kmh 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 30 A particle moves counterclockwise around the ellipse with equation 9 ID: 377034
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Slide1
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:Slide2
30.
A particle moves counterclockwise around the ellipse with equation 9
x2 + 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.Slide3
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.