By James Stewart
This top promoting writer staff explains strategies easily and obviously, with out glossing over tough issues. challenge fixing and mathematical modeling are brought early and strengthened all through, in order that whilst scholars end the path, they've got an excellent starting place within the rules of mathematical considering. This accomplished, lightly paced booklet presents entire insurance of the functionality idea and integrates gigantic graphing calculator fabrics that support scholars strengthen perception into mathematical rules. The authors' recognition to element and readability, as in James Stewart's market-leading Calculus textual content, is what makes this article the marketplace chief.
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Extra resources for Algebra and trigonometry, 2nd Edition
B) Find a formula for the distance d you walk in t seconds. (c) How long do you have to walk to cover a distance of one mile? 40. Mowing the Lawn Maria can mow a lawn at a rate of 150 square feet per minute. (a) What area can she mow in half an hour? (b) Find a formula for the area she can mow in t minutes. (c) How long would it take Maria to mow a lawn that is 80 ft wide and 120 ft long? (d) If she wants to mow the lawn in part (c) in one hour, what would her rate of mowing have to be? 41. Volume of Fruit Crate A fruit crate has square ends and is twice as long as it is wide (see the figure on page 10).
This denominator is the Least Common Denominator (LCD) described in the next example. Apago PDF Enhancer Example 3 Evaluate: Using the LCD to Add Fractions 5 7 ϩ 36 120 Solution Factoring each denominator into prime factors gives 36 ϭ 22 # 32 and 120 ϭ 23 # 3 # 5 We find the least common denominator (LCD) by forming the product of all the factors that occur in these factorizations, using the highest power of each factor. Thus, the LCD is 23 # 32 # 5 ϭ 360. So 5 7 5 # 10 7#3 ϩ ϭ ϩ # 36 120 36 10 120 # 3 ϭ 50 21 71 ϩ ϭ 360 360 360 Use common denominator Property 3: Adding fractions with the same denominator ■ The Real Line The real numbers can be represented by points on a line, as shown in Figure 3.
3 Integer Exponents Example 2 23 Zero and Negative Exponents (a) A 47 B 0 ϭ 1 1 1 (b) x Ϫ1 ϭ 1 ϭ x x 1 1 1 (c) 1Ϫ22 Ϫ3 ϭ ϭϪ 3 ϭ Ϫ8 8 1Ϫ22 ■ Familiarity with the following rules is essential for our work with exponents and bases. In the table the bases a and b are real numbers, and the exponents m and n are integers. Laws of Exponents Law Example 1. a a ϭ a m n 2. mϩn am ϭ a mϪn an 4. 1ab2 ϭ a b n a n an 5. a b ϭ n b b 5 2ϩ5 ϭ3 7 35 ϭ 35Ϫ2 ϭ 33 32 # 132 2 5 ϭ 32 5 ϭ 310 3. 1a m 2 n ϭ a mn n Description 3 #3 ϭ3 2 n 13 # 42 ϭ 3 # 4 2 2 2 To multiply two powers of the same number, add the exponents.