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Unformatted text preview: Ms. Waldron
Ch 4.6 BC Calculus Related Rates Worksheet
1. The radius r and surface area S of a sphere are related by the equation
S = 4 π r2 . Write an equation that relates dS
dt 2. When a circular plate of metal is heated in an oven, its radius increases at the
rate of 0.01 cm/sec. At what rate is the plate’s area increasing when the radius
is 50 cm? 3. John flies a kite at a height of 300 ft, the wind carrying the kite horizontally
away at a rate of 25 ft/sec. How fast must she let out the string when the kite is
500 ft away from her? 4. A spherical balloon is inflated with helium at the rate of 100 π ft 3 / min .
a) How fast is the balloon’s radius increasing at the instant the radius is
5 ft? b) How fast is the surface area increasing at that instant? 5. A particle moves along the parabola y = x2 in the first quadrant in such a
way that its x-coordinate (in meters) increases at a constant rate of 10 m/sec.
How fast is the angle of inclination θ of the line joining the particle to the origin
changing when x = 3? 6. Two ships are steaming away from a point O along routes that make a 120 °
angle. Ship A moves at 14 knots (nautical miles per hour: a nautical mile is
2000 yards). Ship B moves at 21 knots. How fast are the ships are moving
apart when OA = 5 and OB=3? 7. Find
a) c) dY
dx . 2xy + y 2 x2 = tan y = x+y b) x sin y = 1 - xy d) ln (x + y) = 2x ...
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This note was uploaded on 02/16/2012 for the course CALCULUS 0064 taught by Professor Waldron during the Fall '10 term at Broward College.
- Fall '10