Under certain conditions, tsunami waves encountering land will develop into bores. A bore is a surge of water much like what would be expected if a dam failed suddenly and emptied a reservoir into a river bed. In the case of a bore traveling from the ocean into a dry river bed, one study† shows that the velocity V of the tip of the bore is proportional to the square root of its height h. This is expressed in the formula below, where k is a constant. V = kh0.5 (a) A bore travels up a dry river bed. How does the velocity of the tip compare with its initial velocity when its height is reduced to one third of its initial height? (Round your answer to two decimal places.) The velocity changes by a factor of . (b) How does the height of the bore compare with its initial height when the velocity of the tip is reduced to one quarter of its initial velocity? (Round your answer to two decimal places.) The height is reduced to of the initial height. (c) If the tip of one bore surging up a dry river bed is two times the height of another, how do their velocities compare? (Round your answer to two decimal places.) The velocity of the first is times that of the other.
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.
Under certain conditions, tsunami waves encountering land will develop into bores. A bore is a surge of water much like what would be expected if a dam failed suddenly and emptied a reservoir into a river bed. In the case of a bore traveling from the ocean into a dry river bed, one study† shows that the velocity V of the tip of the bore is proportional to the square root of its height h. This is expressed in the formula below, where k is a constant.
(b) How does the height of the bore compare with its initial height when the velocity of the tip is reduced to one quarter of its initial velocity? (Round your answer to two decimal places.)
(c) If the tip of one bore surging up a dry river bed is two times the height of another, how do their velocities compare? (Round your answer to two decimal places.)
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