1) So this is our first hw with related rates and I am having some trouble with this one. It is basically a right triangle, with the horizontal, or x, equalling 100. It says that a person standing at point A (furthest left point) is watching a balloon as it rises from point C to point B (lowest right to highest right). The balloon is moving at a constant rate of 5 m/s.

a) Find the rate of change of z (hypotenuse, between B and A) at the instant when the balloon (y) is 50 feet high (y=50).

b) Find the rate of change in the area of right triangle BCA at the instant when y=50.

c) Find the rate of change in theta ( angle A) at the instant when y=50.

2) Let f(x)=12-x^2 for x> or equal to 0.

a) the line tangent to the graph of f at point (k, f(k)) intercepts the x-axis at x=4. What is the value of k?

b) An isosceles triangle whose base is the interval form (0,0) to (c,0) has its vertex on the graph of f. For what value of c does the triangle have maximum area? Justify.

If anyone can help with any of this let me know, thanks. Even if you can just guide me, I know the guidlines for related rates but it isn't making sense to me. Thanks