Ciara's car is stuck in the mud. Brian and Sophia come along in a truck to help pull her out. They attach one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck starts to pull. Meanwhile, Brian and Sophia get behind the car and push. The truck generates a horizontal force of 315 lb on the car. Brian and Sophia are pushing at a slight upward angle and generate a force of 124 lb on the car. These forces can be represented by vectors, as shown in the figure below. The angle between these vectors is 16.8°. Find the resultant force (the vector sum), then give its magnitude and its direction angle from the positive x-axis. 124 lb 16.8° 315 lb a. The resultant force is ( (Tip: omit degree notations from your answers; e.g. enter cos(45) instead of cos(45°)) b. It's magnitude is lb. c. It's angle from the positive x-axis is

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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.