ (e^(−3 [x^2 ]) /(x^2 +t^2 ))dx with t>0 1. determine a explicit form of f(t) 2. find also g(t) =∫_0 ^∞ (e^(−3[x^2 ]) /((x^2 +t^2 )^2 ))dx 3. find the values of integrals ∫_0 ^∞ (e^(−3[x^2 ]) /(x^2 +3))dx and ∫_0 ^∞ (e^(−3[x^2 ]) /((x^2 +4)^2 )) dx .

$${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\:\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }{dx}\:\:{with}\:{t}>\mathrm{0} \\ $$$$\mathrm{1}.\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\mathrm{2}.\:{find}\:{also}\:{g}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$$\mathrm{3}.\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 60263 Answers: 0 Comments: 1

let U_n =∫_0 ^∞ (e^(−n[x^2 ]) /(x^2 +3)) dx 1) calculate U_n interms of n 2) find lim_(n→+∞) n U_n 3)determine nature of the serie Σ U_n

$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} +\mathrm{3}}\:{dx}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right){determine}\:{nature}\:{of}\:{the}\:{serie}\:\:\Sigma\:{U}_{{n}} \\ $$

Question Number 60257 Answers: 0 Comments: 4

The maximum value of Z=4x+2y subject to constraints 2x+3y≤18 , x+y≥10 and x,y≥0 is ?

$${The}\:{maximum}\:{value}\:{of}\:{Z}=\mathrm{4}{x}+\mathrm{2}{y} \\ $$$${subject}\:{to}\:{constraints}\:\mathrm{2}{x}+\mathrm{3}{y}\leqslant\mathrm{18}\:, \\ $$$${x}+{y}\geqslant\mathrm{10}\:{and}\:{x},{y}\geqslant\mathrm{0}\:{is}\:? \\ $$

Question Number 60256 Answers: 1 Comments: 0

Question Number 60255 Answers: 0 Comments: 0

b=(((kT)/P))^(1/3) . distance molekular prove.

$$\boldsymbol{\mathrm{b}}=\sqrt[{\mathrm{3}}]{\frac{\boldsymbol{\mathrm{kT}}}{\boldsymbol{\mathrm{P}}}}.\:\boldsymbol{\mathrm{distance}}\:\:\boldsymbol{\mathrm{molekular}} \\ $$$$\boldsymbol{\mathrm{prove}}. \\ $$

Question Number 60275 Answers: 0 Comments: 0

Question Number 60274 Answers: 0 Comments: 1

Question Number 60247 Answers: 0 Comments: 0

A uniform pole PQ, 30 m long and of mass 4 kg is carried by a boy at P and a man 8 m away from Q. Find the distance from P where a mass of 20 kg should be attached so that the man′s support is twice that of the boy, if the system is in equilibrium [Take g=10ms^(−2) ]

$$\mathrm{A}\:\mathrm{uniform}\:\mathrm{pole}\:\mathrm{PQ},\:\mathrm{30}\:\mathrm{m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{4}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{carried}\:\mathrm{by}\:\mathrm{a}\:\mathrm{boy}\:\mathrm{at}\:\mathrm{P}\:\mathrm{and}\:\mathrm{a}\:\mathrm{man}\: \\ $$$$\mathrm{8}\:\mathrm{m}\:\mathrm{away}\:\mathrm{from}\:\mathrm{Q}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{from} \\ $$$$\mathrm{P}\:\mathrm{where}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{20}\:\mathrm{kg}\:\mathrm{should}\:\mathrm{be}\:\mathrm{attached} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{man}'\mathrm{s}\:\mathrm{support}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{that} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{boy},\:\mathrm{if}\:\mathrm{the}\:\mathrm{system}\:\mathrm{is}\:\mathrm{in}\:\mathrm{equilibrium} \\ $$$$\left[\mathrm{Take}\:\mathrm{g}=\mathrm{10ms}^{−\mathrm{2}} \right] \\ $$

Question Number 60237 Answers: 0 Comments: 1