A firm's marginal profit, P, as a function of its total cost, C, is given by the equation below. a) Find the profit function, P(C), if P = $8 when C = $223. b) At what cost will the firm break even (P= 0)? dP - 240 dC (C+2)3/2 a) P(C) =O (Type an exact answer, using radicals as needed.)

Physical Science: Height of a Thrown Object. A rock is thrown directly upward with an initial velocity of 50 ft/sec from an initial height of 10 ft.The velocity of this rock is modeled by the function v(t)= -32t +50, where t is in seconds, v is in feet per second, and t=0 represents the moment the rock is released. a) Determine a distance function has a function of t(in this case, "distance" is the same as"height".Be sure to consider the fact that at t=0,the rock is 10ft above the ground. b)Determine the height and the velocity of the rock after 3 sec.

The yearly profit, "P" of your store can be estimated by the function P(n)=15n-45,000 where "n" is the number of items you sell per year, and P is measured in dollars. A) what is your estimated profit if you sell 5,280 items this year? B) Estimate the number of items you must sell to make $150,000 profit? C) Estimate the number of items you must sell to break even ($0 profit)

The spread of oil leaking from a tanker is in the shape of a circle.  If the radius r (in feet) of the spread after x hours is r(x) = nx (n=25). If the equation A(x) = pi (25x)^2 is used to determine the area at a given time, how would you determine the time when the oil patch will reach 100,000 square feet?