Question

At noon, ship A was 9 nautical miles due north of ship B. Ship A was sailing south at 9 knots (nautical miles per hour, a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day. Complete parts (a) through (e) below. a. Start counting time with $t = 0$ at noon and express the distance $s$ between the ships as a function of $t$. $s(t) = \sqrt{(141 - 9t)^2 + (8t)^2}$ b. How rapidly was the distance between the ships changing at noon? One hour later? At noon the distance between the ships was changing at a rate of One hour later, the distance between the ships was changing at a rate of c. The visibility that day was 5 nautical miles. Did the ships ever sight each other? Yes No d. Graph $s$ and $\frac{ds}{dt}$ together as functions of $t$ for $-1 \le t \le 3$. Compare the graphs and reconcile what you see with your answers in parts (b) and (c). Select the correct graph below. Each graph is shown with a window of $[-1, 3]$ by $[0, 50]$. [Graphs] e. The graph of $\frac{ds}{dt}$ looks as if it might have a horizontal asymptote in the first quadrant. This in turn suggests that $\frac{ds}{dt}$ approaches a limiting value as $t \to \infty$. What is this value? What is its relations to the ships' individual speeds? Select the correct answer below and fill in the answer box to complete your choice. (Type an exact answer, using radicals as needed.) A. The limit is. This limit is the square root of the differences of the squares of the individual speeds. B. The limit is. This limit is the square root of the sums of the squares of the individual speeds.

          At noon, ship A was 9 nautical miles due north of ship B. Ship A was sailing south at 9 knots (nautical miles per hour, a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day. Complete parts (a) through (e) below.
a. Start counting time with $t = 0$ at noon and express the distance $s$ between the ships as a function of $t$.
$s(t) = \sqrt{(141 - 9t)^2 + (8t)^2}$
b. How rapidly was the distance between the ships changing at noon? One hour later?
At noon the distance between the ships was changing at a rate of 
One hour later, the distance between the ships was changing at a rate of 
c. The visibility that day was 5 nautical miles. Did the ships ever sight each other?
Yes
No
d. Graph $s$ and $\frac{ds}{dt}$ together as functions of $t$ for $-1 \le t \le 3$. Compare the graphs and reconcile what you see with your answers in parts (b) and (c). Select the correct graph below. Each graph is shown with a window of $[-1, 3]$ by $[0, 50]$.
[Graphs]
e. The graph of $\frac{ds}{dt}$ looks as if it might have a horizontal asymptote in the first quadrant. This in turn suggests that $\frac{ds}{dt}$ approaches a limiting value as $t \to \infty$. What is this value? What is its relations to the ships' individual speeds? Select the correct answer below and fill in the answer box to complete your choice.
(Type an exact answer, using radicals as needed.)
A. The limit is. This limit is the square root of the differences of the squares of the individual speeds.
B. The limit is. This limit is the square root of the sums of the squares of the individual speeds.

At noon, ship A was 9 nautical miles due north of ship B. Ship A was sailing south at 9 knots (nautical miles per hour, a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day. Complete parts (a) through (e) below.
a. Start counting time with t = 0 at noon and express the distance s between the ships as a function of t.
s(t) = √((141 - 9t)^2 + (8t)^2)
b. How rapidly was the distance between the ships changing at noon? One hour later?
At noon the distance between the ships was changing at a rate of
One hour later, the distance between the ships was changing at a rate of
c. The visibility that day was 5 nautical miles. Did the ships ever sight each other?
Yes
No
d. Graph s and (ds)/(dt) together as functions of t for -1 ≤ t ≤ 3. Compare the graphs and reconcile what you see with your answers in parts (b) and (c). Select the correct graph below. Each graph is shown with a window of [-1, 3] by [0, 50].
[Graphs]
e. The graph of (ds)/(dt) looks as if it might have a horizontal asymptote in the first quadrant. This in turn suggests that (ds)/(dt) approaches a limiting value as t →∞. What is this value? What is its relations to the ships' individual speeds? Select the correct answer below and fill in the answer box to complete your choice.
(Type an exact answer, using radicals as needed.)
A. The limit is. This limit is the square root of the differences of the squares of the individual speeds.
B. The limit is. This limit is the square root of the sums of the squares of the individual speeds.

Added by Lorena N.

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