Applying the Concepts and Skills Rental-Car Costs. During one month, the Avis Rent-A-Car rate for renting a Buick LeSabre in Mobile, Alabama, was $68.22 per day plus 25¢ per mile. For a 1-day rental, let x denote the number of miles driven and let y denote the total cost, in dollars. Find the equation that expresses y in terms of x. Determine b0 and b1. Construct a table similar to Table on page 620 for the x -values 50, 100, and 250 miles. Draw the graph of the equation that you determined in part (a) by plotting the points from part (c) and connecting them with a line. Apply the graph from part (d) to estimate visually the cost of driving the car 150 miles. Then calculate that cost exactly by using the equation from part (a). TABLE Times and costs for five word-processing jobs Time (hr) Cost ($) X y 5.0 125 7.5 175 15.0 325 20.0 425 22.5 475
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.
Applying the Concepts and Skills
Rental-Car Costs. During one month, the Avis Rent-A-Car rate for renting a Buick LeSabre in Mobile, Alabama, was $68.22 per day plus 25¢ per mile. For a 1-day rental, let x denote the number of miles driven and let y denote the total cost, in dollars.
- Find the equation that expresses y in terms of x.
- Determine b0 and b1.
- Construct a table similar to Table on page 620 for the x -values 50, 100, and 250 miles.
- Draw the graph of the equation that you determined in part (a) by plotting the points from part (c) and connecting them with a line.
- Apply the graph from part (d) to estimate visually the cost of driving the car 150 miles. Then calculate that cost exactly by using the equation from part (a).
TABLE
Times and costs for five word-processing jobs
| Time (hr) | Cost ($) |
| X | y |
| 5.0 | 125 |
| 7.5 | 175 |
| 15.0 | 325 |
| 20.0 | 425 |
| 22.5 | 475 |
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