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- Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 6x2 + 4y2 + 5z2 = 30 at the point (−1, 1, 2). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)(a) Find the minimum and maximum xcoordinates of points on the cardioid r =1−cosθ.(b) Find the minimum and maximum ycoordinates of points on the cardioid in part (a).find a parametrization for the curve. 1. the left half of the parabola y = x2 + 2x 2. the ray (half line) with initial point (2, 3) that passes through the point (-1, -1) 3. the ray (half line) with initial point (-1, 2) that passes through the point (0, 0)
- 3. The equation (surface) z-x^2-2y^2+2x-4y-2=0 is given. your surface; a) Determine the type of intersection curve with the z = 0 plane and draw it. b) Find the tangent plane and normal line at (0, 0, 2).7. Graph the surface z = f (x, y) = x ^ 2 + 2 y ^ 2 - 2x + 4y + 2. Also write the reduced equation of the intersection curve of the surface with the z = 0 plane.Fast pls solve this question correctly in 5 min pls I will give u like for sure Nidi Find an equation of the tangent plane to the given surface at the specified point. z = 2(x − 1)^2 + 6(y + 3)^2 + 1, (2, −2, 9)
- A space curve Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y = ln (t + 2), z = t.please do not provide solution inimage format thank you. A thin metal plate located in the center of the xy plane has a temperature T(x, y) at the point(x,y) given by T(x, y) = 100/(1 + x^2 + y^2) . (a) What is the temperature on the plate at point (1, 2), approximately? (b) At what point is the temperature as high as possible? (c) If a particle moves away from the origin, moving along the positive x axis, Will the temperature increase or decrease? (d) At what points is the temperature 50? (e) The contour lines of T are called isotherms (because all points on a of these curves have the same temperature). Sketch some isotherms of that function.The curve (x - a) ^ 2 + z ^ 2 = r ^ 2 lying on the plane of XZ- in R ^ 3 region formed by rotating the around the Z- axis (where a and r are positive constants) Cartesian (closed) and parametric Find the equation.
- Consider the equation of the surface S given by x2z2 + xy + yz = 7. An equation for the plane tangent to S at the point (−1, −1, 3) is given by: Answers in the picture:Find equations for all the planes that intersect the y-axis at y = 1 and the z-axis at z = 2, and are tangent to the sphere (x-2)^2 + y^2 + z^2 = 4. Do not use calculusUse a graphing utility to obtain the plane curve represented by the given parametric equations :Cycloid: x = 3(t - sin t), y = 3(1 - cos t);[0, 60, 5] x [0, 8, 1], 0 ≤ t < 6π.