I. Express this statement as a differential equation relating h with time t. II. Show by integration that the general solution of the differential equation relating h and t may be expressed in the form h3 = At + B, where A and B are constants. III. A new slag- heap was started at time t = 0, and after 2 years its height was 18m. Find the time by which its height would grow to 30m.
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.
Waste material from a mining operation is dumped on a “slag-heap”, which is a large mound, roughly conical in shape, which continually increases in size as more waste material is added to the top. In a mathematical model, the rate at which the height h of the slag-heap increases is inversely proportional to h2.
I. Express this statement as a
II. Show by
III. A new slag- heap was started at time t = 0, and after 2 years its height was 18m. Find the time by which its height would grow to 30m.
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