This is for a calculus class (but we're doing the preliminary chapter, and I can't actually use any calculus).

1. Draw the unit circle and plot the point P = (4,2). Find the equation of a line tangent to the unit circle passing through the point, P.

2. A rancher has 300 ft. of fence to enclose two adjacent pastures.

a) Write the total are A of the two pastures as a function of x.

For this, I used the equations for the area and perimeter based on the diagram of the pasture layout we were given, A = x2y, and 300 = 3x = 4y, and got the function A(x) = 150x - 1.5x^2:

300 = 3x + 4y

300 - 3x = 4y

75 - .75x = y

A = x2(75 - .75x)

A = x(150 - 1.5x)

A(x) = 150x -1.5x^2

Firstly, did I do this right?

b) Find the dimensions that yield the maximum amount of area for the pastures by completing the square.