suppose we are planing to make a taco from a round tortilla with diameter 8 inches by bending the tortilla so that it is shaped as if it is partially wrapped around a circular cylinder. We will fill the tortilla to the edge with meat, cheese, and other ingredients. Our problem is to decide how to curve the tortilla in order to maximize the volume of food it can hold. we start by placing a circular cylunder of radius r along a diameter of the tortilla and folding the tortilla around the cylinder. Let x represent the distance form the center of the tortilla to a point P on the diameter. Show that the cross-sectional area of the filled taco in the plane P perpendicular to the axis of the cylunder is A(x) = r root(16-x^2) - (1/2)r^2((r/2)root(16-x^2)) and write an expression for the volume of the filled taco.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
suppose we are planing to make a taco from a round tortilla with diameter 8 inches by bending the tortilla so that it is shaped as if it is partially wrapped around a circular cylinder. We will fill the tortilla to the edge with meat, cheese, and other ingredients. Our problem is to decide how to curve the tortilla in order to maximize the volume of food it can hold.
we start by placing a circular cylunder of radius r along a diameter of the tortilla and folding the tortilla around the cylinder. Let x represent the distance form the center of the tortilla to a point P on the diameter. Show that the cross-sectional area of the filled taco in the plane P perpendicular to the axis of the cylunder is A(x) = r root(16-x^2) - (1/2)r^2((r/2)root(16-x^2)) and write an expression for the volume of the filled taco.
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