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Find the circulation of fluid motion F⃑(x, y) = xi⃑ − xyj⃑ along positively oriented ellipse x
2 + 4y
2 = 4.
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- Find a point on the ellipsoid x2 + 4y2 + z2 = 9 where the tangent plane is perpendicular to the line with parametric equations x = 2 − 4t, y = 1 + 8t, and z = 3 − 2tFind parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 3x2 + 2y2 + 6z2 = 29 at the point (−1, 1, 2).Find a point on the ellipsoid x² 2y2 + z2 = 19 where the tangent plane is perpendicular to the line with parametric equations x = 2 – 8t, y = 5 + 4t, and z = 4 - 2t. (х, у, 2) %3 ( (х, у, 2) %3D ( ) (smaller x-value) ) (larger x-value)
- Find the equation in the x'y 'system obtained by 45 ° rotation of the curve whose equation is xy = 1 in the xy system?Show that 2xyz (x² + y²)² W = = (x² - y²)z (x² + y²)² y are the velocity (x² + y²) components of a possible liquid motion. Is this motion irrotational ?Consider the ellipsoid x^2+2y^2+3z^2=21.
- The motion of a particle in space is defined by the parametric equationx(t) = −t2 + 3t + 1, in meter and y(t) = 2t + 5, in meter. Determine the (a) position, (b) velocity, and (c) acceleration of the particle when t = 5 seconds.The plane y + z = 2 intersects the cylinder x2 + y2 = 5 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (2, 1, 1). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)A space probe in the shape of the ellipsoid 4x2 + y2 + 4z2 = 16 enters Earth’s atmosphere and its surface begins to heat. After 1 hour, the temperature at the point (x, y, z) on the probe’s surface is T(x, y, z) = 8x2 + 4yz - 16z + 600. Find the hottest point on the probe’s surface.
- Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y² + = 3.A space probe in the shape of the ellipsoid 4x +y +4z = 41 enters a planet's atmosphere and its surface begins to heat. After 1 hour, the temperature at the point (x,y,z) on the probe's surface is T(x,y,z) = 8x + 4yz - 16z + 599. Find the hottest point on the probe's surface. ..... The hottest point is D.Two particles travel along the space curves r(t) and u(t). If r(t)and u(t) intersect, will the particles collide? Yes No Maybe