Week+12+Nov+3-7

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November 3rd, 2008
Step 1 helps us understand what is going on in the problem and how the variables are related. In Step 2 we will figure out what you have in terms of calculus and related the variables In Step 3 we will figure out what you need Step 4 relates what you need and what you already have In Step 5 we differentiate with respect to t because related rates are all dependent upon time In part a, we are asked to find dV/dt (the rate at which the volume is changing) when r=15. Using V=(4/3) pi r^3 and parametric chain rule, we are able to find that the volume is changing at a rate of 450pi in^3/sec when the radius of the sphere is 15 inches. In part b, we set the rate at which the volume is changing (dV/dt) equal to the rate at which the radius is changing (dr/dt) and found that the rates are equal when the radius is the square root of 1/4pi inches. In part a, we are asked to find dV/dt (the rate at which the volume is changing) when l=5. Using V=l^3 and parametric chain rule, we found that dV/dt =150 cm^3/sec when l=5. In part b, we are asked to find dS/dt (the rate at which the surface area is changing) when l=5. Using S-6l^2 and parametric chain rule, we found that dS/dt =120 cm^2/sec when l=5. We are asked to find dY/dt (the rate at which the height if the balloon is changing. Using y=500tan(ø) and parametric chain rule, we found that dY/dt= 140 feet/min when ø=pi/4 We are asked to find dX/dt (the rate at which the car is speeding away). Using dL/dT (the rate at which the distance between the police cruiser and the car is increasing) =20 mph, dY/dt (the rate at which the cop car is moving north) = -60 mph, Y=.8, X=.6, L^2= Y^2 + X^2 and parametric chain rule, we find that the car is speeding away at a rate of 70 mph.

November 5th, 2008
We first went over the related rates homework problems: section 4-9 #8-12. Parts of the problems are solved in the graphics below.



Thenext task was to review for the test so we worked some problems requiring us to find the derivative of implicitly defined relations. These problems are shown below.



November 6th
Test today on Implicit Differentiation and Related Rate.We haven't finished related rates yet so 2/3 of the test is on implicit relations. We will tested again, next week, on related rates.

November 7th
Today we did a "Turvey" puzzle which can be found on this [|website]. We also have some AP problems to do for homework. The solutions are shown below.