By James Stewart
This most sensible promoting writer staff explains thoughts easily and obviously, with out glossing over tough issues. challenge fixing and mathematical modeling are brought early and bolstered all through, in order that while scholars end the path, they've got an exceptional beginning within the ideas of mathematical pondering. This finished, frivolously paced e-book offers entire insurance of the functionality suggestion and integrates big graphing calculator fabrics that aid scholars enhance perception into mathematical principles. The authors' consciousness to element and readability, as in James Stewart's market-leading Calculus textual content, is what makes this article the industry chief.
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Extra info for Algebra and trigonometry, 2nd Edition
We say that a is less than b and write a Ͻ b if b Ϫ a is a positive number. Geometrically, this means that a lies to the left of b on the number line. Equivalently, we can say that b is greater than a and write b Ͼ a. 5 œ∑2 _2 _1 0 1 2 3 4 5 6 7 8 Figure 4 Sets and Intervals A set is a collection of objects, and these objects are called the elements of the set. If S is a set, the notation a ʦ S means that a is an element of S, and b S means that b is not an element of S. For example, if Z represents the set of integers, then Ϫ3 ʦ Z but p Z.
A ϭ 2x 2 50 ϭ 2x 25 ϭ x 2 5ϭx 2 Model Substitute A ϭ 50 Divide each side by 2 Take the square root of each side The width of the sheet is 5 ft, so its length is 10 ft. ■ 6 CHAPTER P Prerequisites Example 6 Finding a Formula for Manufacturing At a factory that manufactures cans, circular disks are stamped out of rectangular metal sheets as shown in Figure 2. The unused part of the sheets (called scrap metal) is recycled to form new sheets. 20 in. 12 in. Figure 2 (a) Find a formula for the amount of scrap metal from any number of sheets.
Elevation (km) Temperature (°C) 0 1 2 3 4 5 20° 10° 0° Ϫ10° Ϫ20° Ϫ30° We see that temperature decreases as elevation increases. ■ 4 CHAPTER P Prerequisites (b) We substitute T ϭ 5ЊC in the model and solve for h. 5 km. ■ Finding Models In the next examples we explore the process of finding models for real-life situations. Example 4 12 mi/gal 40 mi/gal Finding a Formula for Gas Mileage The gas mileage of a car is the number of miles it can travel on one gallon of gas. (a) Find a formula for gas mileage in terms of the number of miles driven and the number of gallons of gasoline used.