Complex numbers Questions and Answers

2 Graph each function over a one period interval identify the domain and range when india sinx b y 3 cos2x C y tanx d y 1 3 sin 4x e y 2 cot 4x

Complete the table plot the ordered pairs and graph x y 2 5 Y 5 1 3 ordered pair x y 7 5 1 3 5 7 Choose the correct graph OA Oo

15 A member of a collegiate track and field team recently adopted a new training regimen His times s in the 400 meter event began to improve as described by the function 2 40 46 where s is his time and t is the number of months since beginning the new 1 ekt training regimen Determine k if his times have improved 1 0 second after 6 months Substitute t 0 to determine his 400 m time before the training change Round to the nearest thousandth S

16 The decibel dB is defined as dB 10 log2 where P2 is the power of a particular signal and P Pi is the power of some reference signal In the case of sounds the reference signal is a sound level that is just barely audible How many dBs does a sound have if its power is 60 500 times that of the reference sound Round to the nearest tenth

Complete each statement to illustrate the indicated property of divisibility a Sum Property 2118 and 214 so 2 Select b Difference Property 51200 and 5170 so 5 c Product Property 4140 so 4 43 Select Select C

8 Glove and mitten warmers have become popular over the past few years These devices consist of a paper pouch filled with a chemical mixture that reacts and releases heat when exposed to air At a time t in minutes after being exposed to air at a temperature of 32 F the temperature T of the pouch in F can be modeled by the equation T t 83e 12 1 32 0 t 200 Find the time necessary for the warmer to reach a temperature of 98 F Round to the nearest tenth of a minute

food cost of a meal and the sales tax 40th Street Cafe DATE JUNE09 14 7 38PM TABLE 29 SERVER APRIL Food Total Tax Subtotal TIP TOTAL Thank You 24 50 1 96 26 46 a Calculate the percent of sales tax on the food total al to leave an 18 tip on the food total

7 What is the y intercept in the equation y 45x 65

DETAILS MY NOTES ASK YOUR TEACHER A student s class schedule changes on a three day rotation The student s math class is the last period of every third day This week the student s math class is on Friday The student expects to have math class again on Friday in three weeks Is the student correct or incorrect Assume there are five school days per week The student is correct The student is incorrect

Consider the following a Write the ratio of red marbles to blue marbles Simplify your answer b Write the ratio of green marbles to blue marbles Simplify your answer c Write the ratio of green marbles to all marbles Simplify your answer d Write the ratio of red marbles to all marbles Simplify your answer

6 A national retailer attempts to determine a demand curve for a new product by selling it in different regions of the country for different prices The resulting data is shown in the table below Price Annual Demand 10 000 population 2 00 2 50 3 00 3 50 4 00 The Vice President of Exponential Modeling determines that the demand can be modeled by the function D p 1990 e 1 075p where p is the price in dollars and D p is the annual demand per 10 000 population Use the model equation to estimate the demand if the price is set at 2 8 232 135 79 46 27

a Consider the following 0 Write the addition problem represented by the model 01 2 1 2 20 01 42 01 2 1 2 01 2 1 2 20 Solve the problem Write your answer in simplest form b Consider the following 0 Write the addition problem represented by the model 02 1 2 1 2 201 N N N W G N N W 2 1

CREATE Write and solve a real world problem where you need to find the area of a parallelogram 11 ASSESS REASONABLENESS Joey believes that the area of the trapezoid shown is 108 5 square centimeters Is he correct How do you know Triangle 1 7 cm 11 cm cm Triangle 2 2 cm

The length of the hypotenuse of a right triangle is 20 inches and the length of one of the other sides of the triangle is 14 inches What is the length of the other side of the triangle Round to one decimal place if necessary O 16 inches O 13 8 inches O 6 inches O 14 3 inches

9 The lifetimes of the 60 watt light bulbs produced by the Lucifine Company are distributed randomly with an average lifetime of 560 hours The percentage of bulbs with lifetimes of x hours or less is approximately modeled by 100 f x 1 e 0 04 x 560 The production manager wishes to find the time x that equals or exceeds the lifetime of 68 of the bulbs Solve for this time Round to the nearest hour 10 An initial investment of 2000 doubles in value in 8 1 years Assuming continuous compounding what was the interest rate Round to the nearest tenth of a percent

Find the quadrant in which lies from the information given csc 0 and cos 0 0 01 OII O III ON

on the unit circle 2 Ws an angle OI I radian

12 Consider the graph of y x shown to the right as a dotted curve If it is translated 2 units to the right reflected vertically and then shifted 5 unit up draw the resulting function I 7 6 5 4 3 2 1 2 1 0 1 2 5 1 2 3 4 5 6 7 8 9 10

Look at the graph 10 5 Submit 1011 0 10 5 10 What is the equation of the vertical asymptote

8 Consider the graph of y x If it is translated 4 units to the right and 3 units up what would the resulting equation be A y x 4 3 I B y x 4 3 C y x 3 D y x 4 3

Find the argument angle 0 in radians for the given complex number z 8 5 5 4 i

Consider the data set 30 40 50 80 100 What is the mean absolute deviation of the data set 0 24 29 60

3 Solve the following equations using whatever method you prefer Show all work b 7n 7n 9 0 b b 4ac 2a x OR product A

Solve the following equations using whatever method you prefer Show all work x 2x 48 0 b b 4ac 2a x OR product sum

3 If 4x 36 0 the roots of the equation are 1 6 only 2 6 and 6 3 3 only 4 3 and 3 4 Sam and Jeremy have ages which are consecutive integers The product of their ages 600 Which equation could be used to find Jeremy s age j if he is the younger man 1 j 1 600 2 j 2 600 3 j j 600 1 j 2i 600

1 What is 72 expressed in simplest radical form 1 2 18 2 3 8 3 6 2 4 8 3 tion in the 2 When 5 20 is written in simplest radical form the result is k 5 What is the value of k 1 20 2 10 3 7

Which graph depicts just a MM M XX

Find the minimum of the quadratic function y 4x 2 16x 5

Which measure of center is best to consider when more than 50 of your data is the same value 000 mean median mode range

Solve the equation 5 x 2 4 8x 1 3 x 5 There are no solutions Ox x 10 O x 0 O All real numbers are solutions

Simplify and write answer as a reduced fraction c6 11

Simplity 2 135 For 2 3 you may type 2sqrt 3 Or click in answer box then on Yellow bar to use the Math Quill AL click PREVIEW button before submitting Do not use a calculator to enter answer as a rounded decima Write the exact simplified form

Simplify and write answer as a reduced fraction 98 V50

Find the exact value of the expression if possible Do not use a calculator 67 7 1 sin 57 sin 7 A TU B 7 7 8 7 67 C D 57

A collection of ALL of the objects to be studied is called Sample Population Variable Data

5 Plot each point on the complex number plane and determine the absolute value of each point in simplest terms a 3 6i b 4 3i

Find x Round your answer to the nearest tenth of a degree 19

6 Write a polynomial equation in fact graph that passes through the point 1 36 and has three x intercepts 3 0 2 0 and 4 0

3 Simplify each expression a 4 5i 9 3i b 4 3i 5 2i

termine if each of the following functions has real or complex roots a y 2x 3x 6 b y 2x 3x 6

Question 3 10 points Traveling Sales Person Graph TSP Which of the following is one of the cheapest routes to pass through each vertex once starting and ending with vertex A and using the Nearest Neighbor Algorithm 25 20 17 10 32 28 22 ABCDA 95 ACBDA 97 ACDBA 96 None of the Above 4

11 Write an equation for the graph TT 2 2 0 2 TT 2 TT 31 2 5 2TT

Tree Graphs Which graph below is NOT a tree graph O O O 1 4

Which graph is equivalent to the one shown at the right and proves that the graph is PLANAR i e in a configuration that shows it is planar graph E B D B D B C B C Question 2 10 points Planar Graphs Which graph represents an INCOMPLETE BIPARTITE graph A

Chromatic Numbers Which graph below represents the map shown at the right i e any adjacent regions in the map should correspond to adjacnet vertices in the graph O C B C B C B C B E A E F E F MAP of Pizza Isle B A D E

Euler Circuits Paths Which graph below has an EULER CIRCUIT O OB O F O A A E F E D D E D E

Find the measure of angle A 9 x 71 80 x 51 A

Find the measure of each angle indicated 13 55 85 75 46

sketch the graph of y g x by starting with the graph of y f x and using transformations Track at least three points of your choice and the horizontal asymptote through the transformations State the domain and range of g X a f x 2 g x 2 1 b f x In x g x 10 In 10

Ashley Ravi and Joe sent a total of 82 text messages during the weekend Ravi sent 10 fewer messages than Ashley Joe sent 2 times as many messages as ashley how many messages did they each send