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Question Number 177585    Answers: 0   Comments: 2

looks like my question was deleted. why? i cant find it

$${looks}\:{like}\:{my}\:{question}\:{was}\:{deleted}.\:{why}?\:{i}\:{cant}\:{find}\:{it} \\ $$

Question Number 177579    Answers: 2   Comments: 0

if x^3 +y^3 +((x+y)/4)=((15)/2), find maximum value of x+y.

$${if}\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +\frac{{x}+{y}}{\mathrm{4}}=\frac{\mathrm{15}}{\mathrm{2}},\:{find}\:{maximum} \\ $$$${value}\:{of}\:{x}+{y}. \\ $$

Question Number 177578    Answers: 1   Comments: 6

Question Number 177570    Answers: 1   Comments: 5

lim_(Δx→cos(π/2)) ((sin^3 (Δx+x)−sin^3 x)/(2^(−1) Δx))=?

$$\underset{\Delta{x}\rightarrow{cos}\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{{sin}^{\mathrm{3}} \left(\Delta{x}+{x}\right)−{sin}^{\mathrm{3}} {x}}{\mathrm{2}^{−\mathrm{1}} \Delta{x}}=? \\ $$

Question Number 177560    Answers: 2   Comments: 1

Question Number 177557    Answers: 0   Comments: 0

Question Number 177552    Answers: 0   Comments: 0

Question Number 177548    Answers: 2   Comments: 0

A projectile is fired with velocity(v_o ) such that it passes through two points both a distance(h) above the horizontal.show that if the gun is adjusted for the maximum range of the separation of two position is d=((v_o (√(v_o ^2 −4gh)))/g)

$$\mathrm{A}\:\mathrm{projectile}\:\mathrm{is}\:\mathrm{fired}\:\mathrm{with}\:\mathrm{velocity}\left(\mathrm{v}_{\mathrm{o}} \right) \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{it}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{two} \\ $$$$\mathrm{points}\:\mathrm{both}\:\mathrm{a}\:\mathrm{distance}\left(\mathrm{h}\right)\:\mathrm{above}\:\mathrm{the} \\ $$$$\mathrm{horizontal}.\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{the}\:\mathrm{gun}\:\mathrm{is}\:\mathrm{adjusted} \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{separation}\:\mathrm{of}\:\mathrm{two}\:\mathrm{position}\:\mathrm{is} \\ $$$$\boldsymbol{\mathrm{d}}=\frac{\boldsymbol{\mathrm{v}}_{\boldsymbol{\mathrm{o}}} \sqrt{\boldsymbol{\mathrm{v}}_{\boldsymbol{\mathrm{o}}} ^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{gh}}}}{\boldsymbol{\mathrm{g}}} \\ $$

Question Number 177546    Answers: 0   Comments: 0

A particle is projected vertically upward in a constant gravitation field with initial speed (v_0 ).show that there is retarding proportional to the square of the instantaneous speed,the speed of the partical when it returns on the initial position is ((v_o v_c )/( (√(v_o ^2 +v_c ^2 )))) where v_c is terminal speed

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{vertically} \\ $$$$\mathrm{upward}\:\mathrm{in}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{gravitation} \\ $$$$\mathrm{field}\:\mathrm{with}\:\mathrm{initial}\:\mathrm{speed}\:\left(\mathrm{v}_{\mathrm{0}} \right).\mathrm{show} \\ $$$$\mathrm{that}\:\mathrm{there}\:\mathrm{is}\:\mathrm{retarding}\:\mathrm{proportional} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{the}\:\mathrm{instantaneous} \\ $$$$\mathrm{speed},\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{partical} \\ $$$$\mathrm{when}\:\mathrm{it}\:\mathrm{returns}\:\mathrm{on}\:\mathrm{the}\:\mathrm{initial} \\ $$$$\mathrm{position}\:\mathrm{is}\:\:\:\frac{\boldsymbol{\mathrm{v}}_{\boldsymbol{\mathrm{o}}} \boldsymbol{\mathrm{v}}_{\boldsymbol{\mathrm{c}}} }{\:\sqrt{\boldsymbol{\mathrm{v}}_{\boldsymbol{\mathrm{o}}} ^{\mathrm{2}} +\boldsymbol{\mathrm{v}}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{2}} }}\:\:\boldsymbol{\mathrm{where}}\:\boldsymbol{\mathrm{v}}_{\boldsymbol{\mathrm{c}}} \:\boldsymbol{\mathrm{i}}\mathrm{s} \\ $$$$\mathrm{terminal}\:\mathrm{speed} \\ $$

Question Number 177542    Answers: 3   Comments: 0

Question Number 177541    Answers: 0   Comments: 3

Question Number 177540    Answers: 2   Comments: 0

Question Number 177530    Answers: 3   Comments: 0

f (x ) + f ((( 1)/( ((1 −x^( 3) ))^(1/3) )) )= x^( 3) is given. find the value of: f (−1)=?

$$ \\ $$$${f}\:\left({x}\:\right)\:+\:{f}\:\left(\frac{\:\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}\:−{x}^{\:\mathrm{3}} }}\:\right)=\:{x}^{\:\mathrm{3}} \\ $$$$\:\:\:\:\:\:{is}\:{given}.\:{find}\:{the}\:{value}\:{of}: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:{f}\:\left(−\mathrm{1}\right)=? \\ $$$$ \\ $$

Question Number 177519    Answers: 2   Comments: 0

Question Number 177525    Answers: 1   Comments: 3

Question Number 177510    Answers: 1   Comments: 1

Question Number 177507    Answers: 1   Comments: 0

The angle of elevetion of the top of a tower from a point A in the north is α and the angle of the top of the tower from the point B in the east of the point A is β .prove that the height of the tower is ((ABsin αsin B)/( (√(sin^2 α−sin^2 β))))

$$\mathrm{The}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{elevetion}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\: \\ $$$$\mathrm{A}\:\mathrm{in}\:\mathrm{the}\:\mathrm{north}\:\mathrm{is}\:\alpha\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tower} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\mathrm{B}\:\mathrm{in}\:\mathrm{the}\:\mathrm{east}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point} \\ $$$$\mathrm{A}\:\mathrm{is}\:\beta\:.\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{height} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tower}\:\mathrm{is}\: \\ $$$$\frac{\mathrm{ABsin}\:\alpha\mathrm{sin}\:\mathrm{B}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{2}} \alpha−\mathrm{sin}\:^{\mathrm{2}} \beta}} \\ $$

Question Number 177476    Answers: 1   Comments: 4

Question Number 177475    Answers: 1   Comments: 0

Question Number 177473    Answers: 0   Comments: 0

Question Number 178488    Answers: 1   Comments: 0

I have two children. One is a boy born on a Tuesday. What is the probbility I have two boys

$$ \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{two}\:\mathrm{children}.\:\mathrm{One}\:\mathrm{is}\:\mathrm{a}\:\mathrm{boy} \\ $$$$\mathrm{born}\:\mathrm{on}\:\mathrm{a}\:\mathrm{Tuesday}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{probbility}\:\mathrm{I}\:\mathrm{have}\:\mathrm{two}\:\mathrm{boys} \\ $$

Question Number 178487    Answers: 3   Comments: 0

∫ (dx/(cot^3 x sin^7 x)) =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{{dx}}{\mathrm{cot}\:^{\mathrm{3}} {x}\:\mathrm{sin}\:^{\mathrm{7}} {x}}\:=? \\ $$

Question Number 178486    Answers: 1   Comments: 0

Reduce (((2n)!)/(1×3×5×...×(2n−1)))

$$\:{Reduce}\:\frac{\left(\mathrm{2}{n}\right)!}{\mathrm{1}×\mathrm{3}×\mathrm{5}×...×\left(\mathrm{2}{n}−\mathrm{1}\right)}\: \\ $$

Question Number 177492    Answers: 0   Comments: 0

If 0<a≤b then: ∫_( a) ^( b) ∫_( a) ^( b) ((dx dy)/( (√(xy (x + y))))) ≤ ((b−a)/2) ∙ log ((b/a)) + log^2 ((b/a))

$$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\:\mathrm{then}: \\ $$$$\int_{\:\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\int_{\:\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\:\frac{\mathrm{dx}\:\mathrm{dy}}{\:\sqrt{\mathrm{xy}\:\left(\mathrm{x}\:+\:\mathrm{y}\right)}}\:\:\leqslant\:\:\frac{\mathrm{b}−\mathrm{a}}{\mathrm{2}}\:\centerdot\:\mathrm{log}\:\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\:+\:\mathrm{log}^{\mathrm{2}} \:\left(\frac{\mathrm{b}}{\mathrm{a}}\right) \\ $$

Question Number 177493    Answers: 1   Comments: 2

find the laplace transform of f(t)=ln(t)

$${find}\:{the}\:{laplace}\:{transform}\:{of} \\ $$$${f}\left({t}\right)={ln}\left({t}\right) \\ $$

Question Number 181603    Answers: 0   Comments: 0

calcul Σ_(n=1) ^(+oo) U_n : U_n =(1/n)(E((√(n+1)) −E((√n) )

$${calcul}\:\:\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}{U}_{{n}} : \\ $$$${U}_{{n}} =\frac{\mathrm{1}}{{n}}\left({E}\left(\sqrt{{n}+\mathrm{1}}\:−{E}\left(\sqrt{{n}}\:\right)\right.\right. \\ $$

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