Calculus 3 :

Section 10.9: Problem 3 (1 point) Results for this submission Entered Answer Preview Result 5*sin(-5*t)+1 5 sin(-5t) + 1 correct -5*cos(-5*1)+5 -5 cos(-5t) + 5 correct (1*2)+1 12 + 1 correct cos(5*t)+t cos (5t) + t correct sin(-5*1)+5*1+1 sin(-5t) + 5t + 1 correct 513 ([5*(1*3)]/6)+1+1 itt+1 incorrect At least one of the answers above is NOT correct. 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) = (5sin( -51) + 1) it (-5 cos( -5t) +5) j+ (2 +1) k B. The position vector r(t) = cos( 57 ) + 1 it (sin( -5:) + 5t + 1) j+ +1+1 kSection 10.9: Problem 8 (1 point) Results for this submission Entered Answer Preview Result -52.6378*cos(1) -52.6378 cos(t) incorrect -52.6378*sin(t) -52.6378 sin(t) incorrect 52.6378 52.6378 correct At least one of the answers above is NOT correct. 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 7 (1 point) Match the surfaces with the verbal description of the level curves by placing the letter of the verbal description to the left of the number of the surface. f 1. 2 = \\25 -x2 - 12 2. z= vx' +y 3. 2 = 4. z =1'ty 5. z = 2x + 3y 6. z = cy 7. z = 2x2 + 3y? A. a collection of concentric ellipses B. a collection of unequally spaced parallel lines C. two straight lines and a collection of hyperbolas D. a collection of equally spaced concentric circles E. a collection of equally spaced parallel lines F. a collection of unequally spaced concentric circlesSection 11.1: Problem 9 (1 point) Find an equation for the contour of f(x, y) = 2xly + 10x + 15 that goes through the point (1, 2). Equation:Match the surfaces (a) - (f) below with the contour diagrams (1) - (6) below those. (b) (c) (3) Surface (a) matches contour ? (b) Surface (b) matches contour ? v (c) Surface (c) matches contour ? v (d) Surface (d) matches contour ? v (e) Surface (e) matches contour ? v [f) Surface (f) matches contour ? v y -U.3 0.5 -0.75 (1) (2) (3) -0.5 0.25 -05 (4) (5) (6) 1.5 D 0.5' :-0.5Section 11.1: Problem 13 (1 point) Sketch a contour diagram of each function. Then, decide whether its contours are predominantly lines, parabolas, ellipses, or hyperbolas. ? 1. 2=y-512 7 Lines 2. 2=141 Parabolas Ellipses 3. 2= -512 Hyperbolas 7 V 4. 2=1-Section 11.3: Problem 11 (1 point) Approximate fr(1, 3) using the contour diagram of f(I, y) shown below. 20 18 18 14 12 10 B 10 fr(1, 3)Section 11.3: Problem 12 (1 point) A contour diagram of z = f(x, y) is given in the figure. Determine whether f, and fy are positive, negative, or zero at the points P, Q, R, and S. v 1. fy at the point Q. high high ? v 2. f, at the point P. med ? v 3. fy at the point R. 4. fy at the point P. ? v 5. f, at the point Q. MOI ? 6. frat the point S. . R 7 7. fy at the point S. high ? v 8. f, at the point R. ? Positive (Click on graph to enlarge) Negative No Zero 50%% partial credit for 4 - 5 correct answers, and 75%% partial credit for 6 - 7 correct answers