25. A police car traveling south toward Sioux Falls at 160 km/h pursues a truck traveling east away from Sioux Falls, Iowa, at 140 km/h. At time t = 0,

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25. A police car traveling south toward Sioux Falls at 160 km/h pursues a truck traveling east away from Sioux Falls, Iowa, at 140 km/h. At time t = 0, the police car is 20 km north and the truck is 30 km east of Sioux Falls. Calculate the rate at which the distance between the vehicles is changing:

(b) Find a relation between dx/dt and dy/dt. 30. A particle moves counterclockwise around the ellipse with equation 9x2 + 16y2 = 25. (a) In which of the four quadrants is dx/dt > 0? Explain. (b) Find a relation between dx/dt and dy/dt. (c) At what rate is the x-coordinate changing when the particle passes the point (1, 1) if its y-coordinate is increasing at a rate of 6 m/s? (d) Find dy/dt when the particle is at the top and bottom of the ellipse.

41. A roller coaster has the shape of the graph 41. A roller coaster has the shape of the graph. Show that when the roller coaster passes the point (x, f (x)), the vertical velocity of the roller coaster is equal to f (x) times its horizontal velocity.