Unformatted text preview: 4. If and , determine differentiate implicitly wrt time when at and at then , we have , we have , so 8. If a snowball melts so that its surface area decreases at a rate of cm /min, determine the rate at which the diameter decreases when the diameter is 10 cm. surface area of sphere the given info is that the request is to determine cm /min when differentiate the area function wrt to give and then substitute: cm/min MTH 173, section 3.10 nores, page 1 10. At noon, ship is 150 km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25 km/hr. How fast is the distance bewteen the ships changing at 4PM? distance between ships determine at 4PM at noon, is at after 4 hours, A moved B has moved at 4PM A has position B is at km so and B's position is km km/hr MTH 173, section 3.10 nores, page 2 16. A boat is pulled into a dock by a rope attached to the bow and passing thru a pulley on the dock 1 m higher than the bow. If a rope is pulled in the rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock / is length of rope m/s, determine when 18. A particle is moving along the curve . As the particle passes thru , its -coordinate increases at 3 cm/s. How fast is the distance from the particle to the origin changing then? cm/s MTH 173, section 3.10 nores, page 3 20. A trough that is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled at a rate of 12 ft /min, how fast is the water level rising when it is 6 inches deep? if height then base ! the given information is that foot. from ! , we have
! and ! ft/min, and the request is to determine when ft/min 24. A kite 100 ft above groud moves horizontally with a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string are out? l 100 here we know that we also know that csc cot when , so sin tan rad/s ft/s. the request is to determine csc , so when csc cot MTH 173, section 3.10 nores, page 4 ...
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- Spring '09
- Inch, implicitly wrt time, area function wrt