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nature of mathematics

Questions and Answers of Nature Of Mathematics

Use algebra to show where the formula for dividing fractions comes from.
Completely reduce the fractions in Problems 7–18. a. 2 10 b. 3 12
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. alm + b. + ten
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. -12 35 8 15 b. 2-1 + 3-1
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 3+3-1 b. 2+2-
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) 4. | b. | - elh
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. I b. ol +
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 5lm | b. . + 67
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. x 9 b. 6 x /
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 3- +5-1 b. 2 + 5
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 1/2 + 1/3 + 1/{ b. 2 +3 +5-
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. b. -5
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) 2. 105 -15 b. -11 33
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 7 x 7-1 b. 14 X 14-
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 8 x 8-1 b. 12 X 12-
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 6 6- b. -5-5-1
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) 2. 10 5 b. . 18 25
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 13 31 7-5 b. 3.
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. (3) + (7) 95 95 78 b. (+33) 95
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 28 | b. -7
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. - 7 12 b. + -13 16
Perform the indicated operations in Problems 19–38. (Recall that negative exponents are sometimes used to denote fractions. For example, 1/7 = 7-1.) a. 5+ (-5) b. -3+(-3)
Perform the indicated operations in Problems 39–48. 13 7100 b. 1 + I a.
Perform the indicated operations in Problems 39–48. a. 2 +3-2 2 +3 b. 6+2-1 1/2 + 1/
Use the definition of square root to find the indicated products. S&S a. 3 x 3 b. V4x 4 c. 5 x 5 d. V15 X V15 e. V16 x V16 f. 144 X 144 g. V200 X V200
Approximate e2 and e-3 using your calculator.
If a 13-ft ladder is placed against a building so that the base of the ladder is 5 ft away from the building, how high up does the ladder reach?
A carpenter wants to make sure that the corner of a room is square (is a right angle). If she measures out sides (legs) of 3 ft and 4 ft, how long should she make the diagonal (hypotenuse) in order
Suppose that you need to attach three guy wires to support a large tree, as shown in Figure 5.9. If one guy wire is attached 10 ft away from the center of tree and it is attached 6 ft up on the tree,
Simplify the radical expressions and assume that the variables are positive. If the expression is simplified, so state. a. V441 e. i. m. U|N| 2 5 5x 27y 6 + 35 3 b. 3/2,100 72 V6 f. j. 24(1)(-5) n.
What is the Pythagorean theorem?
Explain the two meanings of the square root symbol—as an operation and as a number.
Discuss the exact and decimal approximations for an irrational number.
What does it mean for a square root to be simplified?
A computer approximation for √2 is 1.4142135623730950488016887242096 9807856967187537694. Give a brief argument showing why that can’t be √2.
What do you think is meant by a triangular number?
Use the definition of square root to find the indicated products in Problems 7–10. Assume the variables are positive. a. 6 x 6 c. 9 x V9 b. 7x 7 d. V14 X V14
Use the definition of square root to find the indicated products in Problems 7–10. Assume the variables are positive. a. 30 x 30 c. V807 X V807 b. 36 X 36 d. V169 X V169
Use the definition of square root to find the indicated products in Problems 7–10. Assume the variables are positive. a. 400 X 400 c. V2.4 X V2.4 b. 2.5 X V2.5 d. V0.25 X V0.25
Use the definition of square root to find the indicated products in Problems 7–10. Assume the variables are positive. a. Vax Va c. 2b x 2b b. xy X xy d. 5w x 8w
Classify each number in Problems 11–16 as rational or irrational. If it is rational, write it without a square root symbol. If it is irrational, approximate it with a rational number correct to the
Classify each number in Problems 11–16 as rational or irrational. If it is rational, write it without a square root symbol. If it is irrational, approximate it with a rational number correct to the
Classify each number in Problems 11–16 as rational or irrational. If it is rational, write it without a square root symbol. If it is irrational, approximate it with a rational number correct to the
Classify each number in Problems 11–16 as rational or irrational. If it is rational, write it without a square root symbol. If it is irrational, approximate it with a rational number correct to the
Classify each number in Problems 11–16 as rational or irrational. If it is rational, write it without a square root symbol. If it is irrational, approximate it with a rational number correct to the
Classify each number in Problems 11–16 as rational or irrational. If it is rational, write it without a square root symbol. If it is irrational, approximate it with a rational number correct to the
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. -V16 c. V125 b. -144 d. V96
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. V1,000 c. 2,240 b. 2,800 d. V4,410
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. 3/75 c. 548 b. 21/90 d. 3/96
Simplify the expressions in Problems 17–36. Assume that the variables are positive. - a. V V C. b. V d. VA
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. -V0.1 c. V0.75 b. -V0.4 d. V0.05
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. C. - b. d. T/Sn=
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. (a + b) b. Va + b
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. x + 4 b. V(x + 2)
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. 5 - 4(3)(2) b. 74(5) (2)
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. V104(5)(-5) b. V122 4(3) (12)
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. V64(3)(-2) b. 24(1)(-1)
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. 6 + 25 2 b. 8- 43 4
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. 12 - 32 6 b. 6-25 4
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. 3 - 9x 3 b. 9 + 3x -3
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. 3 Vx b. -7 Vy
Simplify the expressions in Problems 17–36. Assume that the variables are positive. a. 4x2 25y b. 16x
Simplify the expressions in Problems 17–36. Assume that the variables are positive. -7+7-4(2)(3) 2(2)
Simplify the expressions in Problems 17–36. Assume that the variables are positive. -(-2) - (-2) 4(6)(3) - 2(6)
Simplify the expressions in Problems 17–36. Assume that the variables are positive. -10 V10 - 4(3)(6) 2(3)
Simplify the expressions in Problems 17–36. Assume that the variables are positive. -(-12) + (-12) 4(1)(1) 2(1)
How far from the base of a building must a 20-ft ladder be placed so that it reaches 12 ft up the wall?
How high up on a wall does a 26-ft ladder reach if the bottom of the ladder is placed 10 ft from the base of the building?
If a carpenter wants to make sure that the corner of a room is square and measures out 5 ft and 12 ft along the walls, how long should he make the diagonal?
If a carpenter wants to be sure that the corner of a building is square and measures out 6 ft and 8 ft along the sides, how long should she make the diagonal?
Describe Figure 4.3 on page 151.Figure 4.3 {{ (ooo
Describe a procedure for converting a decimal number into binary representation.
What decimal number is represented by the light bulbs shown in Problems 3–6? & &
What decimal number is represented by the light bulbs shown in Problems 3–6?
What decimal number is represented by the light bulbs shown in Problems 3–6?
What decimal number is represented by the light bulbs shown in Problems 3–6? 888; 71
Write each number given in Problems 7–18 as a decimal numeral.1101two
Write each number given in Problems 7–18 as a decimal numeral.1001two
Write each number given in Problems 7–18 as a decimal numeral.1011two
Write each number given in Problems 7–18 as a decimal numeral.1111two
Write each number given in Problems 7–18 as a decimal numeral.11101two
Write each number given in Problems 7–18 as a decimal numeral.10111two
Write each number given in Problems 7–18 as a decimal numeral.11011two
Write each number given in Problems 7–18 as a decimal numeral.11111two
Write each number given in Problems 7–18 as a decimal numeral.1100011two
Write each number given in Problems 7–18 as a decimal numeral.1110111two
Write each number given in Problems 7–18 as a decimal numeral.10111000two
Write each number given in Problems 7–18 as a decimal numeral.11111111two
Write each number given in Problems 19–30 as a binary numeral.13
Write each number given in Problems 19–30 as a binary numeral.15
Write each number given in Problems 19–30 as a binary numeral.35
Write each number given in Problems 19–30 as a binary numeral.46
Write each number given in Problems 19–30 as a binary numeral.51
Write each number given in Problems 19–30 as a binary numeral.63
Write each number given in Problems 19–30 as a binary numeral.64
Write each number given in Problems 19–30 as a binary numeral.256
Write each number given in Problems 19–30 as a binary numeral.128
Write each number given in Problems 19–30 as a binary numeral.615
Write each number given in Problems 19–30 as a binary numeral.795
Write each number given in Problems 19–30 as a binary numeral.803

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