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

Answered: Image /qna-images/answer/09ca2fcd-bb77-4f23-bb14-f8fe237bbe16.jpg

Answered: 3. A straight river flows east at a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.
Station A is at 130.6 km to the west of station B. At 11:00 am, car left station B north at a speed of 35.8 km/h. At noon, a car left station A toward east at a speed of 40.7 km/h. How fast is the distance between the cars changing at 3:00 pm? Round the final answer to the nearest whole number. Provide a sketch.
There's two points belonging to the same right. If the variation between these two points is "- 4 " according to the X-axis and "+7 " according to the Y-axis, what is the rate of variation ? A) -4/7 B) 4/7 C) 7/4 D) -7/4
v = (5, 2, 4) w = (8, 2, 3) Find the cosine of the angle between v and w. cos 0 =
You will be graded on your written work as well as your answer. You and Austin start at the same place when a dinosaur attacks! At t = 0 hours, you run North at 3 miles/hour while Austin runs West at 9 miles/hour. At the bottom you will answer, "how fast is the distance between us changing at t = 0.5 hours?" In your written work: a) Draw a picture and clearly label the variables. b) What relationship should you use to help you? (some equation from geometry, using your picture and your variables.) Write the relationship using the variables from your picture. c) Use implicit differentiation to take the derivative of your relationship. You do not need to solve or simplify. d) How fast is the distance between us changing at t 0.5 hours? miles/hour
A ship leaves point A and sails north at the constant rate of 12 knots. Two hours later, a second ship leaves A and sails east at the constant rate of 30 knots. How fast are the ships separating when the first ship is 60 nautical miles from A?
When a ship is sailing, the fuel cost is proportional to the square of its speed relative to water. Besides that, there are fixed costs, which do not depend on the speed and are equal to p ($/hour). At what speed the total cost per 1 mile will be the lowest?

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