3. A straight river flows east at a rate of 6 mi/h. A woman launches a boat from the south shore of the river and wants to land at the point directly at the opposite shore. If the speed of the boat relative to the water is 12 mi/h in what direction should she head the boat in order to arrive at the desired landing point?

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 22 knots. How fast (in knots) is the distance between the ships changing at 7 PM?

Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T: R³-R², T(e₁) = (1,3), T(e₂) = (2, -11), and T(e3)= (-3,8), where e₁,e₂, e3 are the columns of the 3x3 identity matrix. a. Is the linear transformation one-to-one? A. T is not one-to-one because the standard matrix A has a free variable. B. T is one-to-one because the column vectors are not scalar multiples of each other. O C. T is not one-to-one because the columns of the standard matrix A are linearly independent. O D. T is one-to-one because T(x) = 0 has only the trivial solution. b. Is the linear transformation onto? O A. T is not onto because the standard matrix A contains a row of zeros. O B. T is onto because the standard matrix A does not have a pivot position for every row. O C. T is not onto because the columns of the standard matrix A span R². O D. T is onto because the columns of the standard matrix A span R².

Jack is driving his car from his home to a nearby city on a straight road. 1.5 hours after his departure from home, he has traveled 75 miles. At that moment, his distance from home is increasing by 45 miles per hour. Using the linear approximation, estimate how far Jack has traveled from home 2 hours after his departure.