Respuesta :
Answer:
The correct answer is 78.87 + [tex]\sqrt{42h^{2} + 43h^{2}}[/tex].
Step-by-step explanation:
Two boats leave a dock with one heading due north, the other due east.
The first boat is 50 miles from the dock traveling at a speed of 42 miles per hour and the second boat is 61 miles from the dock traveling at a speed of 43 miles per hour.
When the first boat is at 50 miles from the dock and the second one 61 miles from the dock, the distance between the two boats can be given by the Pythagoras theorem = [tex]\sqrt{ 50^{2} + 61^{2}}[/tex] = 78.87 miles.
Let the distance between the boats is calculated after h hours.
Distance traveled by first boat in h hours at 42 miles per hour is 42h miles.
Similarly, distance traveled by second boat in h hours at 43 miles per hour is 43h miles.
There fore the rate at which the distance between the boats are changing is given by 78.87 + [tex]\sqrt{42h^{2} + 43h^{2}}[/tex] where h is the time in hours after the first boat has crossed 50 miles and the second one has crossed 61 miles.
