Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 13.7, Problem 21PS
To determine
To verify: That the points R and S are source, the point T is sink and the point U is neither a source nor a sink.
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Check out a sample textbook solutionStudents have asked these similar questions
If F = (2x +y?)i + (3y - 4x)j, evaluate
F.dr around the triangle C of Figure 1, (a) in the indicated
direction, (b) opposite to the indicated direction.
Ans. (a) – 14/3 (b) 14/3
(1,1)
(2,1)
(2,0)
Fig. 1
Fig. 2
A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is
started in motion from the equilibrium position with a downward velocity of 3 feet per second. The air resistance (in
pounds) of the moving ball numerically equals 4 times its velocity (in feet per second).
Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction
is down.)
Take as the gravitational acceleration 32 feet per second per second.
y =
Hint:
e^(-16t)(((1/(2sqrt(2))*e^(8sqrt(2)t)-(1/(2sqrt(2))*e^(-8sqrt(2)t))
The path r(t) = (t) i+ (4t - 1) j describes motion on the parabola y = 4x-1. Find the particle's velocity and acceleration vectors at t= 1, and sketch them as vectors on the curve.
The velocity vector at t= 1 is v(1) = Di+)i
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Enter your answer in the edit fields and then click Check Answer
Chapter 13 Solutions
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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- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.arrow_forwardA hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) Suppose that aftert seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second. y =arrow_forwardThe equation r(t)=(t+2) i+t2−7 j+(2t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t=1 as a product of its speed and direction.arrow_forward
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- ,2 For function f (x, y) x2+1 Write the gradient vector Vfarrow_forwardFind the directional derivative of f(x, y) = x/y at the point (4, 4) in the direction of the vector v = (5, –4). If you didn't get the right answer, it is probably not a syntax error. There is something different in this problem than the previous ones.arrow_forwardThe path r(t) = (t) i + (3t2 +7) į describes motion on the parabola y = 3x + 7. Find the particle's velocity and acceleration vectors at t= - 4, and sketch them as vectors on the curve. The velocity vector at t= - 4 is v(- 4) = (D i+ (Di (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)arrow_forward
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