2) The combined electrical resistance R of R1 and R2, connected in parallel, is
1/R= 1/R1 + 1/R2
where R, R1 and R2 are measured in ohms. R1 and R2 are increasing at rates of 1 and 1.5 ohms per second, respectively. At what rate is R changing when R1= 50 ohms and R2= 75 ohms?
3) Cars on a certain roadway travel on a circular arc of radius r. In order not to rely on friction alone to overcome the centrifugal force, the road is banked at an angle of magnitude Q (theta) from the horizontal. The banking angle must satisfy the equation
rg tanQ= v^2
where v is the velocity of the cars and g= 32 ft/sec^2 is the acceleration due to gravity. Find the relationship between the related rates dv/dt and dQ/dt.
4) A fishing line is reeled in at a rate of 1 foot per second from a bridge 15 feet above the water. At what rate is the angle between the line and the water changing when 25 feet of line is out?