An offshore oil well is 1 mile off the coast. The oil refinery is 4 miles down the coast. Laying pipe in the ocean is twice as expensive as laying it on land. Find x, and consider how finding x helps determine the most economical path for the pipe from the well to the oil refinery. A diagonal line segment, a vertical line segment, and a horizontal line segment are given in the graph. The vertical line segment connects the point labeled Offshore oil well to the left most point of the horizontal line forming a right angle. The horizontal line segement then goes right and ends at the point labeled Refinery. The diagonal line segment is labeled √(x2 + 1), begins at the point labeled Offshore oil well, goes down and right, and ends at a point on the horizontal line segment. The part of the horizontal line segement between the intersection of the vertical and horizontal line segments and the intersection of the diagonal and horizontal line segments is labeled x. The distance between the intersection of the diagonal and horizontal line segments and the rightmost point of the horiztonal line sgement labled Refinery is labeled 4 − x. x =
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
- The vertical line segment connects the point labeled Offshore oil well to the left most point of the horizontal line forming a right angle.
- The horizontal line segement then goes right and ends at the point labeled Refinery.
- The diagonal line segment is labeled √(x2 + 1), begins at the point labeled Offshore oil well, goes down and right, and ends at a point on the horizontal line segment.
- The part of the horizontal line segement between the intersection of the vertical and horizontal line segments and the intersection of the diagonal and horizontal line segments is labeled x.
- The distance between the intersection of the diagonal and horizontal line segments and the rightmost point of the horiztonal line sgement labled Refinery is labeled 4 − x.
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