Find a 3 x 3 stochastic matrix A that has exactly one initial state vector that will generate a Markov chain with a steady-state vector. A= 0.4 0.3 0.3 0.2 0.6 0.2 0.1 0.4 0.5

Q4 Identify the Types of the following Functions: C = f(Q) = Q³ – 5Q² + 14Q + 50,. AR = f(Q) = 15 – Q, .. .

For a certain company, the cost for producing x items is 60x + 300 and the revenue for selling x items is 100x – 0.5x². - The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratio polynomial.) Part b: Find two values of x that will create a profit of $300. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x – 1). The order of the list does not matter. To enter va, type sqrt(a). x = Part c: Is it possible for the company to make a profit of $15,000?

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y = cos(xx/2), y = 0, 0sxs 1 about the y-axis