Taylor Coates Assignment homework4 due 10/07/2017 at 11:00pm EDT ma215-f17 are all correct or if you have at least one error. Enter your answers as roman numerals, either upper or lower case. (1) x 3y (2) x.25 (y + 0.25).75 2 2 (3) x2 y2 ex y (Click on an image to enlarge it. Note that values along the axes always increase in the direction towards you or, in the case of the z axis, increase going up.) 1. (1 point) Math 215 Homework homework4, Problem 1 The velocity of a particle is given by v(t) = 2t, 5, 5e5t . If the particle starts at the position r(0) = h3, 3, 1i, measured from some origin, find the acceleration a(t): the position r(t): Answer(s) submitted: (incorrect) 2. (1 point) Suppose~r(t) = cost~i + sint ~j + 4t~k represents the position of a particle on a helix, where z is the height of the particle above the ground. (a) Is the particle ever moving downward? [?/yes/no] If the particle is moving downward, when is this? When t is in (Enter none if it is never moving downward; otherwise, enter an interval or comma-separated list of intervals, e.g., (0,3], [4,5].) (b) When does the particle reach a point 18 units above the ground? When t = (c) What is the velocity of the particle when it is 18 units above the ground? ~v = (d) When it is 18 units above the ground, the particle leaves the helix and moves along the tangent. Find parametric equations for this tangent line (pick t so that it is continuous through the time when the particle leaves the helix). x(t) = , y(t) = , z(t) = Figure I Figure II Figure III Figure IV Figure V Figure VI Answer(s) submitted: II V VI (score 0.666666686534882) 4. (1 point) Math 215 Homework homework4, Problem 4 Match each of the functions labeled 1-3 with one of the contour graphs I-VI. Note that because this is a matching problem, when you submit your answers you won't be told which are incorrect, only if they are all correct or if you have at least one error. Enter your answers as roman numerals, either upper or lower case. (1) sin(y) 1 (2) 2 2 Answer(s) submitted: (incorrect) (x2) +y +1 3. (1 point) Math 215 Homework homework4, Problem 3 Match each of the functions labeled 1-3 with one of the graphs I-VI. Note that because this is a matching problem, when you submit your answers you won't be told which are incorrect, only if they (3) |xy| (Click on an image to enlarge it. Note that values along the axes always increase in the direction towards you or, in the case of the z axis, increase going up.) 1 Figure I Figure II (b) At point R, fx is [?/positive/negative] and fy is [?/positive/negative]. (c) At point S, fx is [?/positive/negative] and fy is [?/positive/negative]. Figure III Answer(s) submitted: Figure IV Figure V Figure VI Answer(s) submitted: II I III positive positive negative negative negative positive (correct) 7. (1 point) Math 215 Homework homework4, Problem 7 Find the equation of the plane tangent to the graph of the function (correct) 5. (1 point) Math 215 Homework homework4, Problem 5 For the function z(x, y) = 8x2 5y2 + 4x + 8y + 3 f (x, y) = 6x3 y3 exy at the point (x, y) = (10, 4). plane: z = calculate each of the indicated partial derivatives. fx = fy = fxyy = Answer(s) submitted: (incorrect) Answer(s) submitted: 18y3*x2-(e(x*y))*y 18*x3*y2-(e(x*y))*x 108*x2*y-(e(x*y))*(x2)*y-(2e(x*y))*x 8. (1 point) The gas equation for one mole of oxygen relates its pressure, P (in atmospheres), its temperature, T (in K), and its volume, V (in cubic decimeters, dm3 ): (correct) 6. (1 point) Determine the sign of fx and fy at each indicated point using the contour diagram of f shown below. (The point P is that in the first quadrant, at a positive x and y value; Q through T are located clockwise from P, so that Q is at a positive x value and negative y, etc.) T = 16.574 1 1 0.52754 2 0.3879 P + 12.187V P. V V (a) Find the temperature T and differential dT if the volume is 38 dm3 and the pressure is 1.25 atmosphere. T= dT = (b) Use your answer to part (a) to estimate how much the volume would have to change if the pressure increased by 0.2 atmosphere and the temperature remained constant. change in volume = Answer(s) submitted: (a) At point P, fx is [?/positive/negative] and fy is [?/positive/negative]. (incorrect) c Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 2