University:
Massachusetts Institute of Technology
Course:
18.06 | Linear Algebra
Academic year:

2024
Views:

216

Pages:

4
Author:

Mckenna Welch

Question 1 Solve -3.1x + 7 - 7.4x = 1.5x - 6(x - 3/2) Answer -3.1x + 7 - 7.4x = 1.5x - 6(x - 3/2) -3.1x + 7 - 7.4x = 1.5x - 6x + 9 -10.5x + 7 = 1.5x - 6x + 9 -10.5x + 7 = -4.5x + 9 -10.5x = -4.5x + 2 -6x = 2 x = -2/6 x = -1/3 Question 2 Which of the following expressions is written in scientific notation? 0.09 × 10^7 Answer A number is written in scientific notation when the number is written in the form a × 10^n, where n needs to be an integer and a needs to satisfy the inequality 1 ≤ a < 10. 0.09 × 10^7 Comparing the given number with the form a x 10^n, we determine the values of a and n. a = 0.09 n = 7 We need to verify whether n is an integer and a satisfies the inequality 1 ≤ a < 10. n=7 is indeed an integer. However, a=0.09 is smaller than 1 and thus a does not satisfy the inequality 1 ≤ a < 10. We then conclude that the number is not written in scientific notation. Question 3 How do you translate "91 more than the square of a number" into an algebraic expression? Answer Let the number be x, then Square of the number is x² "91 more than the square of a number" will be x² + 91 So, we can write it as an algebraic expression with two variables as: y = x² + 91 Answer: y = x² + 91 Question 4 Simplify the expression. Assume that the variables in the denominators are nonzero. (x^-3 y^2)^-4 / (y^6 x^-4)^-2 Answer Multiply exponent by each term : (x^12 y^-8) / (y^-12 x^8) To make exponents positive, take reciprocal of the base number, and raise it to the corresponding positive power: (x^12 / y^8) / (x^8 / y^12) Then, divide powers, by subtracting the power in the denominator from the power in the numerator: x^(12-8) y^(-8-(-12)) Result: x^4 y^4 Question 5 The sum of the coefficients of (3x - 2y)^10 is (A) 1 (B) 1024 (C) 58.025 (D) 59.049 (E) 9,765,625. Answer THE SUM OF THE COEFFICIENTS OF (3x - 2y)^10 IS THE SAME AS THE VALUE OF (3x - 2y)^10 WHEN x=1 AND y=1: [3(1) - 2(1)]^10 = (3 - 2)^10 = 1^10 = 1