In Problems 17 to 30, for the curve
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- A cylindrical tank, shown to the right, has height 8 m and radius 4 m. Suppose the water tank is half-full of water. Determine the work required to empty the tank by pumping the water to a level 6 m above the top of the tank. Use 1000 kg/m for the density of water and 9.8 m/s² for the acceleration due to gravity. 3 4 m Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0 ≤ y ≤8, find the cross-sectional area A(y). A(y) = (Type an exact answer, using as needed.) 8 marrow_forwardIf you compute the surface area of a sphere as the volume of revolution of the parametric curve c(t) = (cos t, sin t), as t ranges from 0 to 27. you get 0. If you use the same parametrization, but restrict t to the range from () to T, you get 47 (the correct surface area for the sphere of radius 1). Why did you get 0 when t ranged from () to 27? O Having closed the circle parametrized by c, the displacement is zero, so the surface area is zero. O Sine has the same (unsigned) area of its positive part on 0, 27 as its negative part, but on 0, 7|, it is all positive. So the sine contribution cancels out on the longer interval and not on the shorter interval. O Correct. The contribution from t e [0, 7| is exactly cancelled by t e T, 27| because the positive contributions for y(t) = cos tin the first interval are exactly cancelled by the negative contributions in the second interval. O The arc length contribution from the upper semicircle is negative because x' (t) < 0 on that semicircle…arrow_forward- Another bowl has the shape of a paraboloid. The equation of the cross- section with the (x, z)-plane is x² = 2RAZ, where RA is the curvature radius at point A. One releases at a point with height z = h a point mass with initial velocity equal to 0. What is in this case the magnitude of the force exerted by the particle on the bowl when it passes point A?arrow_forward
- 6. 25. Sketch y=. Calculate the radius of curvature at x 2 and sketch the oscillating circle. 26. Find the unit tangent vector and unit normal vector to r(t)= 2ri+e'j+e k. 27. Find equations of the normal and osculating planes of the curve of intersection of the parabolic cylinders x= y and z = x² at the point (1, 1, 1). %3D 28. At what point on the curve x=r,y = 3t,z =1* is the normal plane parallel to the plane 6x + 6y- 8z = 1? %3Darrow_forwardPlease see picturearrow_forwardThe 0.50 lb ball is shot from the spring device shown. The spring has a stiffness k = 10 lb/in. and the four cords C and plate P keep the spring compressed 2 in. when no load is on the plate. The plate is pushed back 3 in. from its initial position. (Eigure 1) If it is then released from rest, determine the speed of the ball when it travels 23 in. up the smooth plane. Express your answer to three significant figure and include the appropriate units. HA Value ft/s v = 30arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage