Complex numbers Questions and Answers

37 3i 5 1 39 3 2 4

Compute each sum below If applicable write your answer as a fraction 2 2 3 2 3 2 3 0 8 X

On which interval s is the following function concave up f x ln x Select all that apply OI 0 00 0 III 0 00 N 4 0 V 0 4 O VI None of the above

Rewrite the given expression with positive exponents and completely simplify if possible 5 3 17x 5 3 17x

Write the radical 5 0 2 7 2 5 9x y with a rational exponent

Rewrite the following radical with a rational exponent 5 3y

Simplify the given expression 8 8 ly

Evaluate the following expression if possible 3 7p 1 3 F 3 30 Pr

Evaluate the following expression if possible 3 3 X 7 x 3 3 5 5 10 ME PC

Which function is the inverse of f x O A f x 36x 2 for x 0 O B f x 6x 2 for x 0 O c f 2 36x 2 for x 0 I O D f 2 6x 2 for a 20

Chris puts one tenth of each paycheck into savings Her current paycheck is 200 She decides to also put into savings any amount she earns over 200 The expression below represents the percent of her paycheck that Chris saves when she makes x dollars more than her current paycheck 100 x 20 x 200 Drag and drop the expressions into the boxes to identify their meaning Original ratio of saved to total money per paycheck Final ratio of saved to total money per paycheck Final amount saved per paycheck

Multiply 2 x 3 4x 2 x x 1 10 x 3 Enter your answer in simplest form in the b

5 5 21 2 uv A C 7 2uv 4u A mn m n 2m n 2m n B 32mn D 8 20 m 8n D m n B 13 6 8 6 A 2yyx 2 C A 9 32 16x 2m n 2nm 2m n 0 m 722 211 7 B D D 16y12 p 6 B 8m n 32m n 12 13 ZO

Factor the following polynomial using the difference of squares 422 81

Exercise 5 Let z z E C Prove 1 Rez 2 2 2 Imz z 7 3 z 2 zz 4 z 7 ZER 5 12 2 z 2 6 2z 2 2 7 2 2 z z z z 8 121 12 1 1 2 1 1 1

Factor the following polynomial using the sum of cubes 8x 125

3 Find the Fourier transform of f x xe if x 0 and f x 0 if x 0

Evaluate the radical 3 1 343 Select the correct choice below and fill in any answer boxes in you O A 1 343 Type an integer or a simplified fraction 3 OB The root is not a real number

Click here to watch the video Simplify the given expression 3 3 Vy

Simplify the radical 3 5x 1

Simplify the given expression 3 3 ly 3 3

Simplify the radical 4 7 4 4

Use the information provided to sketch a possible graph for described on the provided axis Degree 4 Zeros 3 4 6 End behavior As x gets larger and larger in either the positive or the negative direction y gets larger and larger in the negative direction YA H 10 8 6 4 2 2 11 8 4 6 X

Two functions g and fare defined in the figure below 5 7 g Domain of g Range of g Domain of fog 0 Range of f g O 6 8 Find the domain and range of the composition fo g Write your answers in set notatio Domain of f Range of f X

Exponents Rules Simplify Your answer should contain only positive exponents 1 A x 2y xy 2x y x 4 C 3 5 A 2a a b4 2ab 18 1 2x 0y4 A a 16613 17 16614 2u v 2u uv 1 2uv 4u vll B B B D D 1 D 1 2 1 1 V b 2a U 8 20 2 6 4 2 4 A 6 a C ab 4 Ab 2ab 266 1 2a b 3 4 2m n m n A C A 4m n m 3 4 m 11 4n 6 8 2y yx 2 4 32113 x 16x4 y D 3 412 a bo 2 B B n m n17 D 8a D m 8 28 16y 2 y8x6 4

3 Simplify Your answer should contain only positive exponents 11 a 4 12 12 4k A 16a A k 2 C 1 C A 3 15 21 4v A 4v 1 C 2v 17 1 256a4 A w www C 4m 4nm n 1 2m 1 6 4 3m n B D B 1 D 1 a B 41 D 2v B D 1 m n 4 m 14 16 18 14 4 A 4 4 C 4 16 2 x A 4x C x 18 A C 0 3 2u v 2u 1 vou 1 2v B 64k D 16k6 B D B B D 17 11 1 2u 3 x 2

Solve the system with the addition method 2 4x 3y 20x 15y 10 Answer Enter your answers as integers or as reduced fraction s in the form A B If there is no solu type DNE in each blank If there are an infinite number of solutions specify their form in blanks in terms of x eg x 2x 3

Use a half angle identity to find the exact value cos 105 O A cos 105 cos B cos 105 cos Which half angle formula should be used to find the exact value of cos 105 Select the correct choice below and fill in the answer boxes Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OC cos 105 cos O D cos 105 cos 5 11 1 cos 2 1 cos 1 cos 1 cos 1 cos Question 5 5 6 15 Setup Solve Part 1 of 2 1 cos 2 HW Score 86 11 Points 0 67

Graph f x 2 4 2 First drag the two blue points on graph to the correct points that f x passes through Then use the remaining red point to drag the horizontal asymptote to the correct line Note that all three points are adjusted in increments of 1 4 Y

15 1 Determine the force in each member of the truss and state if the members are in tension or compression Set P 45 kN P 30 kN CY P2 D MEMIN B 1 5 m

2 413 A 4v 1 2v 15 C B 4 D 2v 16 2x A 4x C x B D 3x 2 2

oblem 6 A linear dynamical system can be created for two masses connected by springs between one another and connected to opposing walls The state vector at time t is a 4 x 1 vector consisting of the displacement and velocity of each of the two masses The transition matrix for this dynamical system is given by the following matrix 1 0 33232 16 5 1 i 0 1 16 5 30 O 00 25 0 0 8 25 Because the system oscillates there will be complex valued eigenvalues Find the eigenvalue associated with the following eigenvector 1 3323 0 1 5

7 9 Simplify Your answer should contain only positive exponents 8 8 xx 7 3v2v v A 9 Simplify 9 2p A p C 9p 12 B US D 4 B p 2 D 4p 10 A 4x 2 12 6 10 3v A 16v C 16 12 212 B D B 16 2 D 81v4

Integer Exponents Simplify 11 3p 3p 2p A 6p C 6p 3 B 4p D 18p Simplify Your answer should contain only positive exponents 3 2 2 4 2 2 4 A 2 C 1 122 B D 25 2 2 34 34 A 94 C 4 K C 2 B 44 D 945 B 2 D 1

blem 2 In any given year a person may or may not get the flu Past records show that if a person has the flu one year then due to a build up of antibodies there is a 90 chance that they will not get the flu in the following year If they don t have a flu in a given year then there is a 20 chance that they will get the flu the following year a If a person does not have the flu one year what is the probability that they will also not have the flu 2 years later b In the long run what proportion of years does a person not have the flu

13 15 13 3 3 A 36 9 7 15 4 A 4 c 2 1 2v B 1 D 1113 B 4 D 2v 14 16 14 4 A 4 C 4 X 2x A 4x C 16 B D B 4 3 x 2

oblem 3 a Express the complex number 4 3i 3 in the form a bi b Express the below complex number in the form a bi 7 3i i 3 6i c Consider the following matrix A 2 4i 2 4i 1 5i 1 2i Let B A Find b22 i e find the entry in row 2 column 2 of 4

Problem 4 Which of the following is a solution to the equation 3 i A 2 3 cos 17 18 i sin 17 18 B 2 cos 11 9 i sin 117 9 C 21 3 cos 23 18 i sin 23 18 D 2 3 cos 8 9 i sin 8 9 E 2 3 cos 10 9 i sin 10 9 F 2 3 cos 13 18 i sin 13 18 G 2 3 cos 7 9 i sin 7 9 H 2 3 cos 19 18 i sin 19 18

5 em 5 Express 2 3 67 in the form a bi Enter the values of a and b in that order into the answer box below separated with a comma Enter your answer symbolically ac in these examples if your answer is a bi then enter a b in the answer box

Determine whether the positive or negative square root should be selected 1 cos 401 2 sin 200 5 Since 200 5 is in quadrant the 1 5 6 square root should be selected C

Determine the solution set of the quadratic equation by observing the graphing calculator screens Then verify your solutions by solving the equation X Simplify your answers Type an integer or a decimal Use commas to separate answers ED f x 4x 7x 15 Zero x 3 y 0 Q o Q Q 2

12 10 points Solve the rational inequality Write your answer using interval notation x 1 0 2x 9

9 8 points Use long division to perform the indicated operation x 4x 11 x 5

Use the piecewise graph to identify the following 10 B 10 8 6 4 8 10 16 DOMAIN 18 INTERVALS OF INCREASE 20 IDENTIFY THE FUNCTION FOR THIS GRAPH 17 BANGE 19 INTERVALS OF DEC 21 EVALUATE f 4 f 0 f 6

2 2 3k 3k A 9k4 C 4k B 4k7 D 9k

Simplify Your answer should contain only positive expor 3 24 29 44 2 A 28 A C 1 1 28 D 25 B C

PopQuiz On Halloween CC GG and JJ collected 75 candies CC got five more candies than GG and GG got 10 less candies than JJ How many cadies did each one get

x 1 x 2

Give the rule of the function shown below that has the form f x log x Y 5 A 3 2 1 2 3 Shift Scroll to zoom Shift Drag to pan 6 8 S 10 X 8

Ogarithmic function 3 S 10 Shift Scroll to zoom Shift Drag to pan 8 10 11 12 X