Problem 2. Find a recurrence relation for un , the number of bit strings of length n that do not contain two consecutive zeros, by (a): using the recurrence relation zn for the number of bit strings of length n that do contain two consecutive zeros. SOLUTION: We simply observe that all strings of length n either do or don’t have two consecutive zeros; mathematically, this means that zn +un = 2n . Hence, un = 2n −zn = 2n −(zn−1 +zn−2 +2n−2 ). (b): by reasoning from scratch.
Find the next three terms in each geometric sequence. 5. 10, 20, 40, 80, … SOLUTION: eSolutions Manual - Powered by Cognero Page 1 7-7 Geometric Sequences as Exponential Functions Since the ratios are constant, the sequence is geometric. The common ratio is –1. Find the next three terms in each geometric sequence.
(b) Solve the circuit. That is find all unknown currents, voltages, and resistances. 6. Consider the circuit in Figure 4, where R1 = 5.00×102Ω, R2 = 1.00×103Ω, and VB = 10.0V . (a) Find the equivalent resistance Req of the circuit.
Running head: Summative Assessment Summative Assessment Terry W. Jones SED 544 Secondary Curriculum Development & Assessment Grand Canyon University LeeAnn Ritchie May 12, 2011 What’s the Point? M8G1. Students will understand and apply the properties of parallel and perpendicular lines. a. Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically.
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)
Radicals Tips 1. Make sure that one of the two factors of the radicand (expression under the radical) is the largest perfect square: Example: Simplify 72 Correct 72 = 36 ∙ 2 = 62 Incorrect 72 = 9 ∙ 8 = 38 2. To be able to add or subtract radicals, the radicands must be the same. Example 1: Add 32 + 52 Answer: Since radicands are the same, (3 + 5)2 = 82 Example 2: Subtract 73 - 3 Answer: (7 – 1)3 = 63 Example 3: 318 - 52 (Must simplify first) 39 2 - 52 3 ∙ 3 ∙ 2 - 52 92 - 520 Answer: 42
Lesson 44—Table Basics Create Tables • Tables consist of columns and rows of data—either alphabetic, numeric, or both. • Column: Vertical list of information labeled alphabetically from left to right. • Row: Horizontal list of information labeled numerically from top to bottom. • Cell: An intersection of a column and a row. Each cell has its own address consisting of the column letter and the row number (cell A1).
Use the report pages below to record your data. Answer questions A-G found on pages 46 and 47. Name: _________________________ Lab 2 Report Data: Data Table 1: Length Measurements | Object | Length (cm) | Length (mm) | Length (m) | CD or DVD | 12.1 cm | 121 mm | .121 m | Key | 5.1 cm | 51 mm | .051 m | Spoon | 16.1 cm | 161 mm | .161 m | Fork | 18.5 cm | 185 mm | .185 m | NOTE: The instructions indicate to measure the objects to “one degree of uncertainty.” The degree of uncertainty is a property of the instrument used. All three recorded values will have the same precision. On page 29 is the explanation of uncertainty.
Revision Year 12 Maths B, Term 4 1. The function, y=3cosx+5 has an amplitude of 3 and a mean value of 5. Using these values, the range can be found to be 2≤y≤8 . Find the range of the function y=4cosx+7 2. Find the exact value of tan600 (Hint, draw a standard triangle to help) 3.
In the Pledges worksheet, create an Excel table with the Medium 7 table style using data in the range A1:H29. Rename the table as PledgeData. 4. Make a copy of the Pledges worksheet, and then rename the copied worksheet as Q4-6 (for “Question 4-6”). (Hint: Press the Ctrl key and drag the sheet tab to the right of the Pledges sheet tab to make a copy of the worksheet.)