1-When a circular of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min. At what rate is the plate's area increasing when the radiuse is 44 cm?
2-A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 99 feet above the bow. The rope is hauled in at the rate of 33 ?ft/sec. Complete parts a. and b.
a. How fast is the boat approaching the dock when 15 ft of rope are? out? The distance between the boat and the dock is changing at a rate of nothing ?ft/sec.
?(Type an integer or a simplified? fraction.)
b. At what rate is the anglenthetaθ changing at this? instant? ?rad/sec.
3- Find the derivative of y=cos-1(2x9) with respect to x
?4- Find the derivative of y with respect to t. y = t(ln 3t)2 , dy/dt=?
5- Find dy/dx for ln (5y) = ey sin(5x).
6- Find the derivative of y with respect to x of y= 8ln(13x).
7- Find the derivative of y= ln(tan-1(2x5)) with respect to x.
8- A balloon is rising vertically above a? level, straight road at a constant rate of 1 ft/sec. Just when the balloon is 69 ft above the? ground, a bicycle moving at a constant rate of18 ft/sec passes under it. How fast is the distance s(t) between the bicycle and balloon increasing 3 seconds? later?
9- The original 24 m edge length x of a cube decreases at the rate of 3 ?m/min.
a. When x=2 ?m, at what rate does the? cube's surface area? change?
b. When x=2 ?m, at what rate does the? cube's volume? change?