Answer each question appropriately.Suppose the velocity of a body moving along the s-axis is 
= 9.8t - 6.Is it necessary to know the initial position of the body to find the body's displacement over some time interval? Justify your answer.
A. Yes, integration is not possible without knowing the initial position.
B. No, the initial position is necessary to find the curve s= f(t) but not necessary to find the displacement. The initial position determines the integration constant. When finding the displacement the integration constant is subtracted out.
C. No, displacement has nothing to do with the position of the body.
D. Yes, knowing the initial position is the only way to find the exact positions at the beginning and end of the time interval. Those positions are needed to find the displacement.
Answer: B
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Let 
. If x is increased by 4%, how is y affected? Round your answer to two decimal places if necessary.
?
A. y is increased by 2.04% B. y is increased by 1.22% C. y is increased by 22.24% D. ?y is increased by 21.67%
Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion.x = 2 sin t, y = 4 cos t, 0 ? t ? 2?
A. 
+ 
= 1
Counterclockwise from (0, 4) to (0, 4), one rotation
B. 
+ 
= 1
Counterclockwise from (4, 0) to (4, 0), one rotation
C. 
+ 
= 1
Counterclockwise from (0, 2) to (0, 2), one rotation
D. 
+ 
= 1
Counterclockwise from (2, 0) to (2, 0), one rotation
If 
find the domain of 
(x).
What will be an ideal response?
Solve the problem.A certain radioactive isotope decays at a rate of 0.175% annually. Determine the half-life of this isotope, to the nearest year.
A. 396 yr B. 172 yr C. 4 yr D. 286 yr