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Unformatted text preview: dian per hour or 0.122 radians per minute. /ℎ 8. ( Text 4.6 #30)
Sand falls from a hopper at a rate of 0.1 cubic meters per hour and forms a conical pile beneath. If
the side of the cone makes an angle of π 6 radians with the vertical, find the rate at which the height
of the cone increases per hour. At what rate per hour does the radius of the base increase? Give both
answers in terms of h, the height of the pile in meters.
→ = 0.1 =? → ℎ→ tan = ℎ∗ =
= = = ℎ= ℎ= ℎ ∗ 0.1 = = = ∗ = ∗
= ℎ = = = and 9. (Text 4.6 #24)
A train is traveling at 0.8 km/min along a long straight track, moving in the direction shown in the
figure below. A movie camera, 0.5 km away from the track, is focused on the train.
(a) How fast is the distance from the camera to the train changing when the train is 1 km from
the camera? Give units.
(b) How fast is the camera rotating (in radians/min) at the moment when the train is 1 km from
the camera? z
y= 0.5km x→
→ = 0.8 = = 0.5 = 1− = =0 →1 =1 train
2∗ =? = 21 ∗ b) tan = ∗ + =2 ∗ +2 ∗ =2 ∗ 0.8 + 2 0.5 0 = 0.4 3 ≈ 0.693
. / =2 =2∗
=2 . = 0.4 / Distance is changing at a rate of 0.693 km per minute while the angle of the camera is changing at
a rate of 0.4 radians per minute when the train is 1 km from the camera....
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This note was uploaded on 04/11/2013 for the course MATH 124 taught by Professor Wood during the Spring '13 term at ASU.
- Spring '13