Cece draws a graph representing her family's car trip to the beach. She wants to show her father that their gas 300 (9, 279) 250 mileage in miles per gallon was the same for the entire trip. Cece chose three points on the line and drew vertical line segments from the points to the x-axis. How can she use these E 200 (5, 155) 150 100 segments to prove that the gas mileage was constant for the trip? 50 11,31)- 2. 6. 10 The vertical line segments create three similar right triangles. Because the triangles are similar, the quotient of the length of the vertical side to the length of the horizontal side is the same for each triangle. These quotients are slopes between (0, 0) and the points Cece chose. Because Cece could have chosen any points on the line to make the similar triangles, the slope is constant for the whole line. So, the gas mileage is constant for the whole trip. Gasoline Used (gal) For the graph in the Example, find the slope between the origin and each of the points Cece chose. Distance (mi)
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.
For the graph in the Example find the slope between the orgin and each of the points Cece chose?
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