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.

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Evaluate Szdz where y traces the arc of the parabola y = x² from (1,1) to (2,4).

A:

Q: Determine the length of the tangent to the circle x2 + y2 − 4x − 5 = 0 from (8, −2)

A:

Q: The line 2x − y + 1 = 0 is tangent to yhe circle at the point (2,5) and yhe center of the circl lies…

A: Center lies on x-2y=4.let the center be C(4+2t,t).nowradius r=distance of from the…

Q: Sketch one loop of the curve 9y² = x(3x)² Find the area of the surface of revolution generated by…

A:

Q: Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express…

A:

Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: ind point P and Q on the parabola y=(-x^2)+1 so that the triangle ABC formed by the x-axis and the…

A: Given that the curve is                         To find point P and Q on the given parabola, so that…

Q: particle started at A(1,0) circled the origin once  an d returned toA(1,0) .what were the change in…

A: Given: A particle started at A(1,0) circled the origin once  and  returns to A(1,0)

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: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

A:

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

A: