Stuffed Sheets.com - Related Rates Word Problems

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(C-D-RR-1) The area of an equilateral triangle increases at a rate ofAt what rate does a side increase when the area is($1.25)

(C-D-RR-2) The area of a circle increases at a rate ofWhat is the rate of increase of the radius when the area is($1.25)

(C-D-RR-3) A spherical balloon is filled with helium at a rate ofAt what rate does the radius increase when it is 10 feet? ($1.25)
(C-D-RR-4) Airplane A flies in an easterly direction over a building atAfter 15 minutes, airplane B flies over the building attowards due north, at the same altitude. At what rate do the two planes separate 30 minutes after plane B flies over? ($1.25)

(C-D-RR-5) The volume of a spherical mothball decreases at a rate proportional to its surface area as it evaporates. Show that the negative rate of change of the radius is a constant. ($1.25)

(C-D-RR-6) A circular ripple radiates from a certain point in an otherwise still pond. The radius of the circle increases at a rate ofHow fast does the disturbed area increase at the moment the radius is 3 feet? ($1.25)

(C-D-RR-7) The volume of a sphere decreases atAt what rate does the surface area decrease when its volume is ($1.25)
(C-D-RR-8) A balloon is released at Fred's eye level at a point 100 feet from him. If the balloon rises vertically atat what rate will the balloon recede from Fred's eyes after 60 seconds? ($1.25)

(C-D-RR-9) According to Boyle's law for the expansion of a gas,where P is the pressure on a gas in pounds per square inch, V represents volume in units and C is a constant. At a given time, the volume isthe pressure isand the volume increases at a rate ofFind the rate of change of the pressure at that time. ($1.25)

(C-D-RR-10) Sand leaks from a hole in a boardwalk at a rate ofThe sand forms a conical pile in which the diameter of the base is always three times the altitude. What is the rate of change of the height of the pile when the height is 4 feet? ($1.25)
(C-D-RR-11) The radius of a right circular cylinder decreases at a rate ofas the height increases atAt what rate does the volume change when the radius is 3 feet and the height is 8 feet? ($1.25)
(C-D-RR-12) The force F, of repulsion between two like charges is inversely proportional to the square of the distance them withIf the charges are brought together at a rate ofat what rate is the force increasing when the distance r is 2 inches? ($1.25)

(C-D-RR-13) A particle moves along the circular pathAs it moves through the pointits x component of velocityis 2. What is the y component of velocity then and its speed? ($1.25)

(C-D-RR-14) The two spans of a drawbridge each 15 feet long, are raised simultaneously at a rate of How fast do the ends of the spans separate when the angle of elevation is ($1.25)
(C-D-RR-15) The liftoff of a space shuttle is panned by a video camera on the ground 15 miles away. The shuttle's velocity iswhen it is 12 miles above the ground. (Assume that the shuttle's path is always perpendicular to the ground.) (a) At what rate is the distance from the camera to the shuttle changing when it is 12 miles high? (b) What is the rate of change of the angle of elevation of the camera during the pan? ($1.25)

(C-D-RR-16) A lighthouse beacon rotates completely once every 45 seconds. The beacon passes a point on a cliff-face at a rate ofIf the cliff-face at P is perpendicular to the line from P to the lighthouse, what is the distance from the lighthouse to the cliff-face? ($1.25)
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