Answer:
a) D(t) = [tex]\[20*\sqrt{5} * t\][/tex]
b) 178.885 miles
Step-by-step explanation:
Ship A travels north at the rate of 20 mph.
Ship B travels east at the rate of 40 mph.
After t hours, Ship A is at a distance of 20t miles from the origin.
Similarly, Ship B is at a distance of 40t miles from the origin.
(a) Distance D(t) = [tex]\[\sqrt{(20t)^{2}+(40t)^{2}}\][/tex]
= [tex]\[\sqrt{400*t^{2}+1600 * (t)^{2}}\][/tex]
= [tex]\[\sqrt{2000*t^{2}}\][/tex]
= [tex]\[20*\sqrt{5} * t\][/tex]
(b) Distance between the two ships when t = 4,
= [tex]\[20*\sqrt{5} * 4\][/tex]
= [tex]\[80*\sqrt{5} \][/tex] miles
= 80 * 2.236
= 178.885 miles