<span>N(t) = 16t ; Distance north of spot at time t for the liner. W(t) = 14(t-1); Distance west of spot at time t for the tanker. d(t) = sqrt(N(t)^2 + W(t)^2) ; Distance between both ships at time t. Let's create a function to express the distance north of the spot that the luxury liner is at time t. We will use the value t as representing "the number of hours since 2 p.m." Since the liner was there at exactly 2 p.m. and is traveling 16 kph, the function is N(t) = 16t Now let's create the same function for how far west the tanker is from the spot. Since the tanker was there at 3 p.m. (t = 1 by the definition above), the function is slightly more complicated, and is W(t) = 14(t-1) The distance between the 2 ships is easy. Just use the pythagorean theorem. So d(t) = sqrt(N(t)^2 + W(t)^2) If you want the function for d() to be expanded, just substitute the other functions, so d(t) = sqrt((16t)^2 + (14(t-1))^2) d(t) = sqrt(256t^2 + (14t-14)^2) d(t) = sqrt(256t^2 + (196t^2 - 392t + 196) ) d(t) = sqrt(452t^2 - 392t + 196)</span>

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3 years ago