For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and costs C(x)=b+cx+dx², where represents the number of pizzas. 4. C -) Assume that R(x) = 7x, andC (x) = 160-2x + x². How many pizzas sold maximizes the profit? x

Solve the following by setting up the proper equations to describe the facts given and then carrying out the mathematical calculations to solve for the unknown variable(s). Let x represent length and y represent width. Enter your answer in (x, y) format. The length of a rectangle is 3 times the width. The difference between the length and width is 14 feet. Determine the rectangle's length and width.

How do you do this? We have to explain, draw it, and solve it.

Let f(x, y) = xy² and r(t) = (¹/1²,t³). Calculate Vf. (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) Vf= Calculate r' (t). (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) r' (t) = Use the Chain Rule for Paths to evaluateƒ(r(t)) at t = 1.5. (Use decimal notation. Give your answer to three decimal places.) d dt - ƒ(r(1.5)) = = Use the Chain Rule for Paths to evaluate ƒ(r(t)) at t = -1.7. (Use decimal notation. Give your answer to three decimal places.) d dt d f(r(-1.7)) =