Concept explainers
HOW DO YOU SEE IT? Consider the force field shown in the figure. To print an enlarged copy of the graph.
Give a verbal argument that the force field is not conservative because you can identify two paths that require different amounts of work to move an object from
Give a verbal argument that the force field is not conservative because you can find a closed curve C such that
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Calculus (MindTap Course List)
- A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by = (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) V. dS =arrow_forwardq1arrow_forwardEvaluate fa F . dĩ for F = 3x² î + (2xz – y)j + z k along - straight line joining (0, 0, 0) and (2, 1, 3)arrow_forward
- Fill in the table and then sketch the vector field. y F(x, y) = -2 -2 -2 2 -2 -2 -2 3- -2- 2. /- 2.arrow_forwardUsing a graphic calculator, plot the vector field F(r, y) = e j. Explain briefly with words why the plot has this shape.arrow_forwardi+e³ j. shows the direction of the winds 2 in the sky on a windy day, viewing above. If you decide to fly a kite with the coordinates of [0.5, 0.5] in this vector field, what would be the path that your kite travel? Imagine the vector field generated by the function: F = The kite would fly towards the point with [2,-1] coordinate. The kite would fly towards the y = -0.5 line. The kite would fly towards the point with [1,1] coordinate. The kite would fly towards the point with [-2,-1] coordinate.arrow_forward
- HW1 2) Find the curl of F. VxF=arrow_forwardSketch the curve traced out by the vectorvalued function. Indicate the direction in which the curve istraced out.arrow_forwardEvaluate fe z sin(22) dz where C is the union of the lower-half of the unit circe in clockwise direction AND the directed line segment that joins the point (-1, 0) to the point (-3, 4).arrow_forward
- (b). Use Green's Theorem to evaluate SF. dr. F(x, y) = (e³x², 2xy), where C is the triangle from (-2,0) to (2,0) to (0, 2) to (-2, 0).arrow_forwardsketch the space curve represented by the vector-valued function and give the orientation of the curve. I need help with these two problems.arrow_forwardYou are on a rollercoaster, and the path of your body is modeled by a vector function r(t), where t is in seconds, the units of distance are in feet, and t = 0 represents the start of the ride. Assume the axes represent the standard cardinal directions and elevation (x is E/W, y is N/S, z is height). Explain what the following would represent physically, being as specific as possible. These are all common roller coaster shapes/behaviors and can be explained in specific language with regard to units: a. r(0)=r(120) b. For 0 ≤ t ≤ 30, N(t) = 0 c. r'(30) = 120 d. For 60 ≤ t ≤ 64, k(t) = 40 and z is constant. e. For 100 ≤ t ≤ 102, your B begins by pointing toward positive z, and does one full rotation in the normal (NB) plane while your T remains constant.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage