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Question Number 210265 Answers: 1 Comments: 11

If we observe when light source illuminates the surface of an object lets say its a sphere(football) ,the area visible zone decreases as the light source comes near the surface.So calculate rate of change visible area when light source is coming towards the object or moving away from the object.And in the case of earth find the equation in function of time If the light object is coming from space towards earth, express that expression in the function of time

$${If}\:{we}\:{observe}\:{when}\:{light}\:{source}\: \\ $$$${illuminates}\:{the}\:{surface}\:{of}\:{an}\:{object} \\ $$$${lets}\:{say}\:{its}\:{a}\:{sphere}\left({football}\right)\:,{the}\:{area} \\ $$$${visible}\:{zone}\:{decreases}\:{as}\:{the}\:{light}\:{source} \\ $$$${comes}\:{near}\:{the}\:{surface}.{So}\:\:{calculate}\:{rate}\:{of}\:{change} \\ $$$${visible}\:{area}\:{when}\:{light}\:{source}\:{is}\:{coming} \\ $$$${towards}\:{the}\:{object}\:{or}\:{moving}\:{away}\: \\ $$$${from}\:{the}\:{object}.{And}\:{in}\:{the}\:{case}\:{of}\:{earth} \\ $$$${find}\:{the}\:{equation}\:{in}\:{function}\:{of}\:{time} \\ $$$${If}\:{the}\:{light}\:{object}\:{is}\:{coming}\:{from}\:{space} \\ $$$${towards}\:{earth},\:{express}\:{that}\:{expression} \\ $$$${in}\:{the}\:{function}\:{of}\:{time} \\ $$$$ \\ $$$$ \\ $$

Question Number 210263 Answers: 2 Comments: 0

Question Number 210261 Answers: 2 Comments: 0

show that ((sinAcosA−sinBcosB)/(cos^2 A−sin^2 B))=tan(A−B)

$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{\mathrm{sinAcosA}}−\boldsymbol{\mathrm{sinBcosB}}}{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{B}}}=\boldsymbol{\mathrm{tan}}\left(\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}\right) \\ $$

Question Number 210248 Answers: 1 Comments: 0

Question Number 210236 Answers: 2 Comments: 0

Question Number 210235 Answers: 2 Comments: 2

Question Number 210234 Answers: 2 Comments: 2

Question Number 210233 Answers: 2 Comments: 0

Question Number 210231 Answers: 0 Comments: 1

Resoudre dans R { ((acos x−bsin x=c (x≠0))),((sin ((1/(sin x))) =d (−1≤d≤+1))) :}

$$\mathrm{Resoudre}\:\boldsymbol{\mathrm{dans}}\:\mathbb{R} \\ $$$$\begin{cases}{\boldsymbol{\mathrm{a}}\mathrm{cos}\:\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{b}}\mathrm{sin}\:\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{c}}\:\:\:\:\:\left(\boldsymbol{\mathrm{x}}\neq\mathrm{0}\right)}\\{\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{sin}\:\boldsymbol{\mathrm{x}}}\right)\:\:\:\:\:\:\:\:\:=\boldsymbol{\mathrm{d}}\:\:\:\:\left(−\mathrm{1}\leqslant\boldsymbol{\mathrm{d}}\leqslant+\mathrm{1}\right)}\end{cases} \\ $$$$ \\ $$

Question Number 210208 Answers: 4 Comments: 0

∫_0 ^1 e^e^e^x e^e^x e^x dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{{e}^{{e}^{{x}} } } \:{e}^{{e}^{{x}} } \:{e}^{{x}} {dx} \\ $$$$ \\ $$

Question Number 210206 Answers: 0 Comments: 0

Ω=∫_(1/e) ^e (dx/((1+x^2 )(1+xlog^7 x)))

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\frac{\mathrm{1}}{{e}}} ^{{e}} \frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}\mathrm{log}\:^{\mathrm{7}} {x}\right)} \\ $$$$ \\ $$

Question Number 210229 Answers: 3 Comments: 0

Question Number 210228 Answers: 0 Comments: 0

Question Number 210227 Answers: 0 Comments: 0

Question Number 210369 Answers: 0 Comments: 0

Question Number 210194 Answers: 0 Comments: 1

Question Number 210181 Answers: 0 Comments: 3

Question Number 210180 Answers: 1 Comments: 2

Question Number 210172 Answers: 3 Comments: 0

Question Number 210171 Answers: 0 Comments: 0

Find: lim_(n→+∞) (n/((n!)^2 4^n )) Π_(k=1) ^n ((2k−1)^2 + 4) = ?

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow+\infty} {\mathrm{lim}}\:\:\frac{\mathrm{n}}{\left(\mathrm{n}!\right)^{\mathrm{2}} \:\mathrm{4}^{\boldsymbol{\mathrm{n}}} }\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\prod}}\:\left(\left(\mathrm{2k}−\mathrm{1}\right)^{\mathrm{2}} \:+\:\mathrm{4}\right)\:=\:? \\ $$

Question Number 210157 Answers: 3 Comments: 0

Question Number 210156 Answers: 1 Comments: 0

Question Number 210155 Answers: 1 Comments: 0

Question Number 210142 Answers: 0 Comments: 1

Question Number 210133 Answers: 1 Comments: 0

calcul ∫_0 ^1 [nt^(n−1) (1−t)−t^n ]dt

$${calcul} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left[{nt}^{{n}−\mathrm{1}} \left(\mathrm{1}−{t}\right)−{t}^{{n}} \right]{dt} \\ $$

Question Number 210127 Answers: 1 Comments: 0

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