Complex numbers Questions and Answers

Exercise 8 Prove that the following is not an identity by finding a counterexample Verify that it is a counterexample tant sect 1 sect 1 tant a c csc 2x secx csc r 2 sin x 2 cos r

Exercise 9 If sec A 5 with A in QI and sec B 10 with B in QI find sec A B Draw a diagram

Question 1 Suppose we are building a ramp for wheelchair access to an outdoor eating area at the College If the ramp must have a height of 8 feet and the angle of the ramp must be approximately 50 how long will we need to make the ramp 5 8 feet Question 2 Find the area of the parallelogram 4 112

2 3 Points Use the given property of additi a DETAILS b Commutative Prop Associative Proper

Evaluate the series 9 In n n 1 n 3

1 4 pts In the graph below sketch a graph of the parametric curve defined by x t and y t 4t for 2 t 2 Hint You likely want to start with a table of values 5 7 3 N 1 y 42 A 30 a H 7 1 T 2 T 3 T 4 5 x

onsider the following ribe how the model is used to add two intege Combine positive counters

luate the composi 35 tan sin 1 x

Question 4 23 points At a Junk Yard a study was conducted using 48 cars and found that the average mileage on a car before it was junked was 164 000 and the population standard deviation is known to be approximately 28 000 Construct a 99 confidence interval of what the actual average mileage is for a car before it is junked O 136000 192000 O 4 157352 170648 156079 171921

transformation of f x is the same as its inverse f 1 x

Perform the following operations Assume that all variables represent nonnegative real numbers Make sure you write your answers in the low terms 1 5 271229 2 680245 6425 27 3 V273 45x9y V20x1y 5 2x1 6 2 7 4 7 Bo c2 30 y

Find the points that make up this conic Put them in order from least to greatest For instance if the points are on the vertical access type the bottom number first For the directrix use the entire equation of a line with no spaces y 4x 4y 8 0 Vertex Focus Directrix Latus Rectum

Edgar accumulated 13 000 in credit card debt If the interest rate is 10 per year and he does not make any payments for 3 years how much will he owe on this debt in 3 years for quarterly compounding Round your answer to the nearest cent

Consider a triangle ABC like the one below Suppose that a 22 b 64 and c 44 The figure is not drawn to scale Solve the triangle Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth If there is more than one solution use the button labeled or A B C 4 X No solution 5

what 2 numbers add to 15 and multiplies to 225

12 f x log x 1 4 Ay 8 6 4 2 8 6f 2 2 6 X

11 f x log x 2 3 6 Too 19 194 6 4 2 8 of 4 2 y o oo X

10 f x log x 1 2 fool 8 6 4 2 Ay 8 of 2 X

How many real fifth roots does 1 1024 have

Find the basis 1 2i of the matrix A eigenvector s for the eige A 1 0 2 0 2 20 0 01

A researcher was testing the number of pop corn kernels that popped out of a mini bag of 100 kernels after being cooked for the specified time in the microwave The researcher found that on average 72 kernels popped with a standard deviation of 12 What percentage of the bags should have popped 96 kernels or more 15 9 2 3 13 6 34 1 LSS 13 5 34 1 34 1 13 6 POD CORN

Simplify the logarithmic expression log 9 X 1 9 0

JUSETS Tangips is 1634 VIGTI tips Justin s range in tips is the same as TJ s range in tips Question 3 20 points Consider the data set 60 44 56 52 48 Data Points x Mean X 60 52 44 52 56 52 52 52 48 52 0 4 What is the mean absolute deviation of the data set use the table for help 4 8 Deviation 8 8 4 8 Tag 0 4

Question 1 20 points Consider the following unorganized data set 44 49 39 43 50 44 45 49 51 For this data set which summary statistic is NOT correct O The minimum is 39 The lower quartile is 44 O The median is 45 O The maximum is 51 Question 2 20 points Justin and TJ are servers at a local restaurant The table below shows the tips they earned Tips T J Monday 58 Tuesday 48 40 42 42 Wednesday Thursday Friday Justin 32 45 50 33 50 Which student has a higher range tip for the week and by how much

The graph below matches which equation 654 16 21 33 S y 12 1 O y 2 Oy 2 4 Oy 3 4 2

The function f x 2x 3 is graphed at the right What is the range of the function f x shown Range f x 3 Range f x 3 Range f x 1 Range ALL REALS f x 2 3 24 s Asymptote ya 3

Plot the complex number 6 z 5 i HHH 6 4 2 2 2 4 6 2 4 6 X

Factor 11 12 D 2 32x 24x 8x 1 x8 X 4 x 17x 60

4 x 6x 5 6 x 8x 15 8 2x 9x 18

2 Bearcat University hires Mr LeBron to coach its basketball team LeBron s utility function is u w 6e where w denotes his wage and e his effort He can choose either low effort eL 1 or high effort ey 2 If Bearcat wins its division the university s profit will be 600 Otherwise the university s profit will be 200 LeBron s reservation utility is 4 The university cannot observe LeBron s effort The probabilities of outcomes given LeBron s effort are e 1 2 Bearcat does not win its division 71 200 0 8 0 2 Bearcat wins its division T 600 0 2 0 8 a Let w and we be the wage paid to LeBron if profit is and respectively What are the individual rationality condition and the incentive compatibility condition needed to induce ex b Assuming e is the more desirable of the two effort levels find the optimal wage contract What is the university s expected net profit c If the university wanted to induce LeBron to choose e what wage contract should it use What would be the university s expected net profit

Evaluate the limit of the sequence a 11 A 1 4 B 0 C 1 2 D 1 n 4n 1 sin

1 5 Tranformations If functions f x and g x are both even functions then f x g x is Even Odd Neither O O O 4 If functions f x and g x are both odd functions then f x g x is Even Odd Neither OO O If functions f x and g x are both even functions then f x g x is Even Odd Neither OO O If functions f x and g x are both odd functions then f x g x is Even Odd Neither OO O If functions f x and g x are both even functions then f g x is Even Odd Neither OO O If functions f x and g x are both odd functions then f g x is Even Odd Neither OO O If functions f x is even and g x is odd then f g x is Even Odd Neither OO O If functions f x is odd and g z is even then f g x is Even Odd Neither O O O

g 1 for the following functions Round your answer to two decimal places if necessary 4x f x 2 x and g x AnswerHow to enter your answer opens in new window 2 Points

Given the following table of a function identify the type of function represented and find the value of f 10 It will probably be helpful for you to find an equation for f x X X24 2 4 8 16 2 16 128 1024

x 3 y 4 Step 1 of 2 Find four points contained in the inverse Express your values as an integer or simplified fraction Answer 2 Points

Abe bought a new split level for 200 000 Abe put down 30 Assuming a rate of 5 3 4 on a 30 year mortgage Abe s monthly payment is use the table in the handbook

The height in feet of the water level in a reservoir over a 1 year period is modeled by the function H t 2 3 t 4 13 where t 1 represents January t 2 represents February and so on How low did the water level get that year ft When did it reach the low mark Select 200 12 audio apart 55

Consider the system of equation and 2x 3y 2 8 x 4y 2z 1 5x 2y 15 2x 3y z 8 The second system is obtained from the first by adding twice the first equation to the second equation and then swapping the two equations What is true about the solutions of the two systems The two systems have exactly the same solutions A solution to the second system can be obtained from a solution to the first system by multiplying each value by 2 and swapping consecutive values A solution to the second system can be obtained from a solution to the first system by multiplying each value by 2 The solutions of the two systems have no relation

Consider the following polynomial Step 1 of 2 Use the Rational Zero Theorem to list all of the potential rational zeros Answer t x 4x 13x 69x 18 Enter only the positive values Separate multiple answers with commas

Use the coefficient of the dividend x 3 13x 2 47x 35 0 in descending powe 1 13 47 Write c for the divisor

Consider the following series 1 1 n 1 Show that the series is convergent 0 Since this series is Select 1 1 n 1 n 1 lim n n 1 1 1 n 1 n 1 lim ne n terror 0 0000s 0 0 which condition s below show that it converges Select all that apply How many terms of the series do we need to add in order to find the sum to the indicated accuracy

Solve the system of equations by graphing If there is one solution write the solution as an ordered pair If not choose one of the other options For credit both lines must be drawn correctly on the graph Jy 2x 1 y 2 Solution No solution Infinite number of solutions 6 V 5 4 3 2 1 6 5 A 3 2 1 1 2 3 4 1 2 3 4 5 6

Which graph represents the values of x that make the following inequality true 43 2 2 0 0 2 2 HOMD 804 2 3 8000 OD 00

Which of the following is a factor of 2x 4x 3x 16 x 2 X 3 x 3 Ox 6

O Use a graphing calculator to determine which of the following graphs represents the algebraic function f x 2x 3x 2 3 3 2 2 IN N N 3 3 2 3 2 3 4

Let f x 5x 2 and g x 4x 5 Find f g x f g x fg x and 9 f g x Simplify your answer f g x Simplify your answer fg x Simplify your answer x Simplify The domain off g is Type your answer in interval notation your answer The domain of f g is Type your answer in interval notation The domain of fg is Type your answer in interval notation x Gi ww

where Pis the initial amount invested r is the interest rate as a decimal n is the number of times compounded annually and t is the number of years Which function below best represents how the change in the number of compounds per year n increases the value of the account after investing 25 at 12 interest for 25 years Account Value dollars 300 276 250 Account Value dollars 225 200 175 150 126 100 76 50 25 600 450 400 350 300 250 200 150 1000 50 a a 33393 200 1000 900 800 count Value dollars 700 600 500 400 300 1 2 3 4 5 6 7 8 9 10 11 12 Compounds per Year n 2 3 4 5 6 7 Compounds per Year n One 9 10 34547 Compounds per Year n 8

Multiply and Simplify 24 x 16 X42x 13 4x44 E 4 x 2 4 2 2x 20 2x 6x 4 x 2 x 4 K 4 2 4 2 4 2

Solve the inequality for x 3x 356 Oxs11 1 x 11 x2 1

Write the function for the graph of g x g x 2x g x x 2 g x x 2 g x x 2