# Related rates: urgent

• January 6th 2007, 03:45 PM
ml_2007
Related rates: urgent
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?
:)
• January 6th 2007, 04:42 PM
galactus
• January 6th 2007, 05:00 PM
topsquark
Quote:

Originally Posted by ml_2007
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?

$\frac{dR}{dt} = \frac{\partial R}{\partial R_1} \cdot \frac{\partial R_1}{\partial t} + \frac{\partial R}{\partial R_2} \cdot \frac{\partial R_2}{\partial t}$

So:
$R = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}} = \frac{R_1R_2}{R_1 + R_2}$

$\frac{\partial R}{\partial R_1} = \frac{R_2^2}{(R_1 + R_2)^2}$

$\frac{\partial R}{\partial R_2} = \frac{R_1^2}{(R_1 + R_2)^2}$

$\frac{dR}{dt} = \frac{(75 \, \Omega)^2}{(50 \, \Omega + 75 \, \Omega)^2} \cdot \frac{1 \, \Omega}{s} + \frac{(50 \, \Omega)^2}{(50 \, \Omega + 75 \, \Omega)^2} \cdot \frac{1.5 \, \Omega}{s} = 0.6 \, \Omega/s$