Two cruise ships leave port at the same time. Ship A sails north at a speed of 20 mph while Ship B sails east at a speed of 40 mph.

(a) Find an expression in terms of the time t (in hours) giving the distance D between two ships.
D(t) =



(b) Using the expression obtained in part (a), find the distance between the two ships 4 hr after leaving the port. (Round your answer to two decimal places.)
mi

Respuesta :

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

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