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.