By Cohn P. M.

Reports vital history in algebra and introduces extra complicated subject matters, emphasizing linear algebra and the houses of teams and earrings. comprises extra labored difficulties and an entire set of solutions to the workouts. additionally positive factors improved proofs and extra in-depth remedies of affine areas, linear programming, duality, Jordan basic shape and team conception.

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Volume is measured in cubic units such as cubic inches (in3), cubic centimeters (cm3), cubic feet (ft3), and so on. Volume also describes the amount of a substance that can be enclosed within a three-dimensional object. Therefore, volume can also be measured in quarts, liters, gallons, and so on. In the figures, l ϭ length, w ϭ width, h ϭ height, s ϭ length of a side, and r ϭ radius. Volumes of Three-Dimensional Figures Rectangular solid h V ϭ lwh w l V ϭ s3 Cube s s s V ϭ pr 2h Right circular cylinder h r Sphere r Right circular cone h Vϭ 4 3 pr 3 Vϭ 1 2 pr h 3 r Example 6 Find the volume of each.

Write the answer in lowest terms. video a) 2 6 ϩ 11 11 b) 7 19 Ϫ 20 20 a) 8 5 2 ϩ6 11 11 c) 2 9 4 ϩ ϩ 25 25 25 b) 2 1 3 ϩ9 10 10 d) 1 2 ϩ 9 6 c) 7 11 5 Ϫ1 12 12 e) 11 3 ϩ 5 30 d) 3 1 1 ϩ2 5 4 f) 2 13 Ϫ 18 3 e) 5 2 4 Ϫ4 3 15 g) 5 4 ϩ 7 9 f) 9 5 3 Ϫ5 8 10 h) 1 5 Ϫ 6 4 g) 4 3 3 ϩ6 7 4 i) 7 3 3 ϩ ϩ 10 20 4 h) 7 13 4 ϩ 20 5 j) 1 2 10 ϩ ϩ 6 9 27 26) Add or subtract. Write the answer in lowest terms. a) 8 5 Ϫ 9 9 27) Add or subtract. Write the answer in lowest terms. video 28) Add or subtract. Write the answer in lowest terms.

4) Perform addition and subtraction from left to right. Think about the “You Try” problem. Did you evaluate it using the order of operations? Let’s look at that expression: mes47759_ch01_001-025 10/22/2007 16:48 Page 22 pinnacle 201:MHIA038:mhmes2:mes2ch01: 22 Chapter 1 The Real Number System and Geometry Example 3 Evaluate 36 Ϫ 12 Ϭ 4 ϩ (6 Ϫ 1) 2. Solution 36 Ϫ 12 Ϭ 4 ϩ (6 Ϫ 1) 2 36 Ϫ 12 Ϭ 4 ϩ 52 36 Ϫ 12 Ϭ 4 ϩ 25 36 Ϫ 3 ϩ 25 33 ϩ 25 58 First, perform the operation in the parentheses. Exponents are done before division, addition, and subtraction.

### Algebra by Cohn P. M.

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