A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 5¢per square​ centimeter, while the sides are made of material that costs 4¢per square centimeter.   ​(a) Express the total cost C of the material as a function of the radius r of the cylinder. Find the right side of the equation. Express the cost in dollars.   ​C(r)=   ​(Simplify. Type an exact answer in terms of π​.)   ​(b) Graph C=C(r)using your graphing utility. Which graph shown below is the graph of​ C(r), as displayed on a graphing​ utility? All four graphs use the following​ limits:   [0, 12]by[0, 60], Xscl=1, Yscl=8.   For what value of r is the cost C a​ minimum?     r=__ centimeters ​ (Round your answer to two decimal​ places.)

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.