Complex numbers Questions and Answers

03 3 Liten Determine the slope of the line shown in the graph 3 2 1 a 3 2 2 E 3 4 5

8 Given cosa Find the exact values for each of the following Reference Triangles a cos a B b sin a c sin 2a 3r where and tan 3 where d tan 2 e cos a f sin b 1 d 3 each

A matrix A and an echelon form of A are shown below Find a basis for Col A and a basis for Nul A 3 7 22 32 1 3 10 16 A 7 14 42 56 014 8 3 8 26 40 000 0 Find a basis for Col A Simplify your answer Use a comma to separate answers as needed Find a basis for Nul A Simplify your answer Use a comma to separate answers as needed

Graph each function in the interval from 0 to 2 2 sin x 1 4 cos x 3

Which of the following linear transformations in A B R R preserve lengths or angles Just your answers 1 x X A XH 2 31 B XH X

What is the amplitude Ay umun 4 2 0 2 2 X

onvert the given i system to an e system using slack variables Then construct table of all basic solutions of the e system For each basic solution indicate hether or not it is feasible x x 9 X 4x 12 X X 20 HIID Write the associated linear equation for the inequality x x 9 Use as the slack variable Type an equation Do not factor Write the associated linear equation for the inequality x 4x 12 Use 5 as the slack variable Type an equation Do not factor Construct a table of all basic solutions of the e system For each basic solution indicate whether or not it is feasible X X S 52 00 00 00 0 0 F P o 0

2 Sketch by hand one cycle of each sine curve Upload a photo of your graph a y 2sin b y 4sin 2 1 6 0

Compute the average rate of change of the function f z z7 over the interval 6 9 Write the answer as a fraction Enter it using as in 3 4

drawn to scale A 49 Answer X B 10 5 14 E 6 49

X X 22 Enter rigid or non rigid in the appropriate blank a A b A Write your response here Write your response here A transformation maintains the shape of the graph of a basic function transformation changes the shape of the graph of a basic function

But this is redundant because both solutions produce the same values finding the first few values from each solution This means that only one of the general solutions is enough Thus at the solutions for tan r 0 are given by Give expressions to represent al solutions to the equation Give your answer indian Practice sin x 2 3 2

Find an upper bound of the absolute value of the contour integral Compare with the exact value Sc Re z dz C the shortest path from 0 to 1 i

Graph the set x 55x 2 on the number line Then write the set using interval notation 7 6 0 234 6 7 x 55x 2

modeled by the equation 1 where t is the distance from the eye to the glass s is the distance from the glass to the object viewed f is the focal length of the glass Calculate the distance from the glass to the object s if t 6 76 and f 5 75 and Answer 8 Name the next three terms of the arithmetic sequence 8 2 12 fourth term fifth term

5 Identify the seventh term in the sequence in which 4096 and r 1 1 O 16 0 4 0 25 01 6 Factor x 3x 10 x 5 x 2 O x 5 x 2 O x 5 x 2 7 Find the sum of the geometric series

16 Does the following data show a direct or an inverse variation X 18 36 72 Inverse Direct y 15 7 5 3 75 17 Simplify the following polynomial then state the degree 2g h 2g h 7gh 2g h 8 4th degree 5th degree O2nd degree 3rd degree

23 Graph the equation and determine if it is a rational function Remember to solve the equation for y first xy 4x 7 O yes O no 24 The height of a garden is 5 feet more than its width Write an equation for the area of the rectangle in term of width w Area square feet

O 5 94 O 59 4 O 0 594 0 1 O 0 83 g 22 Solve the system of linear equations by elimination x y 24 7x 5y 48 y 11 3 94

25 Write an equation of a line in standard form for the given conditions x intercept 2 and y intercept 8 Hint Write the intercepts as ordered pairs 4x y 16 4x y 16 O y 4x 10 4x y 8 4x y 8 y 4x 10

31 Solve the system of equations 11x 14y 10z 113 15x 8z 49 5z 40 8 y 2 32 Solve the exponential equation 25 625 x 1 X 3

O 1 1 24 1 10 3V O U Ou U 0 U 3 3V 30 10 3 TOV 10V 10V 3 28 Given the formula A r find the area A of a circle whose radius is 50300000 cm 13 O 2 52004 10 7 cm O 2 53009 10 5 cm O 2 19024 10 5 cm O 2 304 x 10 5 cm

26 Which term is the linear term in the equation y 11x 4x 10 11x 4x O 10

2 Name the next three terms of the arithmetic sequen 40 37 34 fourth term fifth term sixth term 3 Find the sum of the geometric series 6

14 Find the sum of the geometric series 5 10 20 40 80 160 320 S7

a1 125 r 136 111 128 105 118 and n 3 None of these are correct 542 567 576 Find S5 of the sum of the geometric series a 729 a5 9 r 535 1 3

Find the sum of the arithmetic series if a1 34 n 18 and d 9 18 Name the first five terms of the arithmetic sequenc a 3 d 1 4 3 2 1 0 3 2 1 0 1 4 5 6 7 8 3 4 5 6 7 2 3 4 5 6 2 1 0 1 2

159 D 147 D 160 0 168 O None of these are correct Name the next term of the arithmetic sequence 21 16 11 6 1 0 5 0 1 6

Consider the following functions f x Answer fog x Step 1 of 2 Find the formula for fog x and simplify your answer Then find the domain for fog x Round your answer to two decimal places if necessa Domain X and g x 5 2 EFF Keyboard

3 Find the sum of the geometric series 10 2 2 1

11 C4 31 5i 3 6 3 8 3 2i 4 1 4 i 6 5

10 Find the first four terms of the geometric sequence a 4096 r 4 first four terms x x x

1 Name the next three terms of the arithmetic sequence 41 49 57 fourth term fifth term sixth term 2 Name the next term of the arithmetic sequence 39 32 25 18 O 11 0 9 O 17 18

How do the factors of a polynomial function relate to the graph of the function

14 Identify what a b and c would equal in standard form 11x 3y 14 a b

f x 2 30 Round your answer to the nearest hundredth if necessa O 6 82 O Undefined O 8 24 O 4 5 O 6 3 4 True or False The relation is a function y 1 2 9 1 x 13 1 5 true

15 Find f 4 f x 32 4r Round your answer to the nearest hundredth if necessar

11 True or False The relation 10 5 1 6 10 8 6 8 is a function true O false

x 5 2 5 9 true O false y 14 5 2 14 2 Find the value of the function If f x 3x 2x 5 find 0 f 0 3 Find the value of the function If f x 2x 3x 4x 2 find 3 f 3

4 Give the range of the set 0 1 8 5 0 4 6 5 and tell if the relation is a function O 5 1 4 5 a function O 8 0 6 a function O 5 1 4 5 not a function O 8 0 6 not a function

Determine whether A is diagonalizable Yes O No A 48 84 Find an invertible matrix P and a diagonal matrix D such that P AP D Enter each matrix in the form row 1 row 2 w each row is a comma separated list If A is not diagonalizable enter NO SOLUTION D P

Let M 12 141 7 9 eigenvalue eigenvector The eigenvalue Find an eigenvalue and a corresponding eigenvector You only need to find one pair corresponds to eigenvector

1 point Find the surface area of the part of the plane 3x 1y z 1 that lies inside the cylinder x y 25

1 Create a table to represent the information given below Your brother has the flu At 6 p m you checked his temperature and it was 100 1 F You then check it at 7 PM and it has increased to 101 F You know a dangerous temperature is anything above 103 a If his temperature continues to increase at this rate what time should you take him to the hospital Create a table of values to justify your conclusion it doesn t have to be pretty just make sure it s clear what s going on b Use your table to calculate the slope and write an equation in slope intercept form c What does the slope mean in this problem d What does the y intercept represent Does it have meaning in this problem e Use your equation to graph a line Mark the place on your graph time when your brother s temperature is critical What are the coordinates of this point f Should you go to the emergency room now or can you wait until tomorrow morning g Using this equation determine what time his

15 Find the length of the diagonal of a rectangle whose dimensions are 14m by 24m Approximate to the nearest hundredth

10 Given AABC when C is the right angle and a 7 and c 16 the length of the leg b is 2 C

9 Find the length of the diagonal of a rectangle whose dimensio are 5m by 2m Approximate to the nearest hundredth O 5 3852 O 5 39 O 5 5517 O 5 55

7 Is AABC a right triangle if the length of the three sides are 5 6 and 6 O cannot be determined O no O yes

2 In ADEF leg d 12 and hypotenuse e 28 What will the leg f equal if this is a right triangle

The number of bacteria in a culture is increasing according to the law of exponential growth After 3 hours there are 400 bacteria and after 5 hours there a 1 600 bacteria Write an equation that can be used to determine the number of bacteria y in the culture after t hours YH How many bacteria will there be after 6 hours bacteria