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

2024
Views:

386

Pages:

6
Author:

Alecai8y

Question 1 Multiply the algebraic expression using a Special Product Formula, and simplify. (3y - 1)2 Answer 1 Simply put: (3y - 1)² Solution: 2 2 We know, (a - b)² - a²-2ab+b² (1) expressed as follows: (3y - 1)², Simplifying further using (1) we get: (3y-1)² = (3y)² - 2(3y) (1) + 12 = 9y2 - 6y + 1 ⇒ (3y - 1)² = 9y² – 6y + 1 So answer: (3y - 1)² = 9y² – 6y + 1 Answer 2 (3y - 1)2 (3y-1)(3y-1) 3y(3y) + 3y -1 -1(3y) – 1-1 9y2-6y +1 Question 2 a = 3y, b = 1 Dermine the solutions of the equation: 462 – 100 = 0 algebraically Answer 1 We will simply solve the equation to find the value of b. Solution of the above problem is the step below. 462-100 = 0 4b2 = 100 100 b² = 4 b² = 25 b = ±(250.5) = ±5 Hence, solution is b = 5, -5 Answer 2 Use the quadratic formula to find the solutions. -b+b²-4(ac) 2a Substitute the values a 4,b = 0, and c = -100 into the quadratic formula and solve for x. 0 ±√02-4-(4-100) 2.4 Simplify. x = ±5 The final answer is the combination of both solutions. x = 5,-5 Answer 3 Add 100 to both sides of the equation. 4x2 = 100 Divide each term by 4 and simplify. x² = 25 Take the square root of both sides of the equation to eliminate the exponent on the left side. x = ±√25 The complete solution is the result of both the positive and negative portions of the solution. x=5, -5 Question 3 What does it mean "to solve a problem algebraically"? Answer 1 Well, for example, solving an algebraic equation just means manipulating the equation so that the variable is by itself on one side of the equation and everything else is on the other side of the equation. Answer 2 In mathematics, to solve an equation is to find its solutions, which are the values that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign. When seeking a solution, one or more free variables are designated as unknowns. Question 4 1 What is rational, irrational number, natural, whole or integer? 3 Answer 1 1 is a rational number. 3 Answer 2 It is not a natural number, whole number or integer, so as it is not irrational, so we find out that it is rational. Answer 3 From that list can only have the characteristics of a rational number. Question 5 Which digit is in the ten thousands place in 782,341,693? Answer Given number 782,341,693 has 3 - unit 9- ten 6- hundred 1- thousand 4-ten-thousand 3- hundred-thousand 2 - million 8-ten-million 7- hundred-million Therefore, the digit 4 is in ten-thousand place.