Avan starts off 191 miles directly north from the city of morristown. it travels due east at a speed of 25 miles per hour. after travelling 119 miles, how fast is the distance between the van and morristown changing?

Distance between the van and Morristown is changing at the rate of 13.22 miles per hour.

Step-by-step explanation:

From the figure attached,

Van starts from C (City of Morristown), reaches the point A 191 miles due North and then it travels with a speed of 25 miles per hour due East from A towards B.

We have to calculate the rate of change of distance BC, when the van reaches point B which is 119 miles away from A.

By Pythagoras theorem in the triangle ABC,

Distance AC is constant equal to 191 mi.

By differentiating the equation with respect to time 't'

Since BC² = (119)²+ (191)²

BC = √50642 = 225.04 miles

From the differential equation,

[Since miles per hour]

miles per hour

Therefore, distance between the van and Morristown is changing at the rate of 13.22 miles per hour.

10

step-by-step explanation:

a negative exponent is translated as follows:

so, we have