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AllQuestion and Answers: Page 447

Question Number 176804 Answers: 0 Comments: 1

Question Number 173736 Answers: 1 Comments: 0

Show that x^2 + 2xy + 3y^2 = 1, is a solution to the differential equation (x + 3y)^2 (d^2 y/dx^2 ) + 2(x^2 + 2xy + 2y^3 ) = 0

$$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{2xy}\:\:\:+\:\:\:\mathrm{3y}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{1},\:\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{differential}\:\mathrm{equation}\:\:\:\:\:\left(\mathrm{x}\:\:\:+\:\:\:\mathrm{3y}\right)^{\mathrm{2}} \:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:\:\:\:\:+\:\:\:\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{2xy}\:\:\:+\:\:\:\mathrm{2y}^{\mathrm{3}} \right)\:\:\:=\:\:\:\mathrm{0} \\ $$

Question Number 173734 Answers: 1 Comments: 0

lim_( n→∞) (n +2) ∫_0 ^( 1) x^( n) ln( 1+x )dx=?

$$ \\ $$$$\:\mathrm{lim}_{\:{n}\rightarrow\infty} \:\left({n}\:+\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:{x}^{\:{n}} \:\mathrm{ln}\left(\:\mathrm{1}+{x}\:\right){dx}=? \\ $$$$ \\ $$

Question Number 173733 Answers: 0 Comments: 3

Show that x^3 + y^3 = 1 is a solution to the differential equation 20x^3 + 3y^2 (d^2 y/dx^2 ) + 6y((dy/dx))^2 = 0

$$\mathrm{Show}\:\mathrm{that}\:\:\:\:\mathrm{x}^{\mathrm{3}} \:\:+\:\:\mathrm{y}^{\mathrm{3}} \:\:=\:\:\mathrm{1}\:\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{differential} \\ $$$$\mathrm{equation}\:\:\:\:\mathrm{20x}^{\mathrm{3}} \:\:\:+\:\:\:\mathrm{3y}^{\mathrm{2}} \:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:\:\:\:+\:\:\:\mathrm{6y}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\mathrm{2}} \:\:\:=\:\:\:\:\mathrm{0} \\ $$

Question Number 173732 Answers: 4 Comments: 1

solve for x∈R (√(x^2 −4))+2(√(x^2 −1))=x^2

$${solve}\:{for}\:{x}\in{R} \\ $$$$\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}+\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}={x}^{\mathrm{2}} \\ $$

Question Number 173729 Answers: 2 Comments: 0

Evaluate lim_(x→0) ((x−(1/( (√x)−x))+1)/(x^2 +((√x)/( (√x)−1))−1))

$${Evaluate} \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \frac{{x}−\frac{\mathrm{1}}{\:\sqrt{{x}}−{x}}+\mathrm{1}}{{x}^{\mathrm{2}} +\frac{\sqrt{{x}}}{\:\sqrt{{x}}−\mathrm{1}}−\mathrm{1}} \\ $$

Question Number 173768 Answers: 0 Comments: 0

Total factors of 20! = ?

$${Total}\:{factors}\:\:{of}\:\:\mathrm{20}!\:=\:? \\ $$

Question Number 173721 Answers: 1 Comments: 0

Question Number 173709 Answers: 0 Comments: 0

In triangle △ABC prove: cos(∡(A/2))>(1/4)∙((2a+b+c)/( (√(R(R+2r_a )))))

$$\mathrm{In}\:\mathrm{triangle}\:\bigtriangleup\mathrm{ABC}\:\mathrm{prove}: \\ $$$$\mathrm{cos}\left(\measuredangle\frac{\mathrm{A}}{\mathrm{2}}\right)>\frac{\mathrm{1}}{\mathrm{4}}\centerdot\frac{\mathrm{2a}+\mathrm{b}+\mathrm{c}}{\:\sqrt{\mathrm{R}\left(\mathrm{R}+\mathrm{2r}_{\mathrm{a}} \right)}} \\ $$

Question Number 173707 Answers: 3 Comments: 0

Let x,y∈R such that 2x^2 +3y^2 =5 Find the minimum and maximum of expression: P=x^3 −y^3 +x−2y

$$\mathrm{Let}\:\mathrm{x},\mathrm{y}\in\mathbb{R}\:\mathrm{such}\:\mathrm{that}\:\mathrm{2x}^{\mathrm{2}} +\mathrm{3y}^{\mathrm{2}} =\mathrm{5} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{and} \\ $$$$\mathrm{maximum}\:\mathrm{of}\:\mathrm{expression}: \\ $$$$\mathrm{P}=\mathrm{x}^{\mathrm{3}} −\mathrm{y}^{\mathrm{3}} +\mathrm{x}−\mathrm{2y} \\ $$

Question Number 173706 Answers: 2 Comments: 1

Question Number 173697 Answers: 1 Comments: 0

Question Number 173696 Answers: 0 Comments: 0

Question Number 173695 Answers: 1 Comments: 0

Question Number 176812 Answers: 1 Comments: 1

tan(a−b)=x and tan(a+b)=y then tan2α=?

$${tan}\left({a}−{b}\right)={x}\:\:\:\:{and}\:\:\:{tan}\left({a}+{b}\right)={y} \\ $$$${then}\:\:\:\:{tan}\mathrm{2}\alpha=? \\ $$

Question Number 176811 Answers: 0 Comments: 1

Question Number 176806 Answers: 0 Comments: 0

Σ_(k=0) ^(2n) cos^(2n) (θ+((kπ)/(2n)))

$$\underset{{k}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}{cos}^{\mathrm{2}{n}} \left(\theta+\frac{{k}\pi}{\mathrm{2}{n}}\right) \\ $$

Question Number 176821 Answers: 0 Comments: 2

Question Number 176820 Answers: 0 Comments: 20

Question Number 173687 Answers: 2 Comments: 0

Q : ((ln(a ))/(c−b)) =((ln(b))/(a−c)) = ((ln(c))/(b−a)) ⇒ a^( a) . b^( b) . c^( c) =?

$$ \\ $$$$\:\:\:{Q}\::\:\:\:\:\:\frac{{ln}\left({a}\:\right)}{{c}−{b}}\:=\frac{{ln}\left({b}\right)}{{a}−{c}}\:=\:\frac{{ln}\left({c}\right)}{{b}−{a}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:{a}^{\:{a}} .\:{b}^{\:{b}} .\:{c}^{\:{c}} \:=? \\ $$$$ \\ $$

Question Number 176083 Answers: 2 Comments: 0

can you find f(x)? f(x)−f(1−x)= x

$${can}\:{you}\:{find}\:{f}\left({x}\right)? \\ $$$${f}\left({x}\right)−{f}\left(\mathrm{1}−{x}\right)=\:{x} \\ $$

Question Number 173678 Answers: 3 Comments: 0

if f(x) is 2^(nd) digre function f(x−1)+f(x)+f(x+1)=x^2 +1 then faind f(2)=?

$${if}\:{f}\left({x}\right)\:{is}\:\mathrm{2}^{{nd}} \:{digre}\:{function}\:\:\: \\ $$$${f}\left({x}−\mathrm{1}\right)+{f}\left({x}\right)+{f}\left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${then}\:{faind}\:\:{f}\left(\mathrm{2}\right)=? \\ $$

Question Number 173677 Answers: 0 Comments: 2

Find tangent equation of two circles : L_1 : (x−5)^2 + (y+1)^2 = 9 L_2 : (x+4)^2 + (y−11)^2 = 144

$$\mathrm{Find}\:\:\mathrm{tangent}\:\:\mathrm{equation}\:\:\mathrm{of}\:\: \\ $$$$\mathrm{two}\:\:\mathrm{circles}\:: \\ $$$${L}_{\mathrm{1}} \::\:\left({x}−\mathrm{5}\right)^{\mathrm{2}} \:+\:\left({y}+\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{9} \\ $$$${L}_{\mathrm{2}} \::\:\left({x}+\mathrm{4}\right)^{\mathrm{2}} \:+\:\left({y}−\mathrm{11}\right)^{\mathrm{2}} \:=\:\mathrm{144} \\ $$

Question Number 173668 Answers: 3 Comments: 1

Question Number 181426 Answers: 1 Comments: 1

Question Number 181424 Answers: 1 Comments: 1

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