A golfer launches a tee shot down a horizontal fairway and it follows a path given by r(t) = (at, (75 -0.1a)t, - 5t + 80t), where t20 measures time in seconds and r has units of feet. The y-axis points straight down the fairway and the z-axis points vertically upward. The parameter a is the slice factor that determines how much the shot deviates from a straight path down the fairway. a. With no slice (a = 0), sketch and describe the shot. How far does the ball travel horizontally (the distance between the point the ball leaves the ground and the point where it first strikes the ground)? b. With a slice (a = 0.4), sketch and describe the shot. How far does the ball travel horizontally (along the y-axis)? c. How far does the ball travel horizontally (along the y-axis) with a = 3.5? OA. OB. Oc. The ball travels horizontally 1200 feet. (Round to two decimal places as needed.) b. Choose the correct graph below. A. O B. OC. OD. The ball travels horizontally feet. (Round to two decimal places as needed.)
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.
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