related rates notes.notebook
October 13, 2015
Related
Rates
Related Rates Strategy
(Condensed from Stewart, p.258)
1.) Draw a diagram if possible. Assign symbols to all quantities that are functions of time. Don’t include information which is only true for a particular point in time. 2.) Express the given information and the desired rates in terms of derivatives.
3.) Write an equation that relates the quantities of the problem. If necessary, use the geometry
of the problem to eliminate one of the variables by substitution.
4.) Use the chain rule to differentiate (implicitly) with respect to t. 5.) Substitute the given information (including quantities at a particular point in time) into the
new equation and solve for the desired rate. A common error is to substitute the given numerical information too early.
This should be done only after differentiating! related rates notes.notebook
October 13, 2015
volume / area
9) A spherical snowball is melting in such a way that its volume is
decreasing at a rate of 1cm3/min. At what rate is the diameter
decreasing when the diameter is 10 cm?
right­angle motion
22) At noon, ship A 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 between them changing at 4:00 P.M.?
related rates notes.notebook
October 13, 2015
filling a vessel
27) Water is leaking out of an inverted conical tank at a rate of
10,000 cm3/min at the same time that water is being pumped into
the tank at a constant rate. The tank has height 6m and the
diameter at the top is 4m. If the water level is rising at the rate of
20 cm/min when the height of the water is 2m, find the rate at
which water is being pumped into the tank.
angular motion
40) A light in a lighthouse 1 km offshore from a straight shoreline is
rotating at 2 revolutions per minute. How fast is the beam moving
along the shoreline when it passes the point ½ kilometer from the
point opposite the lighthouse?