At noon, ship A is 180 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 35 km/h. How fast is
the distance between the ships changing at 4:00 PM?
1 answer:
Answer:
≈ 29 km/h
Step-by-step explanation:
If t is the number of hours since noon, then the distance between ship A and the origin is 180 − 40t, and the distance between ship B and the origin is 35t.
Using Pythagorean theorem, the distance between the ships is:
d² = (35t)² + (180 − 40t)²
d² = 1225t² + 32400 − 14400t + 1600t²
d² = 2825t² − 14400t + 32400
Taking derivative with respect to time:
2d dd/dt = 5650t − 14400
dd/dt = (2825t − 7200) / d
First, find d when t = 4.
d² = 2825 (4)² − 14400 (4) + 32400
d² = 20000
d = 100√2
Now find dd/dt.
dd/dt = (2825(4) − 7200) / (100√2)
dd/dt = 41/√2
dd/dt ≈ 29 km/h
You might be interested in
When you see a "%" you need to ask " a percent of what"?
Here, it's a percent of the original prize, so the discount is 20% of the original prize, that is 20% of 35.
20% is also 20/100 or 1/5, so we can calculate this like this:
so the discount is 7 dollars.
Here, it's a percent of the original prize, so the discount is 20% of the original prize, that is 20% of 35.
20% is also 20/100 or 1/5, so we can calculate this like this:
so the discount is 7 dollars.