Complex numbers Questions and Answers

C A 19 9 13 9 If AB has length 13 9 an Ghas length 19 9 find The length of AC 1 The measure of angle B in degrees The measure of angle C in degrees B

14 cos sin cos sin 1

1 x 3x 2 3 n 8n 12 5 m 3m 10 7 m 15m 56 9 b 6b 40 11 m 4m 12 13 x 4x 45 2 m 13m 36 4 p 2p 24 6 x x 20 8 x 3x 40 10 v 2v 3 12 x x 72 14 p 14p 40

15 2r r 6r 3 40r 171 16 40 27 5 8r 21 5H 20 5 19 9x 6x 15x 10 14 6n 108n 480 16 15x 3x 40x 8 18 28x 35x 12x 15 20 7n 28n 8n 32

5 36 216 4 56 35 7 2la 49a 9a 21 9 7 8 28r 32 6 40x 35x 448x 42 40x 48x 42 8 2k 16k 7k 56 16K 7k 56 10 49x 35x 2lx 15

8 Sketch the graph of the function below being sure to include at least two full periods y sin 2x T y

a Use rotation of axes to show that the following equation represents a parabola Write the equation in XY coordinates Use a rotation angle that satisfies 0 y 2 and that eliminates the xy term 2 2 x y 7x 9y X Find the XY and xy coordinates of the vertex and focus vertex focus x coordinates x y XY coordinates Your answer cannot be understood or graded More Information Find the equation of the directrix in XY and xy coordinates Y coordinates X xy coordinates x y x y

X 5 Describe the behavior of the function below as x approaches f x 3 cotx O f 1 as x O f as x O f 1 as x n O O f o as x T f 0 as x T

X 18 Use the formula asin BO bcos B0 a b cos B0 C where C arctan a b C arctan a b a 0 to rewrite the trigonometric expression in the form asin BO bcos BO cos e O 9 O SVT in 6 DVE cos 6 9 2 9 2 T 9 2 sin 0 9 2 cos 8 O 6 3 cos 6 sin 8 2 2 0 V2 sim 6 VE cos 6 9 2 9 2

X 8 A television camera is on a reviewing platform a meters from the street on which a parade will be passing from left right see figure Write the distance d from the camera to a particular unit in the parade as a function of the angle x a 25 Not drawn to scale Od 25sec x Od 25cos x O d 25cotx O d 25sin x O d 25tan x am Camera

T X 19 Find if possible the complement of 14 O 3T 7 O 13 T 14 O 11 28 O 13 T 28 not possible

6 Period COS 4x Amplitude 11 12 O Period 7 Amplitude O Period 7 Amplitude 7 O Period 27 Amplitude 1 O Period Amplitude 7 2

X 10 Find the point x y on the unit circle that corresponds to the real number t O O O t t t t t t 29 6 29 6 29 29 29 6 29 corresponds to the point corresponds to the point corresponds to the point corresponds to the point 1 1 1 11 1 3 corresponds to the point 3 1

problem Round rates to the nearest percent and dollar amounts to the nearest Solve the whole Cent marked down Points 2 The Galerie d Art paid 239 20 for a limited edition Graux point The original Selling Price was 358 80 But this was 53 to make room for incoming piecies what reduced selling Price sale price Does the art gallery lose money if the print sells for the reduced price is the

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night For the United States the sample mean was 391 minutes and for Mexico the sample mean was 426 minutes Suppose that the sample standard deviations were 25 minutes for the U S sample and 42 minutes for the Mexico sample The report concludes that on average adults in the United States get less sleep on work nights than adults in Mexico Is this a reasonable conclusion Support your answer with an appropriate hypothesis test Use 0 05 Use for Mexico and for the United States USE SALT State the appropriate null and alternative hypotheses in minutes Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value MY NOTES State the conclusion in the problem context We fail to reject Ho It is not reasonable to conclude that on average adults in the United States get less sleep on work nights than adults in Mexico We fail to reject Ho It is reasonable to conclude that on average adults in the United States get less sleep on work nights than adults in Mexico We reject Ho It is not reasonable to conclude that on average adults in the United States get less sleep on work nights than adults in Mexico We reject Ho It is reasonable to conclude that on average adults in the United States get less sleep on work nights than adults in Mexico M BA Projec 1 p ompare RP1 Biki Bik Forum Project C Screen 023 0 Screen

The following table lists all of your coworkers An X denotes the pairs of people who do not get along Andy Dylan Han Tayshaun Andy X X Dylan Han X X O Dylan and Han O Dylan and Tayshaun X Tayshaun X In making a graph to represent these conflicts which of the following coworkers would have an edge between them O Andy and Dylan Han and Tayshaun

1 Tane Tane 1 1 Tane

A XC N THE HD 24 2 RI 12 Libe F midt U

Which graph represents the function of f x 0 D THIM HII DE DE TRE MINE THE HOME HUO WA M DE TRES HOME CHI HAR EN AMA MEMOR DE SPESAN KAM MENU MERE FLE A ZERNETU PAMUZINMOTO MEHRERE DOL BIENTE TWEETS DE RE 3 6 4 S Ang off BETE C 12 10 All 8 IN APANIE THEMONE 100 CO de 14 HEARN IN MOME 12 8 10 12 10 MI 5 NO 15 T 0 VEN TAMAAN CENAZIMEN 14 me HIILARIN m HIIL CON 9x 367 3x 6 I THE J HE M

Given 3x x 4 what are the domain and range X 1 OD XER X 1 R ye R ly 1 OD XER X 1 R ye Rly 1 OD X E R X 1 R ye Ry 7 E OD X E R X 1 R ye Ry 7

f sin tane cos 1 tan 0

22 sin x sec x x sin X

32 y csc 2x

14 cos sin cos sin 1

1 1 0 If A 2 2 1 0 1 1 0 denotes Null matrix then a B is B 3 D 3 where A 1 C 4 3 2 and A A 4A B 0

Graph the inequality on a number line Then write the solution in interval notation x1 7 x 4 Select the correct graph below OA OC 10 7 4 10 Now enter the solution in interval notation 0 0 10 10 OB O D 10 10 0

Solve the system using substitution Write your answer as an ordered pair If there is no solut or infinite solutions leave the solution blank and select no solution or infinite soltutions x y 4 y x 4 Solution This system has infinite solutions one solution no solution

In what important way does receptor mediated endocytosis differ from phagocytosis It transports only small amounts of fluid It does not involve the pinching off of membrane It brings in only a specifically targeted substance It brings substances into the cell while phagocytosis removes substances

Which equation best models the set of data shown in this table 4 27 O A 0 11 2 19 y 2z 17 OB y 11 2 0 3 4 3 O c y 11 z 0 3 4 3 OD y 2x 17 6 35 8 37 10 40 12 44 14 45 16 48

REVIEW Final Sum Factor each completely 1 8x 28x Simplify each expression 2x 2x x 3 x 2 3 A B 5 C D A B 5 x 4 C D 5r2 5x 6 2x x 3 4x 10x x 3 x 2 6x 3x x 1 2x 1 2x 3x 2 2x x 3 4x x 3 5x 15 4x x 4 17x x 12 4x x 4 x 13x 12 4x x 4 4x 11x 15 x 4 x 3 6 2 4 2 6x 4x 3 x 4 2 6 A B C D A 2m 2 2 3m m 3 2 2m 2m 6 B 2 4x 6 6x 5x 4 2 2x 3 6x 7x 1 2 2x 3 6x 9x 2 C D 2 2x 3 3x 3 4 1 x 3m m 3 2 4m 9 m 3 m 3 5m 4 3m 6m 5m 6 3m 6m

3 To approximate the length of a marsh a surveyor walks 275 meters from point A to point B then turns 76 and walks 245 meters to point C s figure Approximate the length AC of the marsh C a B b A

4 The baseball player in center field is playing approximately 300 feet from the television camera that is behind home plate A batter hits a fly bal that goes to the wall 390 feet from the camera see figure The camera turns 7 to follow the play Approximately how far does the center fielde have to run to make the catch aft

10 Find the magnitude of vector v t 5 4 4 3 f 3 2 V 1 1 2 3 4 X

6 Given a 11 b 5 and c 14 use the Law of Cosines to solve the triangle for the value of B Round your answer to two decimal places A b C a B Fimm not dam

11 Find the exact value of the given expression sin 105 cos 345 sin 345 cos 105 19 0 01 14 0 3 1 2 2 8

10 Simplify the following expression algebraically 7cos x O cosx 3 2 O O 7 cos x O 3 COS X 7 sin x 7 cos x

8 Use a graphing utility to graph the function f x 2 sin x cos x

3 Factor then use fundamental identities to simplify the expression below and determine which of the following is not equivalen cot a cot a tan a 1 cos a 2 O sec a D 1 1 cos a O csc a

8 A television camera is on a reviewing platform a meters from the street on which a parade will be passing from left right see figure Write the distance d from the camera to a particular unit in the parade as a function of the angle x a 25 Not drawn to scale am Camera

4 Evaluate the following expression x 2 n where n is a whole numbe sec5x sec x tan x sec x sec x tan x O 4 sec x tan x O sec x tan x O sec x tan5x 4 secx tan X 4 sec x tan x

2500 invested for 6 years Pnnual rate is 01 0001 when will the investment double 9

lives in quadrant 4 x 9 y 5 T 106 1 sin 0 2 cos 0 3 tan 0 4 sec 0 5 csc 0 6 cot 0 5 106 9 106 5 9 106 9 5 9 106 5 tan 0 and sin 0 G

X 3 Write 87 without radicals 3 8 2

Find mZZ 4 Z X Y Write your answer as an integer or as a decimal rounded to the nearest tenth mZZ 5 O

Enter the correct answer in the box Write the sum of 7 28x6 4 7x6 in simplest form if x C

A class of 195 students went on a field trip They took 7 vehicles some cars and some buses Find the number of cars and the number of buses they took if each car holds 5 students and each bus hold 45 students

Solve the right triangle 4 I H 10 Write your answers as integers or as decimals rounded to the nearest tenth GI mZH G mZG O O

f x x 3x 9x 5

Find mZG G 9 mZG H 4 I Write your answer as an integer or as a decimal rounded to the nearest tenth

Find mZW W 7 mZW Y 5 X Write your answer as an integer or as a decimal rounded to the nearest tenth