bounds -2 ≤ x ≤ 2π for 1 ≤ i ≤ n (here n = 2) n f(x) = x² + 25 Σ sin² Xi i=1 i=1 n

Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t > 1 a new node is added to the network. The node arrives together with m = 2 new links, which are connected to m = 2 different nodes already present in the network. The probability II, that a new link is connected to node i is: N(t-1) II¿ = ki - 1 Ꮓ with Z=(k-1) j=1 where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at timet - 1.

Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7900 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = Interpret C(200). O When this many helmets are produced the cost is $200. O This is the cost (in dollars) of producing 200 helmets. O For every additional helmet produced the cost increases by this much. O For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) =