A hot-air balloon is 160 ftabove the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 45 mi divided by hr(66 ft divided by s).If the balloon rises vertically at a rate of 14 ft divided by s, what is the rate of change of the distance between the motorcycle and the balloon 7 secondslater?

73.77 ft/s

Step-by-step explanation:

Let's imagine this situation as a right triangle where the distance between the two points is the hypotenuse.

-Applying Pythagoras theorem:

#Take the derivative of the first equation and solve for :

#We then substitute the values given in the question to solve for :

Hence, the rate of change of the distance between the motorcycle and the balloon 7 seconds later is 73.77 ft/s

a. 19,958,400

step-by-step explanation:

hope this

the answer is 31.27mph