Determine a∈R such that ∫CF⋅dr = −2−(3π/4), where F (x, y) = (ay, (x^2 − y)/2) and C is the part of the circle with center at the origin and radius 1, with y≥0, followed by the part of y = x^2−1 of x = −1 a x = 1.

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A: The given equation is: xy2+2xy=8...(1)

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A: A graph is concave up if f''x>0 and concave down if f''x<0. When f''x>0, it means…

Q: Evaluate where C is the portion of the circle centered at the origin with radius 2 in the 1st…

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Q: Q4) Show that the point (-1, 0) lies on the curve 6x² + 3xy + 2y2 + 17y – 6 = 0. Then find the…

A: Put x=-1 and y=0 in the equation of curve that is…

Q: 5) Find the distance between the pole and the point (r, 0) = (-1, ). %3D

A: A detailed solution is given below.

Q: Evaluate S (* + 7)i + (2») 5).dF. where Lis the quarter-circle with parametric form z = cos (t) and…

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Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Find the equation of the family of circles whose center is at the y-axis. A. y "+ 3y + 7 = 0 В. ху "…

A: Please refer the attached image for complete solution.

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Q: A' C C' B'X 0 2 4 6 . 8. 2.

A: