Student's Solution and Survival Manual for Calculus
7th Edition
ISBN: 9781524934040
Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J
Publisher: Kendall Hunt Publishing
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Question
Chapter 13.6, Problem 27PS
To determine
To find: The value of given integral by Stoke’ theorem.
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1. Please
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 =
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 + 3,z²) and the net is decribed by the equation y = 1 - x² - z², y ≥ 0, and oriented in the positive y-
=
direction.
(Use symbolic notation and fractions where needed.)
[[ v. ds =
Incorrect
8π
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Chapter 13 Solutions
Student's Solution and Survival Manual for Calculus
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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- 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 v = (x - y, z + y + 9, z?) and the net is decribed by the equation y = V1 - x² – z7, y > 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) v · dS = 10n Incorrectarrow_forward3. Use grad h(-3,4)=5i +3j and h(-3,4)=10 to answer the following questions. a) Find the differential of h at (-3,4). b) Find a normal vector to the contour of h at (-3,4). c) Find an equation of a tangent line to the contour of h at (-3,4). d) Find a normal vector to the surface of h at (-3,4,10). e) Find an equation of a tangent plane to the graph of h at (-3,4,10).arrow_forwardA 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 v = (x – y, z + y + 9, z?) and the net is decribed by the equation y = V1- x2 - z?, y > 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) v • dS = Incorrectarrow_forward
- 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 v = (x - y, z + y + 6, z? ) and the net is decribed by the equation y = 1 – x - z', y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) · dS = Incorrectarrow_forwardfellas is it controversial to existarrow_forward2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk toarrow_forward
- 3. Let F = (x - y, xy) and C be arc of the circle x? + y? = 4 traversed counter-clockwise from (2,0) to (-2,0). A sketch of the vector field a curve are below. (a) Using the image above, determine whether F- dr is positive or negative. (b) Evaluate | F . dĩ. You may use that sin?(t) = /2. (Hint: the answer is 16/3 + 27)arrow_forwardIncorrect. Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the vector field v = y² i + 1.1x² j using 5 steps with At = 0.1. Find the exact values of x1,.…. ,X5 and yı, , y5 and then fill in the blanks rounding your numbers to •.... three decimal places. X1 = i 1.1 ,Yi = i 2.51 X2 i 1.2 ,y2 3.273 X3 = i 1.3 ,Y3 = i 4.50283 X4 = i 1.4 , Y4 i 6.7162 X5 = i 1.5 , Y5 = i 11.4427 eTextbook and Media Hint I| ||arrow_forwardA 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 v = (x - y, z + y +7,z²) and the net is decribed by the equation y = √1-x²-2², y 20, and oriented in the positive y-direction. (Use symbolic notation and fractions where needed.) 1.45-1 yasarrow_forward
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