AB is the diameter of a circle. A is (1, 3) and B is (7, -1). i) Find the coordinates of the centre C of the circle. [2] ii) Find the radius of the circle. [2] iii) Find the equation of the circle.
Given any input (a0,a1,a2,…a2n-1 describe the permutation of the leaves of the recursion tree. (Hint: write indices in binary and see what the relationship is of the bits of the ith element of the original sequence and the ith element of the resulting permutation of elements as they appear on the leaves on the recursion tree.) 3) Timing Problem in VLSI chips. Consider a complete balanced binary tree with n = 2k leaves. Each edge has an associate positive number that we call the length of this edge (see picture below).
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.
They are interchangeable because 1g=1mL. 5. A solid block with a length of 6.0 cm, a width of 3.0 cm, and a height of 3.0 cm has a mass of 146 g. What is the block’s density? Show all work. V=lxwxh v=6.0cmx3.0cmx3.0cm= 54cm D=m/v d= 146g/54cm= 2.7g/cm3 6.
Set up the matrix equation to solve this system. 2. Given the inequality y < x2 + 2x – 3, is the point (0, -3) part of the solution? Name a point that is part of the solution and one that is not. 3.
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.
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
He increases his jogging time by 4 minutes each week. Write the general term of this arithmetic sequence, and find how many weeks it takes for him to reach a jogging time of one hour. A) a n = 10 + 4n ; 12 weeks B) a n = 14 + 4n ; 13 weeks C) a n = 14 + 4n ; 12 weeks D) a n = 10 + 4n ; 13 weeks 27) 4 Provide an appropriate response. 28) Determine whether the sequence is arithmetic, geometric, or neither. If the sentence is geometric, find the common ratio r. If the sequence is arithmetic, find the common difference d. 3 3 3 3 3 , , , , ,... 2 4 8 16 32 A) arithmetic, d = C) geometric, r = 1 6 1 2 B) neither D) geometric, r = 2 28) 29) Determine whether the sequence is arithmetic, geometric, or neither.
The diagram below shows the graph of y = –x . 2 y O x (–3, k) y = –x2 The point (–3, k) lies on the graph. Find the value of k. 1 6. C B 12 cm A 1 1 In triangle ABC, AB = 12 centimetres, sin C = 2 and sin B = 3 . Find the length of side AC.
1,248 b. 1,238 c. 1,148 d. 1,338 4. Multiply: 4,628 x 226 a. 1,045,928 b. 1,054,848 c. 1,405,888 d. 1,045,828 5.