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Question Number 169807 Answers: 0 Comments: 0

Given that U=x^4 −6x^2 y^2 +y^4 , find v and w such that w=u+iv is analytic Mastermind

$${Given}\:{that}\:{U}={x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +{y}^{\mathrm{4}} ,\:{find} \\ $$$${v}\:{and}\:{w}\:{such}\:{that}\:{w}={u}+{iv}\:{is}\:{analytic} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169702 Answers: 1 Comments: 0

determinant ((0,4,1,1),(4,0,0,1),(3,5,2,1),(2,2,5,1))=

$$\begin{vmatrix}{\mathrm{0}}&{\mathrm{4}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{4}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{3}}&{\mathrm{5}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{2}}&{\mathrm{2}}&{\mathrm{5}}&{\mathrm{1}}\end{vmatrix}=\: \\ $$

Question Number 169774 Answers: 1 Comments: 3

Question Number 169771 Answers: 3 Comments: 0

(1/(1+cos^2 x)) + (1/(sin^2 x+1)) = ((48)/(35))

$$\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:+\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{1}}\:=\:\frac{\mathrm{48}}{\mathrm{35}} \\ $$

Question Number 169770 Answers: 0 Comments: 4

Question Number 169677 Answers: 2 Comments: 0

M = ∫ (dx/((x−4)(√(x^2 −6x+8)))) =?

$$\:\:\:\:{M}\:=\:\int\:\frac{{dx}}{\left({x}−\mathrm{4}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{8}}}\:=? \\ $$

Question Number 169671 Answers: 0 Comments: 0

Question Number 169669 Answers: 1 Comments: 0

Question Number 169668 Answers: 0 Comments: 1

Question Number 169667 Answers: 1 Comments: 0

find the domain of (i) (x/( (√(x+5)))) (ii) (√x)+2 (iii) (3/( (√(x+2))+5))

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{domain}}\:\boldsymbol{{of}} \\ $$$$\left(\boldsymbol{{i}}\right)\:\frac{\boldsymbol{{x}}}{\:\sqrt{\boldsymbol{{x}}+\mathrm{5}}} \\ $$$$\left(\boldsymbol{{ii}}\right)\:\sqrt{\boldsymbol{{x}}}+\mathrm{2} \\ $$$$\left(\boldsymbol{{iii}}\right)\:\frac{\mathrm{3}}{\:\sqrt{\boldsymbol{{x}}+\mathrm{2}}+\mathrm{5}} \\ $$

Question Number 169664 Answers: 1 Comments: 0

Given that n(A)=10 and n(B)=6 i) what is the largest possible of n(A∪B) ii) what is the smallest possible value of n(A∪B) iii) what is the smallest possible value of n(A∩B)

Question Number 169658 Answers: 1 Comments: 2

Question Number 169655 Answers: 1 Comments: 0

Question Number 169654 Answers: 2 Comments: 0

∫_0 ^1 ((3x^3 −x^2 +2x−4)/( (√(x^2 −3x+2)))) dx = ?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:\mathrm{d}{x}\:=\:? \\ $$

Question Number 169653 Answers: 1 Comments: 0

solve for x x^2 + (x^2 /((x+1)^2 )) = 3

$$ \\ $$$$\:\:\:{solve}\:{for}\:{x} \\ $$$$\:\:\:\:\:\:{x}^{\mathrm{2}} \:+\:\frac{{x}^{\mathrm{2}} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\:\:\:=\:\:\mathrm{3} \\ $$

Question Number 169650 Answers: 0 Comments: 1

f(x)= 3∣ sin(x)∣ −4∣cos(x)∣ R_( f) =?

$$ \\ $$$$\:\:\:\:\:\:\:{f}\left({x}\right)=\:\mathrm{3}\mid\:{sin}\left({x}\right)\mid\:−\mathrm{4}\mid{cos}\left({x}\right)\mid \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{R}_{\:{f}} \:=? \\ $$

Question Number 169646 Answers: 0 Comments: 0

If f(x)=[(x^(2x^4 ) /(x^x^2 +3))] then what will be the unit digit of f(10)?

$${If}\:{f}\left({x}\right)=\left[\frac{{x}^{\mathrm{2}{x}^{\mathrm{4}} } }{{x}^{{x}^{\mathrm{2}} } +\mathrm{3}}\right]\:{then}\:{what}\:{will}\:{be}\:{the}\:{unit}\:{digit}\:{of}\:{f}\left(\mathrm{10}\right)? \\ $$

Question Number 169640 Answers: 0 Comments: 1

∫cos(x^7 )dx =

$$\int\mathrm{cos}\left({x}^{\mathrm{7}} \right){dx}\:= \\ $$

Question Number 169635 Answers: 1 Comments: 1

lim_(x→−3) (((√(x^2 +7))+(√(25−x^2 ))−8)/( (√(−3x))−6+(√(18+3x)))) =?

$$\:\:\:\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{7}}+\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }−\mathrm{8}}{\:\sqrt{−\mathrm{3}{x}}−\mathrm{6}+\sqrt{\mathrm{18}+\mathrm{3}{x}}}\:=? \\ $$

Question Number 169631 Answers: 1 Comments: 4

Question Number 169620 Answers: 0 Comments: 3

Question Number 169626 Answers: 1 Comments: 0

Question Number 169613 Answers: 0 Comments: 3

Question Number 169612 Answers: 1 Comments: 0

Differentiate w.r.t ′x′ x^y +y^x =c Mastermind

$${Differentiate}\:{w}.{r}.{t}\:'{x}'\: \\ $$$${x}^{{y}} +{y}^{{x}} ={c} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169610 Answers: 1 Comments: 0

Question Number 169600 Answers: 3 Comments: 2

give : x,y,z∈R x+y+xy=8 y+z+yz=15 z+x+zx=35 ⇒x+y+z+xyz=?

$${give}\::\:{x},{y},{z}\in\mathbb{R}\: \\ $$$${x}+{y}+{xy}=\mathrm{8} \\ $$$${y}+{z}+{yz}=\mathrm{15} \\ $$$${z}+{x}+{zx}=\mathrm{35} \\ $$$$\Rightarrow{x}+{y}+{z}+{xyz}=? \\ $$

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