Complex numbers Questions and Answers

Given BC 691 in and AB 732 in find and B

Analyze the graphs below and answer the questions a 7 6 5 4 3 2 7H 6 4 3 2 b 3 Lof 76 3 4 3 2 f State the parent function Write a formula for the above graph f x 74 6 5 4 3 H 4 2 3 4 5 6 2 7 4 5 6 23 State the parent function

Calculate 2 2i Give your answer in a bi form Give the solution with smallest positive angle Round to at least one decimal place Question Help Video Submit Question

Find the conjugate of 181 26 91 27 26 140 9 4 67

find the values of the variables for which the equality is correct x 3 42 y 8 2022 0 43 1285 326 8 5 4 5 125 7x 1 x 2 495x 1 1 2 7 42 n Z 2 13x 2 3229

2 Use a graphing calculator to solve by graphing Round the answer to the nearest hundredth if necessary If there is no solution explain why 2x3 4

Given the vectors A 4 and B 3 i Find AB ii Based on your result from part i write two possible parametric equations for the straight line passing through points 1 2 4 and 2 1 3 iii Calculate A B iv Calculate A x B v Calculate the angle between A and B vi Find the length of the projection of A on B vii Find the vector projection of A on B

14 LET f x 4x 2 COSX IN THE INTERVAL 0 21 DETERMINE THE LOCATION OF THE POINT S OF INFLECTION OF THE FUNCTIE A P 0 1 AT X 12 2 223 P 041 AT X 1 2 2 1 312 N x 1 12 7 B P 0 1 AT X 2 D P 0 1 AT X TL 37 2 2

A woman worked from July through February never quitting She worked between 14 and 36 hours per week Determine the graph which illustrates this situation Choose the correct graph below OA Ahours week 80 months Q O B Ahours week months Q O C Ahours week months

elz What is the equation for the vertical asymptote of the graph of the function shown 8 8 40 X

Consider the following figure 20 eo bo co Z Given In the figure a e 66 Also YZ ZW If YW 13 2 in and YZ 7 9 in find the perimeter of AXYW to the nearest tenth of an inch in

Use similar triangles to solve for x 4 14 18 12 5 7 10 6

section 11 3 Evaluate the following determinant using expansion by minors method Ton 1 5 2 3 4 1 2 3

Find the total amount for the investment using compound interest Round your answer to the nearest cent Do not roum intermediate steps Principal 17 000 Annual interest rate 4 Compounded Semiannually Time 6 years

A new species of bird is introduced into a sanctuary Conservationists monitor the population of the birds for many years The results are shown in the following graph Bird Sanctuary Population Population 2007 1701 150 128 100 153 50 10 Years M Question 5 1 point Over what time period is the rate of change of population positive

1 point A particle is traveling along a straight line Its position at time t is given by s t 5t 7 Find the velocity at time t 5 The velocity at t 5 is

15 Does the following data show inverse variations Round any calculations you make to the nearest whole number x 3 179 3 991 18 81 18 101 916 O yes y 62 282 49 61 11 2 439 1 943

2 What kind of variations does the following data show 23 46 192 O Inverse Direct 2 21 1 0 5

8 Does the following data show a direct or an inverse variation XC 24 19 2 15 36 O Inverse O Direct y 15 12 9 6

44 ds of j 4 2 3 gjo b A Diamond or Heart j As shown above a classic deck of cards is made up of 52 cards 26 are black 26 are red Each color is split into two suits of 13 cards each clubs and spades are black and hearts and diamonds are red Each suit is split into 13 individual cards Ace 2 10 Jack Queen and King If you select a card at random what is the probability of getting Round to 4 decimal places where possible a A 10 of Hearts Enter an integer or decimal number accurate to at least 4 decimal places more c A number smaller than 8 counting the ace as a 1

X t eat ult k Which of the following represents the ROC on the same coordinate system for the x t signal to have a pole zero diagram and a Laplace transform Im s d Im s a b Re s Im s e 19 Reis Im s

W A ne 4 a Is f 4 negative Yes No b For which value s of x is f x 0 If there is more than one value separate them with commas 0 c For which value s of x is f x 0 Write your answer using interval notation

Find the sum of the following series 3 3 0 7 1 4 2 1 c n n 1 2n

find all Solutions of the eavation in the interval 0 2 sin x 3x sinx X X find all solution of the equation in the interval 0 2 rwass cos x 7 Cosx 1 0 x x smaller valve larger valve 27 Smaller Valve latser valve

marks 3 a Consider the region in R defined by the following inequalities x x 4 27 2 i Sketch the region ii Is the region convex Give a reason for your answer with reference

Let W be a subspace of a vector space V let y EV and define the set CLA 1 2 5 Let W be a subspace of a vector space V let y EV and define the set y W x V x y w for some we W Show that y W is a subspace of V if and only if y W

From a window 34 0 ft above the street the angle of elevation to the top of the building across the street is 52 0 and the angle of depression to the base of this building is 16 0 Find the height of the building across the street The height of the building across the street is Round to the nearest whole number as needed ft COD 52 0 16 00

Which statement is true about f x 3x 41 62 O The graph of f x has a vertex of 4 6 O The graph of f x is a horizontal stretch of the graph of the parent function O The graph of f x opens upward O The graph of f x has a domain of x 6

Melissa collected the data in the table X 1 23 4 Given 2 3 00 8 9 Predicted 1 4 7 10 Residual 1 1 1 When x 4 what is the residual O 3 O 1 O 1 O 3

In parts a f use the given figure a Solve f x 6 b Solve f x 9 c Solve f x 0 d Solve f x 6 e Solve f x 9 f Solve 0 f x 9 24 0 y f x 24 648 9 X Q

drea has 5 hours to spend training for an upcoming race She completes her training by running full speed the distance of the race and walking back the sam stance to cool down If she runs at a speed of 9 mph and walks back at a speed of 3 mph how long should she plan to spend walking back

Write an equation of the line passing through 2 5 and having slope 5 Give the answer in slope intercept form The equation of the line in slope intercept form is 0

Question 10 5 points Do rusal somonto opismeyen bir sistemin d rto tepkesi h n n 1 n 5 tin Sistemin giri ine x n u n uygulan rsa sistemin k y n asgadakilerden hangisidir au n 1 u n 5 bu n u n 4 cu n 1 u n 6 C du n 5 u n 1 eu n u n 5 fu n u n 6

Consider the relationship below given X O sin cos 1 Which of the following best explains how this relationship and the value of sin e can be used to find the other trigonometric values The values of sine and cos e represent the legs of a right triangle with a hypotenuse of 1 therefore solving fo e finds the unknown leg and then all other trigonometric values can be found O The values of sine and cos e represent the angles of a right triangle therefore solving the relationship will fin three angles of the triangle and then all trigonometric values can be found O The values of sine and cos represent the angles of a right triangle therefore other pairs of trigonometric rat have the same sum 1 which can then be used to find all other values The values of sine and cos e represent the legs of a right triangle with a hypotenuse of 1 since e is in Quad therefore solving for cos e finds the unknown leg and then all other trigonometric values can be found

PROBLEM The data shown below were obtained on a highway determine the maximum flow and R square using Greenshield s and Greenberg Model X 50 472228 45 40 34 13 12 10 9 8 6 Y 18 25 41 58 71 88 99 105 110 124 122

29 A 20 You will upload a PDF of your work after you submit the test You are to show all of you work on these problems on a separate sheet of paper

Write an equation a in standard form and b in slope intercept form for the line described through 4 10 parallel to y 10 a The equation of the line in standard form is Type your answer in standard form

Find the slope and y intercept of the line with equation x 8y 8 Then graph the line The slope is TvD integer or a simplified fraction

Write the following number in the polar form rete 0 0 2m Be sure to draw the picture to help you do it 5 8i 0 0 4 154 T 89 You are required to upload work and it must include a graph hand drawn is fine of

Use the following matrix A 10 2 42 1 50 4 If matrix A has element a3 0 what is j j

Use the following matrix 1130 4 2 1 1 3201 B How many rows does matrix B have

TO 1 11 7 Find the characteristic equation and the eigenvalues for the matrix 1 0 1 L1 1 01

AL 1 If g 4 4 2 2 0 0 2 2 4 4 and 4 8 2 6 1 4 3 2 4 0 determine the following K a g f x b f g 4 c fog 2 below draw the resulting graph of f g x in the blank grid below K 10 I 2 Given f x and g x 10tv

2 P 3 53 O 4 QR is tangent to circle P at point Q 5 6 R 7 8 9 10 What is the measure of angle R O 37 53 90 97

12 3pts Find an equation for the following graph f x 8 6 4 2 T 3TT tr TT 0 2 2 2 4 6 8 11 X 3TT 2TT 2

Given the graph of the following degree 5 polynomial function find all of the zeros and their multiplicities Provide your answer below 7654321 6 SE 5 2 7 6 5 4 3 2 11 1 2 3 n 123S 2 3 4 5 6 7 69

Select one x intercept None y intercept 5 Horizontal asymptote at the x axis x intercept 5 y intercept None Vertical asymptote at the y axis x intercept None y intercept 1 Horizontal asymptote at the x axis x intercept 0 y intercept 1 Horizontal asymptote at the x axis

me graph of a piecewise defined function is given Write a definition for the function that best describes this graph 31 0 0 1 2 G

or x X 7 3 ft 8 2 ft 75 6 5 cm 109 33

Enter the coordinates of the point on the unit circle at the given angle 225 2 2