dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II
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.
![MATH 252 – TRACTRIX
1) Suppose that you are holding a rope of length a and you are going to walk and drag an object
behind you.
In particular suppose that your initial position is (0,0) and that the object's initial position is
(a, 0) and that you will walk in the direction of the positive y-axis.
We wish to find an equation for the path of the dragged object. Let's only worry about the
upper portion (matching walking in positive y direction)
Tractrix with object initially at b
(4,0)
YOU DO: Suppose the object is at (x, y). Determine the y - coordinate of the puller.
HINT: Set up a right triangle. You know 2 of its measurements.
The pulled object is always going towards the puller. We need that following the slope of the
curve would result in the object meeting the current position of the puller. We also have an
initial condition that y(a)
= 0. These conditions give us a differential equation:
dy
Va²-x²
with initial condition y(a) = 0.
dx
Va2-t2
dt
This can be solved by y =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb3011a6-3af3-4fd4-9cf4-3cfe78786069%2Fda765c19-433c-4ee1-80ed-ec9085cf3593%2F740hv0s_processed.jpeg&w=3840&q=75)
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