Calculus 3 :

Section 10.9: Problem 3 (1 point) Given that the acceleration vector is a(t) = (-25 cos(-5t))i + (-25 sin(-5t))j + (2t)k, the initial velocity is v(0) = i + k, and the initial position vector is r(0) = i + j + k, compute: A. The velocity vector v(t) (5 sin( -5t) + 1) it (-5 cos ( -5t) + 5) it (12+ 1 k B. The position vector r(t) = (-5t) + it (sin ( -5t) + 5t + 1) i+ +t+1 kSection 10.9: Problem 6 (1 point) A projectile is fired from ground level with an initial speed of 300 m/sec and an angle of elevation of 30 degrees. Use that the acceleration due to gravity is 9.8 m/ sec?. (a) The range of the projectile is | 7953.3 |meters. (b) The maximum height of the projectile is 2828.7 meters. (c) The speed with which the projectile hits the ground is | 300 m/sec.Section 10.9: Problem 7 (1 point) A ball is thrown at an angle of 45 degrees to the ground, and lands 50 meters away. The initial speed of the ball was 17.14 m/sec. Preview My Answers Submit AnswersSection 10.9: Problem 8 (1 point) A body of mass 6 kg moves in a (counterclockwise) circular path of radius 8 meters, making one revolution every 6 seconds. You may assume the circle is in the xy-plane, and so you may ignore the third component. A. Compute the centripetal force acting on the body. -52.6378 cos (t) -52.6378 sin t B. Compute the magnitude of that force. 52.6378 Note: Use exact forms or at least 4 significant digits in your answers.Section 11.1: Problem 1 (1 point) Evaluate the function at the specified points. h(r, y, z) = yZ, (2, -5, -2), (3,4, -2) At (2, -5, -2): At (3, 4, -2):Section 11.1: Problem 7 {1 point] Match the surfaces with The verbal description 01 the level curves by placing the letter oi the verbal description to the left of the number of The surface. .1.z= \"253393 A. a collection of concentric ellipses B. a collection of unequally spaced parallel lines C. two straight lines and a collection of hyperbolas I}. a collection of equally spaced concentric circles E. a collection ofequalljr spaced parallel lines F. a oollection of unequally spaced concentric circles Section 11.1: Problem 8 (1 point) On a map showing the Superstition mountains, the contour lines are: OA. closely spaced OB. far apart On a map showing the Bonneville Flats of Utah, the contour lines are: O A. closely spaced OB. far apartSection 11.1: Problem 11 (1 point) Match each of the tables shown below with the contour diagrams below them. yr -10 1 y\\ -10 1 2 1 0 |1 (a) b 1 0 1 2 1 2 1 2 0 1 0 y\\ -10 1 y\\ -10 1 -1 2 2 2 (c) 10 12 (d) 0 0 0 0 1 2 1 1 2 2 2 1 : 10 Table (a) : graph ? V Table (b) : graph ? Table (c) : graph ? Table (d) : graph v 1. 6. 0 2