Suppose that a barrel with maximum radius R and height h can be constructed by rotating a parabola about the x-axis. The parabola is defined as: h y = R-cx', 2 2 where c is a positive constant. (a) Sketch the curve and show that the radius of each end of the barrel is r = R– d where d = ch? 4 (b) Show that the volume of the barrel is 1 V =-th 2R? +r² - d° 3 d²

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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.