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- Obtain the center of gravity of the skin of the rotating object that occurs if the arc y = √9 - x2; (0≤x≤3) is rotated on the x-axisFind an equation for the tangent plane to the hyperboloid x2+y2−z2=1 at thepoint (3,1,3).Evaluate fc 2x ds, where consists of the arc of the parabola y= x2 from to followed by the vertical line segment from (1, 1) to(1, 2)
- Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point (3,2,4).Find the orthogonal trajectories of the family of curves (rectangular hyperbolas) given by xy = c. Show work here:The parametric curve x=2sin(t)+2, y=3cos(t)-2 describes a clockwise traveling vertical ellipse with centered at (2,-2). T or F?
- find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse x2/a2+y2/b2=1.about x-axis.given that a2-b2=1?Find the radius of curvature of the parabola y² = 4px at (0, 0).The curve in the plane defined by the equation (*) (x^2 + xy + y^2 = 7) is a rotated ellipse, shown in the figure. a) Use implicit derivation to find dy/dx expressed by x and y. (b) Show that the curve passes through the point (2,1) and find the equation of the tangent line to the curve at the point (2,1).
- Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer correct to 2 decimal places.)Find parametric equations for the semicircle x2 + y2 = a2, y> 0, using as parameter the slope t = dy/dx of the tangent to the curve at (x, y).What is the size of the largest segment parallel to the y axis inside the ellipsoid determined by the equation below? 4x2+5y2+3z2+6x+8y+5z−4=0