Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is formed by y = x, x² + y² = 4 and y-axis for which х, у 2 0.

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

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Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: Find the distance between point A(-1,4,6) and the line of parametril equations x = 2-3t, y = -4+t, z…

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Q: 5. Let L₁ be the line with parametric form (x, y, z) = (1, 0, 2) + (-1,2,3), and let L₂ be the line…

A: Given,The parametric form of the line ,The parametric form of the line ,.Aim: (a) To find the angle…

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: Suppose parametric equations for the line segment between (7, 4) and (0, 6) have the form: S#(t)…

A: Values of constants

Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: c. Evaluate f 3x ds, where C consists of arc C₁ of parabola y = x² from (0,0) to (2,4), followed by…

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Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

Q: 3. Find the 1-parametric equation of the line in the plane passing through the vector P=[]-[9] Hint:…

A: p = [-3,2]q = [0,-3]now find parametric equation lines

Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given:

Q: Corsider the curve given by C = CqU Cz U Cg Ine value of (1. 1) C: y- 32 A) 15 24 B) 72 C) 15 11 D)…

A: We have to evaluate the integral ∫Cxdx+x2dy Now we have three curves.  Now, C=C1∪C2∪C3, therefore,…

Q: 23. Let w x₁ + iy₁ and 2 = x₂ + y₂. (a) Show that the distance WZ between the points w and z is |z −…

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Q: If UW = 4t- 16 and UY = t + 14, find UY in rhombus VWXY.

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Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…