1. (5 points) At 6pm, ghost A is 5 kilometers due west of ghost B. Ghost A is flying west at 15 km/hr and ghost B is flying north at 20 km/hr. How fast is the distance between
the ghosts changing at 10pm?

The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.

Step-by-step explanation:

At first we assume that north and east directions both represent positive quantities. Let suppose that and . If both ghosts moves at constant velocity such that and , then the final positions of both ghosts are, respectively:

Ghost A

(Eq. 1)

Ghost B

(Eq. 2)

Where is the time, measured in hours.

Then, the equations of motion of each ghost are, respectively:

Ghost A

Ghost B

Then, the distance between both ghosts is:

(Eq. 3)

The magnitude of the relative is represented by the following Pythagorean identity:

Then, we find the rate of change of the relative distance (), measured in kilometers per hour, by implicit differentiation:

(Eq. 4)

If we know that , then the rate of change of the relative distance at 10 PM is:

The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.

b i think

step-by-step explanation:

not really sure

answer:

your answer is: c. 196 7/8 in^3.