Name Class Date 8-1 1. 3s3t3 Practice Adding and Subtracting Polynomials Form K Find the degree of each monomial. 2. 3n 3. 5xy 4.
Find the next three terms in each geometric sequence. 5. 10, 20, 40, 80, … SOLUTION: The common ratio is 2. Multiply each term by the common ratio to find the next three terms. 80 × 2 = 160 160 × 2 = 320 320 × 2 = 640 The next three terms of the sequence are 160, 320, and 640.
176 b. 352 c. 1936 d. 968 12. Solve: 28 = y – 4. a. y = 24 b. y = -32 c. y = -4 d. y = 32 13. Solve: 6y = 54. a. y= 9 b. y = 60 b. y = 48 d. y = 8 14. Evaluate: 4a + (a – b)³, when a = 5 and b = 2. a.
Then divide each term by GCF to determine what is left inside the parentheses.) Example 2: 18x2y3z5 - 24x5y2z + 30x3y4z2 Solution: 6x2y2z(3yz4 - 4x3 + 5xy2z) 2. Look to see if it is a difference between two perfect squares. (need 4
2 4. (a) Factorise x2 + x – 6. 2 (b) Multiply out the brackets and collect like terms. (3x + 2)( x2 + 5x – 1) 3 [ X100/201] Page four Marks 5. The diagram below shows the graph of y = –x .
Adding the two cases above, we arrive at the answer: un = un−1 + un−2 . (c): Use either (a) or (b) to determine the number of bit strings of length 7 that do not contain two consecutive zeros. SOLUTION: We note directly that u1 = 2 and u2 = 3. Then u3 = 2 + 3 = 5, u4 = 3 + 5 = 8, u5 = 5 + 8 = 13, u6 = 8 + 13 = 21, and u7 = 13 + 21 = 34. Problem 3.
Assignment #2 1) Improve the result from problem 4 of the previous assignment by showing that for every e> 0, no matter how small, given n real numbers x1,...,xn where each xi is a real number in the interval [0, 1], there exists an algorithm that runs in linear time and that will output a permutation of the numbers, say y1, ...., yn, such that ∑ ni=2 |yi - yi-1| < 1 + e. (Hint: use buckets of size smaller than 1/n; you might also need the solution to problem 3 from the first assignment!) 2) To evaluate FFT(a0,a1,a2,a3,a4,a5,a6,a7) we apply recursively FFT and obtain FFT( a0,a2,a4,a6) and FFT(a1,a3,a5,a7). Proceeding further with recursion, we obtain FFT(a0,a4) and FFT(a2,a6) as well as FFT(a1,a5) and FFT(a3,a7). Thus, from bottom up, FFT(a0,a1,a2,a3,a4,a5,a6,a7)
Chapter 1 review questions 1. Which of the following is true about 1 bit? a. Can represent decimal values 0 through 9 b. Can be used to represent one character in the lowercase English alphabet c. Represents one binary digit d. Represents four binary digits 2.
Identify if the order triple (1, 2,3) is a solution of the given system of equations. 3x 5 y z 16 7 x y 3z 4 x 5 y 7 z 10 4. Identify if the system of equations given below has unique solution, infinitely many solutions, or no solution. 2 x 5 y 16 3x 7.5 y 24 5. Given is the augmented matrix of a system of equations: 1 5 6 2 7 1 3 5 1 5 7 13 Write the new form of the augmented matrix after the following row operations.
42x 2 1 35x 1 7 17. 212x 2 2 x 1 11 Lesson 1.4 Factor the expression. If the expression cannot be factored, say so. 18. 80x 2 1 68x 1 12 Solve the equation.