Find the Valume Vesultingfrom Therotationof the areer defineed by he caurke X=-y+y The ayis about the Straig Ant line y- Using the Lisk methe

Q: Find the length of the curve over the given interval. r = 8, [0, π/6]

A:

Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

A: Given that x23+y23=a23 To find the length of the curve:…

Q: Consider the region in the Second and third awadrants between the sirttt Circles xty?-4 and…

A:

Q: Sketch the grafph Following Funcfions Tor the :も L) 2=4- y bx+2y t3でンと *)モ x3+ +y2

A: Here we have to sketch the graph for the following function. i) 6x2+2y2+3z2=6j) z=x2+y2k) z=x3+y2L)…

Q: OMNPQ, with T the midpoint of MN and S the midpoint of QP AQMS = ANPT and MSPT is a O Given: Prove:…

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Q: R Given: m ZRTS = 90; M MN is the 1 bisector of TS. Prove: TM is a median. T. N

A: In a triangle RTS , angle of RTS is 90 and MN↔ is perpendicular bisector of TS Midsegment Theorem:…

Q: Find the midpoint OF the line seament given the FOllowing endpaints:(s,2)and(-u,1)

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Q: 3 Show thot tfe fundion fae Ax +26T* +C with A = AT E IR E IR", CE IR is strongly Convex if and only…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the length of the curve y = x³/2 from x = 0 to x = 5. O 12.407 O None of these O 14.702 O…

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Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

Q: 2人+人 2X PM the From Pi (x,,y,z,) to Pz (xz, Yz, Zz Prove that the Midpoint of the line Ssegment 12…

A: Let the 2 points in the line segment be,

Q: Find the are length of the polav Curve r=3° from o-0 to 0= 1

A: Solve the following

Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

Q: with Lagrange Inter lola tion » fmd the Pelynomie with minimum degree that involves the Points be Po…

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Q: 7 Cansder the surtace 2=9-x²-y?. a)Shetch the folloing secions Idbeling nlercepts Desonbe.in words,…

A: Given the surface z=4-x2-y2

Q: Compute the length of the curve 3ti – 6tk over the interval 8 <ts 18.

A:

Q: be chown that y,= é" and can e are Jolutions to the diffierential ニ equatiune dy dy 4. w Cy, yz)= ?…

A: Given- It can be shown that y1 = e2x and y2 = xe2x are solutions to the differential equation d2ydx2…

Q: (1) whot is 'the value of n that the xyn=c are per pendicular Curves とっ the Curves 1- mx

A: 1) What is the value of n so that the xn+yn=c curves are perpendicular to the y=x1-mxcurveGiven…

Q: Compute the length of the curve r(t) = (-6t,4t + 4, –5t – 3) over the interval 0 < t < 7. (Use…

A: The curve rt=-6t, 4t+4,-5t-3 over the interval 0≤t≤7

Q: By using Green's theorem evaluate (4.ry – y') dr + (x + 3ry) dy where C is a closed curve starting…

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Q: where Projuct of in tegra tion SÃr dR A-zi-xj-YK and =dxi +arj +dzK dR and %3D the seguent of the…

A: Use line integral

Q: compute the length of the curve over the given interval. r(t) = 2ti − 3tk, 11 ≤ t ≤ 15

A:

Q: OFind all Max. , Min, seddle Point for the fure tiens below: 3xy - 15 X +.

A: We need to find max. min. and saddle points of given function.

Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

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Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: and (X, ÿ) for Hae Find My, My, laminas the graph? of fim) - 9-x* Pamd' yoo of mus wi tt repert to x…

A: Compute, M using the formula, M=ρ∫abf(x)-g(x) dx .  Compute, My using the formula, My=ρ∫abxf(x)-g(x)…

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F.…

A:

Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

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Q: Y is neither on the interior, nor the exte Y lies in the interior or in the exterior of Y lies on…

A: In this question we will use basic of algebra. We will use basic concept of interior angle and…

Q: Examples Fid io av ed of the vegim borodkl by ke vegin Cuve and line hy mlars of double ifegrafin,…

A: Please refer the attached image for complete solution.

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: graph'the Sorution to the follow imy inginequratityon animber line nur (x-2) (x+5) z O

A: Solving the problem by doing the graph.

Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

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Q: Os Find the Taylor seaies af the gien funkon Point as conter and deteamina the with the vadius af…

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Q: A Bezier curve is defined by PO (0,0), PI (2,5), P2 (5,5) and P3 (7,0). Sub divide the curve at u…

A: We will get only one point as we have only one value of u. The given points are P00,0, P12,5, P25,5,…

Q: et whose A = T be standard matsix teans bormaton is the lineas 2. 3. Does maps R3 onto R4? s Ta one…

A: Given that T is a linear transformation whose standard matrix is given by A=203032005000. We have to…

Q: Let H = H4 U H, be the class of "positive" and "negative" circles in R² (the "negative" circles are…

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Q: Compute the length of the curve r(t) = (2t, In(t), t² ) over the interval1<t < 4. (Use symbolic…

A:

Q: let he Kegneion Iihe equibuon is y=3X+ lo and Ncoif I=65 Find the Kegrodli on Eg vubion line x

A: In this question, we find the regression line x on y from the given line y on x.

Q: Find the absolite marima and minima points between [o,u] gf y : * + 2dx' sunchion is porsbl.

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Q: O A parhcle moves on a straight Iimes with velouty funchon V() = Sinwt uslwt f ind its position…

A: To find the position function from the given velocity function.

Q: In the 0 are parel line bisects LAEG.Tf M<CGE = T2 Of CA EF diagram below lines ATB cand then what…

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Q: apply stok's Theorem to evaluate (Ydz +7dy+ xdz) whereCiB the curve of intersection of x²+ y²+z² =…

A:

Q: Prove that segment WN is a dilation of segment ZX by a scale factor of , using the distance formula.…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.