Part a: Assume that the height of your cylinder is 4 inches. Consider A as a function of r, so we can write that as A (r) = 2 ar² + 8 ar. What is the domain of A (r)? In other words, for which values of r is A (r) defined? Part b: Continue to assume that the height of your cylinder is 4 inches. Write the radius r as a function of A. This is the inverse function to A (r), i.e to turn A as a function of r into. r as a function of A. r(A) = Hints: • To calculate an inverse function, you need to solve for r. Here you would start with A = 2 ar2 + 8 r. This equation is the same as 2 rr2 + 8 ar – A = 0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. 3 n+1 z+1 more information in the Introduction to Mobius unit. • If you want to type in in Mobius, in text mode you can type in (3*pi+1)(x+1). There is Part c: If the surface area is 200 square inches, then what is the rardius r? In other words, evaluate r (200). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as V17.3, you could • Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3) • Use a browser to connect to the Internet and type in sqrt(17.3) into a search field • Use a calculator The radius is Number inches if the surface area is 200 square inches.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.