Complex numbers Questions and Answers

Do Now 12 5 1 How are you today Is there anything you want your teacher to know 2 If 4 x 8 what is the value of x 2 3 if 3x 5 4x 6 what is the value of 3x 2 4 If Glenn is ffeet and 3 inches tall what is the value of fif Glenn is 51 inches tall 5 A pound of cement costs 75 If a construction company has a bill of 5 250 for cement

5 3 6 a 5 a 2 A B 7 C D A B C D 28 a a 6 a 5 7a 36 a x 5 5x x 4 x 2 a 5 a 2 28 5a a 6 a 5 9a 36 a 5 a 2 5x 17x 6 x 4 x 2 6x 2 x 2 6x 21x 6 x 4 x 2 6x 23x 10 x 4 x 2 6 8 6 4 5 2b 6 b 1 A B C D 8 5p A B C D 216 25 26 2 b 3 b 1 10 b 3 b 1 15b25 2 b 3 b 1 7b 13 b 3 b 1 P 4 18p 114p 120p 5p 3 4p 90p 570p 600p p 4 6p p 5 3p 4 2 4p 2p 5 10p p 3 p 2

Include a title and a short explanation of your data DO NOW 19 On the grid below solve the system of inequalities equations graphically for x and y 3x y 2 3 x 2y 4

Do the following for the points 5 2 3 1 1 1 3 1 If you are entering decimal approximations enter at least five decimal places a Find the equation for the best fitting parabola y ax bx c for these points y 7 176 x 2 7x 220 673 880 b Find the equation for the best fitting parabola with no constant term y ax bx for these points y c Find the equation for the best fitting parabola with no linear term y ax c for these points y

3 Determine the surface area of his can 7 inches height 10 inches Show your work here SA 2 TT r 2 rh

5 Determine the minimum amount of aluminum needed to make this can Deca radius 2 in height 5 inches Show your work here SA 2 TT r 2 rh 2 3 14 4 2 3 14 2 5 25 13

h eight radius A r A lw A 2 rh A r Circle examples of surface area below The amount of wrapping paper for a gift The amount of carpet for a room The amount of cereal in a box The amount of water in a fishtank The amount of paint on a wall

Problem 3 20 points In AABC let a 4 in b 5 in and angle C 101 32 13 the remaining side and angles of the triangle Round all answers to the neares

Area of Cylinders 4 Determine the surface area of the pot diameter 8 in 4 r 4 height 12 in Show your work here SA 2 TT r 2 rh SA 2 4 2 4 12 2 3 14116 2 3 14 48 6 28 16 2 3 14 48 100 48 2 3 14 48

Find the following power Write the answer in rectangular form 3 2 3 21 4 CIDE O Points 0 of 1 3 2 3 21 4 1296 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

Given that z 5 cos 60 i sin 60 then the following is true 125 cos 180 isin 180 125 1 i 0 11 125 Oi or simply 125

Write the expression as a single logarithm 3 log3x 3 log3z 3 log3y log 7 3

Raise the number to the given power and write the answer in rectangular form 2 cis 55 6 GCEE 2 cis 55 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

Find the power Write the answer in rectangular form 2 2 3 4 6 8 4 13 HW Score 0 0 of 9 poi O Points 0 of 1 2 2 3 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

The one to one function fis defined below f x 5x 10 Find f the inverse of f Then give the domain of fusing interval notation Domain of 8 6 0 0 0 0 QUO 0 0 0 0 8

Do 5 In the movie Diehard the prop gold bars are 10 0 inches by 2 50 inches by 1 50 inches one inch 2 54 cm exactly If these were a real gold bar what would their mass be the density of gold Au is 19 3 g cm 12k9

2x 20 3x 15 20 15 3x 2x 5ax x 5 2x 15 3x 20 5x 20 15 5 5 x 1 Equation Checklist Note You will not have all of these steps in every problem Distribute the outside factor to all terms within parentheses Check the left side of the equation combine like terms Cancel out the constant term Check the right side of the equation combine like terms If there are variable terms on both sides of the equation cancel out the one with the lower coefficient

Write the complex number 5 cos 358 isin 358 in the form a bi 5 cos 358 isin 358 Type your answer in the form a bi Round to the nearest tenth as needed

Write the complex number in rectangular form 20 cos 300 i sin 300 The complex number is Simplify your answer including any radicals Type your answer in the form a bi Use integers or fractions for any numbers LOVER

Write the complex number in trigonometric form r cos 0 i sin 0 with 0 in the interval 0 360 4 4i 0 4 4i 0 cos isin Type the value for r as an exact answer using radicals as needed Type the value for 0 as an integer or decimal rounded t

Write the following complex number in the form a bi 14 cos 0 i sin 0 14 cos 0 i sin 0 Type an exact answer

11 5 points Use the graph of f x to sketch the graph of y f x 1 3 f x 31 4 1 1 0 F 2 1

12 5 points Let f x x 3 find and simplify the difference quotient f x h f x h 0 h

7 4 points Circle the letter of any of the following graph s that represent a function a b 54 21 t 24 1 47 3 2 d co 1 I da 3 5 4 3 2 1

Use synthetic division to show that x is a solution of the third degree polyno Enter your answers as a comma separated list x 2 x 4x 2x 8 0

Consider the following function Function f x 6x 35x 8x 12 a Verify the given factors of f x 2x 1 1 1 20 3x 2 w N 6 35 Factors 2x 1 3x 2 6 35 6 32 4 6 39 3 8 26 8 16 12 12 b Find the remaining factor s of f x Enter your answers as a comma separated list c Use your results to write the complete factorization of f x

Factor and simplify cos x cos xsec x Choose the correct simplification below OA cos x OB sin x O C 1 OD tan x sin x

Find all zeros of the function and write the polynomial as a product of linear factors 3 f x x x 25x 25 2 O A f x x 1 x 5 x 5i O B f x x 25 x i x 1 O C f x x 1 x 1 x 25

Write the complex number in polar form Answer exactly in radians with r 0 and 0 0 2 A 1 16 HIG cis

Consider the function f x 11 Graph the exponential function by hand 2 Identify any asymptotes Identify any intercepts 2 250 200 150 100 3 O S 250 200 150 100 50

Find the sum j 3 3

Consider the following Y 2 In 2 In x yz In 4x e Use a graphing utility to graph the two equations in the same viewing window O b Use the table feature of the graphing utility to create a table of values for each equation Round your answers to two decimal places If an answer does not 0 1 2 3 L K S Vy

10 Illustrate the following Use rectangles or circles for the wholes 5 15 18 6

Determine intervals on which the function is increasing decreasing and constant On what intervals is the function increasing OA 4 2 O B 9 4 and 3 8 O C 4 2 and 6 8 O D 3 8 On what interval is the function decreasing On what interval is the function constant 10 W 10 10 e X 10 Time Remaining 01 41 09 G

The formula S 16t is used to approximate the distance S in feet that an object falls freely from rest in t seconds The height of a building is 1005 feet How long would it take for an object to fall from the top The object would fall for seconds Simplify your answer Type an integer or a decimal rounded to the nearest tenth

Evaluate the expression 14 11 3 14 11 3 Simplify your answer Type an integer or a fraction

Name the integers from the list below 1 5 8 33 18 0 75 6 71 14 1 D 1 What are the integers Select all that apply DA 5 33 G 1 1515515551 1 1515515551 B 6 71 E 18 H 75 C 0 0 V 6

Graph the following function Check your result using a graphing calculator f x O A x 2 for x 5 2 for 5 x 6 Choose the correct graph below 8 1 2 forx26 Q OB A THA cal to Ay 2 H ta G O C 20 i tot do 8 HTT 10 g BEL O 20 O D LINY e Ay

Find the inverse of f x x 3 by thinking about the operations of the function and then reversing or undoing them Choose the correct answer below OA f x x 3 OB f x x 3 OC f x y 3 OD f x y 3

The graph shown below approximates the number of children in a country who lived with only their grandparents in the years from 1991 through 2009 The number of children is a Function f of the year x Approximate the number of children living with only grandparents n 1991 That is find f 1991 Number of children in millions 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 91 93 95 97 99 01 03 05 07 09 Year The number of children living with only grandparents in 1991 is appro million Type an integer or a decimal T

Use the graph to find the following a f 2 b the domain c any x values for which f x 1 d the range VITAL I Pit anys UCIC BIG CUITCUL CIVICE UCIOW au cuessary answer box es to complete your choice O A y ly OB y lyz OC yl sys OD ylys O E The range is all real numbers i 4 S 7 This question 1 point s pos 3 4 64 B 10 1 More 10

Suppose a polynomial function of degree 5 with rational coefficients has the given numbers as zeros Find the other zero 4 3 1 4i 3 The other zero is

Determine the other factor for 2ax 4ay 3bx 6by if one of the factors is 2a 3b A B C x 4y x 2y x 2y D x 2y 2

Factor the following quadratic expression 15x 35x A 7x 5x 6 B 5x 3x 7 C 3z 5x 1 Not factorable

Use the graph to find the following a f 2 D the domain c any x values for which f x 1 d the range For what x value s is f x 1 Select the correct choice below and if necessary fill in the answer box to complete your choice A X Use a comma to separate answers as needed OB There is no value of x for which f x 1 What is the range Select the correct choice below and if necessary fill in the answer box es to complete your choice CO 10 k 7 10 8 8 4 2 6 10 O 0 10

Determine whether the correspondence is a function Domain 4 3 6 Range 4 Is the correspondence a function O A Yes because each element in the range corresponds to exactly one element in the domain OB No because an element in the domain corresponds to more than one element in the range C No because an element in the range corresponds to more than one element in the domain OD Yes because each element in the domain corresponds to exactly one element in the range

10 28v 16v 21v 12 12 49x 35x 56x 4

Factor each completely 1 8r 647 r 8 3 12x 2x 30x 5 5 63n 54n 105n 90

The perimeter P in yards of a soccer field is represented by the formula P 21 2w where is the length in yards and w is the width in yards W 10 yd l 100 yd a Solve the formula for W b The perimeter of the soccer field is 330 yards Find the width of the field Width yards c About what percent of the field is inside the circle Round to the nearest tenth of a percent The percent of the field is C

f x 2x 5 Find fog 3 fog 3 g x is as defined in the function below 9 8 7 6 5 3 2 1 9 8 7 6 5 4 3 2 1 N 2 3 45678 5 6 8 y 3 0 2 8