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

2024
Views:

220

Pages:

3
Author:

Alecai8y

Question 1 To write: The fraction 47 100 as a decimal. Answer Step 1 The given fraction is 47 100 There are two zeros in the denominator, So, the number of decimal point should be two. Thus, put decimal point two spaces from right in the number 47. Therefore, the required decimal is 0.47. Question 2 a) Simplify the expression 4x + 6x by combining the like terms. b) Simplify the expression y - 5y by combining the like terms. 2 c) Simolify the expression 3x² + 5x² - 2 by combining the like terms. Answer Step 1 The given expression is 4x + 6x Since both terms have same variables have equal power (exponent), they are the like terms. To add the terms simply, add the numbers before the variable. Since, 4 + 6 = 10, The given expression can be simplified to 4x+6x10x The simplified form of the given expression is 10x Step 2 The given expression is y 5y Since both terms have same variables and the variables have equal power (exponent), they are the like terms. To add the terms simply, add the numbers before the variable. Since, 1-5 = -4, the given expression can be simplified to y - 5y = -4y The simplified form of the given expression is -4y. Step 3 2 The given expression is 3x² + 5x2 2 Here, the like terms are 32 and 52. Combine these two terms by adding the numbers before the variables as follows: 8x2-2 2 The simplified form of the given expression is 8x² - 2 Question 3 To multiply: the given binomial using FOIL method. 2 62 3 2 (a-b²)(a²+b²) Answer Step 1 We must examine the claim that the population mean score in anthropology differs from 492 in this particular hypothesis case. F stands for the product of first terms. O stands for the product of outer terms. I stand for the product of inner terms. L stands for the product of last terms. The given equation is (29+200)(29-00) 3 a b² 3 3 Now, multiply the given binomial usinf FOIL method, 2 2 a-b²+b² 3 =(a))+(a)(b)+(-b²)(3)+(62) (-b²) 2 (a-b²)(a²+b²) 4 = a²+ 2 2 2 = a² + b²-3ab² – b4 9 3 2 a -b² 3 2 4 a² + b² a²-b² 9 Hence, the multiplication of the given binomial is 2 3 a-b² 2 2 = a²-b² 4 9 Question 4 To multiply: the given binomial using FOIL method. 5x2 (3x2 - x + 2) Answer Step 1 The given equation is 5x2(3x x+2) Now, multiply the given trinomial by applying distributive property, 5x2 (3x2 - x + 2) = ((3x²) (5x2) - (x) (5x2) + (2)(5x2)) 5x2 (3x2 - x + 2) = (15x4 - 5x3 + 10x²) 5x2(3x2 - x + 2) = 15x45x³ + 10x2 Hence, the multiplication of the given expression is 5x2 (3x2 x + 2) = 15x4 - 5x3 + 10x2 Question 5 Plese, tell why is the square root of a negative number impossible? Answer 1 2 The square root of a number y is defined to be the value x such that z² = y. However, for any real number x, z² ≥ 0. When we say that the square root of a negative number "doesn't exist", we mean that there is no real number solution. Answer 2 Any number times itself is a positive number or zero. This means you cant