Time, t (sec) 10 15 22.5 30 Velocity, v(m/s) 227.04 362.78 517.35 602.97 901.67 (a) Determine the value of the velocity at t = 16 seconds using third order Lagrangian polynomial to the nearest 3 significant figures. m/s. (b) Find the absolute relative approximate error for the third order polynomial approximation to the nearest 3 significant figures. percent. (c) Using the third order polynomial interpolant for velocity, find the distance covered by the jet from t = 11 seconds to t = 16 seconds to the nearest four significant figures. metres. (d) Using the third order polynomial interpolant for velocity, find the acceleration of the jet at t = 16 seconds to the nearest four significant figures. metres per square seconds. 20

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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.