University:
Carleton College
Course:
MATH 111 | lntroduction to Calculus
Academic year:

2024
Views:

322

Pages:

3
Author:

Alecai8y

Question 1 The total cost of the fencing. Cost of fencing per feet/foot = $2 Answer Step 1 From exercise 20, To completely enclose the garden, 182 feet of fencing are required. Thus, we must determine the price of fencing for 182 feet. Total cost of fencing = cost of fencing per foot total foot of fencing = 2. total foot of fencing = 2.182 = 364 Thus, total cost of fencing is $364 Question 2 Which pair of numbers is relatively prime? a. 15 and 25 b. 29 and 58 c. 40 and 63 d. 261 and 513 Answer Relatively Prime: Two integers are said to be relatively prime if there is no integer greater than one that divides them both. (a): Factorization of 15 is 15 = 3 x 5 and the factorization of 25 is 25 = 5 x 5 Since 5 is the common factor in factorization of both the numbers, therefore they are not prime numbers. (b): Factorization of 29 is 291 x 29 and the factorization of 58 is 58 = 2 x 29 Since 29 is the common factor in factorization of both the numbers, therefore they are not prime numbers. (c): Factorization of 40 is 401 × 2 ×2×2×5 and the factorization of 63 is 631×3×3×7 Since in the factorization of both the numbers, there is no common number than one, thus 40 and 63 are prime numbers. (d): Factorization of 261 is 2 613x3 x 29 and the factorization of 513 is 5133 x 3 x 3 x 19 Since 3 is the common factor in factorization of both the numbers, therefore they are not prime numbers. Thus, the pair 261 and 513 are not relatively prime. Question 3 To find: The pounds of a person if the weight of person is 82 kilograms. Answer Step 1 Consider 82 kilograms Convert 82 kilograms to pounds. Recall the approximate conversions: 0.45kg ≈ 1lb This fact gives us two unit fractions: 0.45kg 1lb =1 1lb 0.45kg Use the unit fraction with ounces in the denominator so that these unit divide out. 23lb 0.45kg 23lb ≈ X 1 1lb 82 82kg ≈ lb 0.45 82kg = 182.221b 82lb ≈ 182.22pounds Therefore, theweight of the person is 182.22 pounds Question 4 To convert: 20 cups to gallons Answer Step 1 The relation between cupsand gallons is given by 1 cup = 0.0625gallons Therefore, 20cups = 10 × 0.0625gallons = 1.25gallons Hence, 20 cups is equivalent to 1.25 gallons. Question 5 To perform: the operation 2700 mL+1.8L Answer Step 1 To perform operation on metric units of capacity, use the arithmetic operations. The metric units of capacity are the same before adding, subtracting, multiplying or dividing. As the units are different, convert both to liters or both to milliliters before adding the capacities together 2700ml = 2.7L (·.: 1ml = 0.001L) 2.7L +1.8L 4.5L Or, 1.8L = 1800ml (.: 1L = 1000ml) 2700mL +1800mL 4500mL The total capacity is 4.5 L or 4500 ml, both represent the same capacity.