The demand x is the number of items that can be sold at a price of $p. For x equals p cubed minus 7 p squared plus 600 commax=p3−7p2+600, find the rate of change of p with respect to x by differentiating implicitly.

Acompany's income statement showed the following: net income, $145,000 and depreciation expense, $36,300. an examination of the company's current assets and current liabilities showed the following changes as a result of operating activities: accounts receivable decreased $11,500; merchandise inventory increased $22,200; and accounts payable increased $5,500. calculate the net cash provided or used by operating activities. $209,500 $139,000 $176,100 $186,500 $142,100

You are thinking of making your mansion more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs, and insulating part or all of your exterior walls. each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.† your mansion has 150 light fittings and 3000 sq ft of uninsulated exterior wall. to impress your friends, you would like to spend as much as possible, but save no more than $750 per year in energy costs (you are proud of your large utility bills). how many compact fluorescent light bulbs and how many square feet of insulation should you purchase? how much will you save in energy costs per year? (if an answer does not exist, enter dne.)

Identify at least 3 body language messages that project a positive attitude