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Question Number 49736 Answers: 1 Comments: 1

there is two small and one grater circles that [two]are tangent to [one]and all three circles are inscribed in an ellipse with: [(a/b)=2(√2)]and tangent to it at two points such that center of circles are on major axe of ellipse. find: ((radi of great circle)/(radi of small circle)) .

Question Number 49731 Answers: 1 Comments: 0

one vertex of a equilateral triangle lies on one vertex of a square and two anothers lie on opposite sides of square such that triangle have the maximum area. find: 1.ratio of: ((square side)/(triangle side)) 2.angle between square side and triangle side.[need additional data?]

Question Number 49730 Answers: 0 Comments: 1

find the largest ellipse inscribed in a given rectangle and its major axe of:ellipse lies on rectangle diagonal.

Question Number 49725 Answers: 2 Comments: 1

Question Number 49708 Answers: 0 Comments: 0

Please integrate ∫(((e^(cos x) sin x)/(1−x^2 )))dx

$${Please}\:{integrate} \\ $$$$\int\left(\frac{\mathrm{e}^{\mathrm{cos}\:{x}} \mathrm{sin}\:{x}}{\mathrm{1}−{x}^{\mathrm{2}} }\right){dx} \\ $$

Question Number 49703 Answers: 0 Comments: 0

Given f(x)= sin2x+2cos2x find f′((π/4)) hence given g(x) = { ((x, 0≤x≤2)),((3x−x^2 , 2≤x≤3)) :} for a total range of 0≤x≤3 sketch the graph for y=g(x) and find the area with makes with the x−axis otherwise, find the composite function gf in the range 2≤x≤3.

$${Given}\:{f}\left({x}\right)=\:{sin}\mathrm{2}{x}+\mathrm{2}{cos}\mathrm{2}{x} \\ $$$${find}\:{f}'\left(\frac{\pi}{\mathrm{4}}\right) \\ $$$${hence}\:{given}\:{g}\left({x}\right)\:=\:\begin{cases}{{x},\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}}\\{\mathrm{3}{x}−{x}^{\mathrm{2}} ,\:\:\mathrm{2}\leqslant{x}\leqslant\mathrm{3}}\end{cases} \\ $$$${for}\:{a}\:{total}\:{range}\:{of}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{3}\:\:{sketch}\:{the}\:{graph}\:{for}\:{y}={g}\left({x}\right) \\ $$$${and}\:{find}\:{the}\:{area}\:{with}\:{makes}\:{with}\:{the}\:{x}−{axis} \\ $$$${otherwise},\:{find}\:\:\:{the}\:{composite}\:{function}\:\:{gf}\:\:{in}\:{the}\:{range} \\ $$$$\mathrm{2}\leqslant{x}\leqslant\mathrm{3}. \\ $$

Question Number 49696 Answers: 1 Comments: 1

Question Number 49680 Answers: 1 Comments: 0

Question Number 49678 Answers: 1 Comments: 1

Question Number 50924 Answers: 1 Comments: 0

factor the expression: E=x^5 +x^4 +1

$$\mathrm{factor}\:\mathrm{the}\:\mathrm{expression}: \\ $$$$\mathrm{E}={x}^{\mathrm{5}} +{x}^{\mathrm{4}} +\mathrm{1} \\ $$

Question Number 49692 Answers: 1 Comments: 0

The vectors a=xi+(x+1)j+(x+2)k, b=(x+3)i+(x+4)j+(x+5)k and c=(x+6)i+(x+7)j+(x+8)k are coplanar for

Question Number 49691 Answers: 1 Comments: 0

simplify ((log_3 64 × log_4 243)/(log_2 16))

$${simplify}\:\frac{{log}_{\mathrm{3}} \mathrm{64}\:×\:{log}_{\mathrm{4}} \mathrm{243}}{{log}_{\mathrm{2}} \mathrm{16}} \\ $$

Question Number 49748 Answers: 1 Comments: 0

Question Number 49661 Answers: 1 Comments: 2

calculateA_n =(1/(2i)) ∫_0 ^1 {(1+ix)^n −(1−ix)^n }dx

$${calculateA}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}{i}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left\{\left(\mathrm{1}+{ix}\right)^{{n}} −\left(\mathrm{1}−{ix}\right)^{{n}} \right\}{dx} \\ $$

Question Number 49660 Answers: 2 Comments: 1

Question Number 49647 Answers: 1 Comments: 3

let p(x) =x^(2n) −x^n +1 1) determine the roots of p(x) 2) factorize inside C[x] the polynom p(x) . 3)solve p(x)=0 and p(x) =2

$${let}\:{p}\left({x}\right)\:={x}^{\mathrm{2}{n}} \:−{x}^{{n}} \:+\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right)\:. \\ $$$$\left.\mathrm{3}\right){solve}\:{p}\left({x}\right)=\mathrm{0}\:\:{and}\:{p}\left({x}\right)\:=\mathrm{2} \\ $$

Question Number 49646 Answers: 0 Comments: 0

calculate ∫∫_D (x^2 −y^2 )(√(x^2 +y^2 ))dxdy with D ={(x,y)∈R^2 / −1≤x≤1 and 0≤y≤2 }

$${calculate}\:\int\int_{{D}} \left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{0}\leqslant{y}\leqslant\mathrm{2}\:\right\} \\ $$

Question Number 49645 Answers: 1 Comments: 0

calculate ∫∫_C ∣x+y∣dxdy with C=[−1,1]×[−1,1]

$${calculate}\:\int\int_{{C}} \:\mid{x}+{y}\mid{dxdy}\:\:{with}\:{C}=\left[−\mathrm{1},\mathrm{1}\right]×\left[−\mathrm{1},\mathrm{1}\right] \\ $$

Question Number 70360 Answers: 1 Comments: 0

l_(n→+∞) im (((√(n + 1 ))− n)/((√(n + 1)) + n)) = ?

$$\underset{{n}\rightarrow+\infty} {\mathrm{l}im}\:\:\:\:\frac{\sqrt{{n}\:+\:\mathrm{1}\:}−\:{n}}{\sqrt{{n}\:+\:\mathrm{1}}\:+\:{n}}\:\:=\:\:? \\ $$

Question Number 49642 Answers: 1 Comments: 0

if a+b =s and a^3 +b^3 =t find a^2 +b^2 and a^4 +b^4 interms of s and t .

$${if}\:\:{a}+{b}\:={s}\:{and}\:{a}^{\mathrm{3}} \:+{b}^{\mathrm{3}} \:={t}\:\:{find}\:{a}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \:\:{and}\:{a}^{\mathrm{4}} \:+{b}^{\mathrm{4}} \:{interms}\:{of}\:{s}\:{and}\:{t}\:. \\ $$

Question Number 49640 Answers: 1 Comments: 2

if x ∈[p,(√(p^2 +2))] calculate [x]

$${if}\:{x}\:\in\left[{p},\sqrt{{p}^{\mathrm{2}} \:+\mathrm{2}}\right]\:\:{calculate}\:\left[{x}\right] \\ $$

Question Number 49639 Answers: 1 Comments: 1

find a relation betwen [x]^2 and [−x]^2

$${find}\:{a}\:{relation}\:{betwen}\:\left[{x}\right]^{\mathrm{2}} \:{and}\:\left[−{x}\right]^{\mathrm{2}} \\ $$

Question Number 49638 Answers: 1 Comments: 0

let a>2 and f(a) =∫_(−(1/a)) ^(1/a) ((x^2 dx)/((√(1+x^2 ))+(√(1−x^2 )))) 1) calculate f(a) interms of a 2) calculate f^′ (a) .

$${let}\:{a}>\mathrm{2}\:{and}\:{f}\left({a}\right)\:=\int_{−\frac{\mathrm{1}}{{a}}} ^{\frac{\mathrm{1}}{{a}}} \:\:\:\frac{{x}^{\mathrm{2}} {dx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right)\:{interms}\:{of}\:{a} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({a}\right)\:. \\ $$

Question Number 49637 Answers: 1 Comments: 0

Question Number 49636 Answers: 1 Comments: 2

1) calculate A_n =∫_0 ^∞ e^(−n[x]) sin(x)dx with n integr and n≥1 2) find nature of Σ_(n=1) ^∞ A_n

$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{n}\left[{x}\right]} {sin}\left({x}\right){dx}\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{A}_{{n}} \\ $$

Question Number 49635 Answers: 1 Comments: 1

1)find f(x) =∫_0 ^(π/4) ((sint)/(2+x cos(2t)))dt 2) find g(x) =∫_0 ^(π/4) ((sint sin(2t)/((2+x cos(2t))^2 ))dx 3) find the value of ∫_0 ^(π/4) ((sint)/(2+3 cos(2t)))dt and ∫_0 ^(π/4) ((sin(t)sin(2t))/((2+3cos(2t))^2 ))dt

$$\left.\mathrm{1}\right){find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{sint}}{\mathrm{2}+{x}\:{cos}\left(\mathrm{2}{t}\right)}{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{sint}\:{sin}\left(\mathrm{2}{t}\right.}{\left(\mathrm{2}+{x}\:{cos}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{sint}}{\mathrm{2}+\mathrm{3}\:{cos}\left(\mathrm{2}{t}\right)}{dt}\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{sin}\left({t}\right){sin}\left(\mathrm{2}{t}\right)}{\left(\mathrm{2}+\mathrm{3}{cos}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}} }{dt} \\ $$

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