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Exercise (D):y=x−1 directed by u^→ (1;1). his normal vector is v^→ (2;−2). 1) Determinate the equation of (Δ) such as t_v^→ =S_((D)) °S_((Δ)) 2)Determinate the nature and caracteristics of this application h=S_((D)) °t_v^→

$$\mathrm{Exercise} \\ $$$$\: \\ $$$$\left(\mathrm{D}\right):\mathrm{y}=\mathrm{x}−\mathrm{1}\:\:\mathrm{directed}\:\mathrm{by}\:\:\:\overset{\rightarrow} {\mathrm{u}}\left(\mathrm{1};\mathrm{1}\right). \\ $$$$\mathrm{his}\:\mathrm{normal}\:\mathrm{vector}\:\mathrm{is}\:\overset{\rightarrow} {\mathrm{v}}\left(\mathrm{2};−\mathrm{2}\right). \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determinate}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\:\left(\Delta\right)\: \\ $$$$\mathrm{such}\:\mathrm{as}\:\mathrm{t}_{\overset{\rightarrow} {\mathrm{v}}} =\mathrm{S}_{\left(\mathrm{D}\right)} °\mathrm{S}_{\left(\Delta\right)} \\ $$$$\left.\mathrm{2}\right)\mathrm{Determinate}\:\mathrm{the}\:\mathrm{nature}\:\mathrm{and}\:\mathrm{caracteristics} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{application}\:\mathrm{h}=\mathrm{S}_{\left(\mathrm{D}\right)} °\mathrm{t}_{\overset{\rightarrow} {\mathrm{v}}} \\ $$$$ \\ $$

Question Number 92860 Answers: 0 Comments: 2

(√(1−x^2 )) sin^(−1) (x) dy + y dx = 0

$$\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{dy}\:+\:\mathrm{y}\:\mathrm{dx}\:=\:\mathrm{0}\: \\ $$

Question Number 92852 Answers: 3 Comments: 1

y′′+2y′+y = x^2 e^(−x) cos x what is particular solution

$$\mathrm{y}''+\mathrm{2y}'+\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \mathrm{e}^{−\mathrm{x}} \mathrm{cos}\:\mathrm{x} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{particular}\:\mathrm{solution} \\ $$$$ \\ $$

Question Number 92839 Answers: 1 Comments: 0

let a is complex number such that a^(10) + a^5 +1 = 0. find a^(2005) + (1/a^(2005) ) ?

$$\mathrm{let}\:\mathrm{a}\:\mathrm{is}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{such}\: \\ $$$$\mathrm{that}\:\mathrm{a}^{\mathrm{10}} \:+\:\mathrm{a}^{\mathrm{5}} \:+\mathrm{1}\:=\:\mathrm{0}. \\ $$$$\mathrm{find}\:\mathrm{a}^{\mathrm{2005}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2005}} }\:? \\ $$

Question Number 92838 Answers: 0 Comments: 4

(x+y)(dy/dx) = x^2 +xy+x+1

$$\left(\mathrm{x}+\mathrm{y}\right)\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{x}+\mathrm{1} \\ $$

Question Number 92835 Answers: 0 Comments: 3

Question Number 92831 Answers: 1 Comments: 5

Question Number 92820 Answers: 1 Comments: 0

a convergent geometric sequence with first term a is such that the sum of the terms after the n^(th) term is three times the n^(th) term, find the common ratio and show that its sum to infinity is 4a.

$${a}\:{convergent}\:{geometric}\:{sequence}\:{with} \\ $$$${first}\:{term}\:{a}\:{is}\:{such}\:{that}\:{the}\:{sum}\:{of} \\ $$$${the}\:{terms}\:{after}\:{the}\:{n}^{{th}} \:{term}\:{is} \\ $$$${three}\:{times}\:{the}\:{n}^{{th}} \:{term},\:{find}\:{the} \\ $$$${common}\:{ratio}\:{and}\:{show}\:{that}\:{its}\: \\ $$$${sum}\:{to}\:{infinity}\:{is}\:\mathrm{4}{a}. \\ $$

Question Number 92808 Answers: 0 Comments: 0

Can you prove it: t=Φ

$$\mathrm{Can}\:\mathrm{you}\:\mathrm{prove}\:{it}: \\ $$$${t}=\Phi \\ $$

Question Number 92807 Answers: 2 Comments: 1

Question Number 92804 Answers: 1 Comments: 12

Solve the following differential equations: (i). e^(x−y) dx +e^(y−x) dy=0 (ii). (dy/dx) = (√(y−x)) (iii). (dy/dx)= ((3xy+y^2 )/(3x^2 ))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{differential}\:\mathrm{equations}: \\ $$$$\:\left(\mathrm{i}\right).\:\mathrm{e}^{\mathrm{x}−\mathrm{y}} \:\mathrm{dx}\:+\mathrm{e}^{\mathrm{y}−\mathrm{x}} \:\mathrm{dy}=\mathrm{0} \\ $$$$\:\:\left(\mathrm{ii}\right).\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\sqrt{\mathrm{y}−\mathrm{x}} \\ $$$$\:\left(\mathrm{iii}\right).\:\frac{\mathrm{dy}}{\mathrm{dx}}=\:\frac{\mathrm{3xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{3x}^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 92805 Answers: 1 Comments: 0

Evaluate: ∫_R ∫ ((xy)/(√(1−y^2 ))) dx dy where the region of integration is the positive quadrant of the circle x^2 +y^2 =1.

$$\:\mathrm{Evaluate}: \\ $$$$\:\int_{\boldsymbol{\mathrm{R}}} \int\:\frac{\boldsymbol{\mathrm{xy}}}{\sqrt{\mathrm{1}−\boldsymbol{\mathrm{y}}^{\mathrm{2}} }}\:\boldsymbol{\mathrm{dx}}\:\boldsymbol{\mathrm{dy}}\:\mathrm{where}\:\mathrm{the}\:\mathrm{region}\:\mathrm{of}\:\mathrm{integration}\:\mathrm{is}\:\mathrm{the} \\ $$$$\:\mathrm{positive}\:\mathrm{quadrant}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{1}. \\ $$$$ \\ $$

Question Number 92801 Answers: 0 Comments: 0

Integrate following : (i).∫ (( dx)/(sin x( 3+2cos x))) (ii).∫(√((sin(x−α))/(sin(x+α)))) dx

$$\boldsymbol{\mathrm{Integrate}}\:\boldsymbol{\mathrm{following}}\:: \\ $$$$\:\:\left(\boldsymbol{\mathrm{i}}\right).\int\:\frac{\:\:\mathrm{dx}}{\mathrm{sin}\:\mathrm{x}\left(\:\mathrm{3}+\mathrm{2cos}\:\mathrm{x}\right)} \\ $$$$\:\:\left(\boldsymbol{\mathrm{ii}}\right).\int\sqrt{\frac{\mathrm{sin}\left(\mathrm{x}−\alpha\right)}{\mathrm{sin}\left(\mathrm{x}+\alpha\right)}}\:\:\mathrm{dx}\: \\ $$$$ \\ $$

Question Number 92799 Answers: 0 Comments: 2

Show that the function x→x^3 is of Riemann within the interval [−1,2] then calculate ∫_(−1) ^2 x^2 dx

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{x}\rightarrow\mathrm{x}^{\mathrm{3}} \:\mathrm{is} \\ $$$$\mathrm{of}\:\mathrm{Riemann}\:\mathrm{within}\:\mathrm{the}\:\mathrm{interval}\:\left[−\mathrm{1},\mathrm{2}\right] \\ $$$$\mathrm{then}\:\mathrm{calculate}\:\int_{−\mathrm{1}} ^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \mathrm{dx} \\ $$

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