dx Assume that x = x(t) and y = y(t). Let y = x + 4 and 5 when x = 1. dt dy Find when x = 1. dt dy dt || (Simplify your answer.) Assume that x = x(t) and y = y(t). Find dx dt ' using the following information. dy x + y = 10.17; = -2 when x = -2.1 and y = 2.4 dt dx (Type an integer or a simplified fraction.) dt dy dx Assume x and y are functions of t. Evaluate for 2xy - 3x+4y = - 144, with the conditions = 12, x 4, y= -3. dt dt dy dt (Type an exact answer in simplified form.) 32 A point is moving along the graph of x3y = 1728. When the point is at (3,8), its x-coordinate is changing at the rate of -7 units per minute. How fast is the y-coordinate changing at that moment? The y-coordinate is changing by (Type an integer or a fraction. Simplify your answer.) Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by 2 C=90,000+20x, R=200x P=R-C 20 where the production output in 1 week is x calculators. If production is increasing at a rate of 400 calculators per week when production output is 5,000 calculators. Find the rate of increase (decrease) in cost, revenue, and profit. A) Costs are at the rate of $ per week at this production level. (Simplify your answer.) A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by C = 0.3x + 8,000. How fast is the cost per month changing when production is changing at the rate of 18 units per month and the production level is 80 units? Costs are at the rate of $ per month at this production level. (Round to the nearest dollar as needed.)