Solve the problem.The velocity field F of a fluid has a constant magnitude k and always points towards the origin. Following the smooth curve y = f(x) from (a, f(a)) to (b, f(b)), show that the flow along the curve is 
ds = k[(a2 + (f(a))2)1/2 - (b2 + (f(b))2)1/2]
What will be an ideal response?
Answers will vary.
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Solve the problem.The hyperbola 
- 
= 1 is shifted horizontally and vertically to obtain the hyperbola
- 
= 1Find the foci of the new hyperbola.
A. (-23, 2), (27, 2) B. (-18, 2), (22, 2) C. (2, -23), (2, 27) D. (2, -18), (2, 22)
Determine the indefinite integral.
A. ln(1 + cosh x) + C
B. 
+ C
C. cosh2 x + C
D. -ln(1 + cosh x) + C
List all equally likely outcomes in the sample space for the indicated experiment.A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. List the sample space of picking a blue card followed by a green card.
A. {(1, 2, 3)} B. {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)} C. {(2, 3)} D. {(1,1), (1,2), (2, 1), (2, 2), (3, 1), (3, 2)}
Simplify. Write your answers in the form of a+bi, where a and b are real numbers.(6 - 
) (3 + 
)
A. 78 - 42 i B. 78 + 42 i C. -78 + 42 i D. 3618 + 708 i