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Question Number 58789 Answers: 0 Comments: 2

Question Number 58785 Answers: 1 Comments: 0

Find the general solution of differential equation below : (cos x cos y + sin^2 x) dx − (sin x sin y + cos^2 y) dy = 0

$${Find}\:\:{the}\:\:{general}\:\:{solution}\:\:{of}\:\:\:{differential}\:\:{equation}\:\:{below}\:\:: \\ $$$$\left(\mathrm{cos}\:{x}\:\mathrm{cos}\:{y}\:+\:\mathrm{sin}^{\mathrm{2}} {x}\right)\:{dx}\:\:−\:\left(\mathrm{sin}\:{x}\:\mathrm{sin}\:{y}\:+\:\mathrm{cos}^{\mathrm{2}} {y}\right)\:{dy}\:\:=\:\:\mathrm{0} \\ $$

Question Number 58780 Answers: 1 Comments: 0

367×25 397×45 484×79

$$\mathrm{367}×\mathrm{25} \\ $$$$\mathrm{397}×\mathrm{45} \\ $$$$\mathrm{484}×\mathrm{79} \\ $$

Question Number 58779 Answers: 0 Comments: 0

What is area of the square. L=3^2 Width=1.3

$$\mathrm{What}\:\mathrm{is}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}.\:\mathrm{L}=\mathrm{3}^{\mathrm{2}} \\ $$$$\mathrm{Width}=\mathrm{1}.\mathrm{3} \\ $$

Question Number 58778 Answers: 0 Comments: 0

4.8×1.3

$$\mathrm{4}.\mathrm{8}×\mathrm{1}.\mathrm{3} \\ $$

Question Number 58776 Answers: 1 Comments: 0

81^(sin^2 x) +81^(cos^2 x) =30 0≤x≤π.solve for x.

$$\mathrm{81}^{{sin}^{\mathrm{2}} {x}} +\mathrm{81}^{{cos}^{\mathrm{2}} {x}} =\mathrm{30} \\ $$$$\mathrm{0}\leqslant{x}\leqslant\pi.{solve}\:{for}\:{x}. \\ $$

Question Number 58775 Answers: 0 Comments: 0

solve exactly: x^8 −8x^7 −16x^6 +208x^5 −152x^4 −928x^3 +704x^2 +1088x−368=0

$$\mathrm{solve}\:\mathrm{exactly}: \\ $$$${x}^{\mathrm{8}} −\mathrm{8}{x}^{\mathrm{7}} −\mathrm{16}{x}^{\mathrm{6}} +\mathrm{208}{x}^{\mathrm{5}} −\mathrm{152}{x}^{\mathrm{4}} −\mathrm{928}{x}^{\mathrm{3}} +\mathrm{704}{x}^{\mathrm{2}} +\mathrm{1088}{x}−\mathrm{368}=\mathrm{0} \\ $$

Question Number 58774 Answers: 0 Comments: 3

let f(x) =∫_(π/3) ^(π/2) (dθ/(1+xtanθ)) with x real 1) find a explicit form for f(x) 2) determine also g(x) =∫_(π/3) ^(π/2) ((tanθ)/((1+xtanθ)^2 )) dθ 3) let U_n (x) =f^((n)) (x) give U_n (x) at form of integral. 4) calculate ∫_(π/3) ^(π/2) (dθ/(1+2tanθ)) and ∫_(π/3) ^(π/2) ((tanθ dθ)/((1+2tanθ)^2 ))

$${let}\:{f}\left({x}\right)\:=\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{d}\theta}{\mathrm{1}+{xtan}\theta}\:\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)\:=\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{tan}\theta}{\left(\mathrm{1}+{xtan}\theta\right)^{\mathrm{2}} }\:{d}\theta \\ $$$$\left.\mathrm{3}\right)\:{let}\:{U}_{{n}} \left({x}\right)\:={f}^{\left({n}\right)} \left({x}\right)\:\:{give}\:{U}_{{n}} \left({x}\right)\:{at}\:{form}\:{of}\:{integral}. \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{d}\theta}{\mathrm{1}+\mathrm{2}{tan}\theta}\:\:{and}\:\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{tan}\theta\:{d}\theta}{\left(\mathrm{1}+\mathrm{2}{tan}\theta\right)^{\mathrm{2}} } \\ $$

Question Number 58772 Answers: 1 Comments: 0

(1/6)×(2/5)

$$\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$ \\ $$

Question Number 58771 Answers: 0 Comments: 0

decompose inside R(x) the fraction F(x) =(1/((x^2 −4)^n ))

$${decompose}\:{inside}\:{R}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)\:=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{{n}} } \\ $$

Question Number 58770 Answers: 2 Comments: 1

find the value of integrals I =∫_0 ^∞ (dx/((x^2 +1)^3 )) , J =∫_0 ^∞ (dx/((x^2 +1)^5 ))

$${find}\:{the}\:{value}\:{of}\:{integrals} \\ $$$$\:{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\:\:\:,\:{J}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{5}} } \\ $$

Question Number 58769 Answers: 0 Comments: 1

decompose the fractions inside C(x) 1) (1/((x^2 +1)^3 )) 2) (1/((x^2 +1)^5 ))

$${decompose}\:{the}\:{fractions}\:{inside}\:{C}\left({x}\right) \\ $$$$\left.\mathrm{1}\right)\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{5}} } \\ $$

Question Number 58756 Answers: 3 Comments: 0

Question Number 58754 Answers: 2 Comments: 0

Question Number 58753 Answers: 1 Comments: 1

find lim_(x→0) ((1−cos(x)cos(x^2 )....cos(x^n ))/x^n ) with n natural integr ≥2

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{1}−{cos}\left({x}\right){cos}\left({x}^{\mathrm{2}} \right)....{cos}\left({x}^{{n}} \right)}{{x}^{{n}} }\:\:\:{with}\:{n}\:{natural}\:{integr}\:\geqslant\mathrm{2} \\ $$

Question Number 58750 Answers: 0 Comments: 2

Question Number 58720 Answers: 2 Comments: 0

find (dy/dx) given that y = cos(x°)

$${find}\:\frac{{dy}}{{dx}}\:{given}\:{that}\:\:{y}\:=\:{cos}\left({x}°\right) \\ $$

Question Number 58717 Answers: 1 Comments: 1

Question Number 58716 Answers: 1 Comments: 0

(1/3)+(1/4)

$$\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 58700 Answers: 0 Comments: 5

a, b, c ∈ R^+ Find triple of positive real numbers (a, b, c) that satisfy a⌊b⌋ = 5 b⌊c⌋ = 5 c⌊a⌋ = 12

$${a},\:{b},\:{c}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{triple}\:\:{of}\:\:{positive}\:\:{real}\:\:{numbers}\:\left({a},\:{b},\:{c}\right)\:\:{that}\:\:{satisfy} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{a}\lfloor{b}\rfloor\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{b}\lfloor{c}\rfloor\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{c}\lfloor{a}\rfloor\:\:=\:\:\mathrm{12} \\ $$

Question Number 58698 Answers: 1 Comments: 4

▽^→ ∙((e^(br) /r^2 ) e_r ^∧ )=? b is a constant.

$$\overset{\rightarrow} {\bigtriangledown}\centerdot\left(\frac{{e}^{{br}} }{{r}^{\mathrm{2}} }\:\overset{\wedge} {{e}}_{{r}} \right)=?\:\:\:\:{b}\:{is}\:{a}\:{constant}. \\ $$

Question Number 58696 Answers: 1 Comments: 3

Question Number 58686 Answers: 0 Comments: 1

Question Number 58682 Answers: 1 Comments: 0

3(1/5)+2(1/(15))

$$\mathrm{3}\frac{\mathrm{1}}{\mathrm{5}}+\mathrm{2}\frac{\mathrm{1}}{\mathrm{15}} \\ $$

Question Number 58675 Answers: 0 Comments: 5

Question Number 58671 Answers: 3 Comments: 2

lim_(x→0) ((1−cos5x)/x^2 )

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\:\frac{\mathrm{1}−{cos}\mathrm{5}{x}}{{x}^{\mathrm{2}} } \\ $$

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