Complex numbers Questions and Answers

Suppose that the number y of otters t years after otters were reintroduced into a wild and scenic river is given by the formula below y 2500 2490e 0 1t a Find the population when the otters were reintroduced at t 0 otters b How long will it be before the otter population numbers 1400 Round your answer to one decimal place yr

Answer the following using interval notation Domain Range 8 6 4 2 O 83 4 6 2 4 2 6 2 4 6 8 I

Find two numbers a and b such that the following system of linear equations is consistent independent x 6y 5 ax 3y b Note that the ALEKS graphing calculator may be helpful in checking your answer 11 X

10 Solve and graph 2 x 4 3x 4x 1 2x

rag the purple X on the graph below to vary the length of the interval h ii the length of h is 3 iii the length of h is 1 160 y iv the length of h is 0 5 140 120 100 80 60 40 20 h 6 00 4 22 40 2 6 a Use the applet above to determine the value of the difference quotient the average rate of change near the point 4 f 4 whe i the length of h is 5 Preview Preview Preview 10 00 80 00 Preview 8 10 12 14 16 X

A water tower to located 300 ft from a building see the figuro From a nindon in the building on obiarvor cotos that the angle of civation to the top of the toner is 39 and that the ongle of depression to the bottom of the tonor 25 How tall in the tower Round your answer to the noorest fool X It Nood Help 394 How high is the window Itound your aneuor to the noorest foot X 1 Moall 25 Walth B WATER 3

A state lotto has a prize that pays 500 each week for 15 years Find the total value of the prize 390000 0 If the state can earn 8 interest on investments how much money will they need to put into an accou now to cover the weekly prize payments

A train leaves a train station at a constant rate and arrives at its final stop 2 hours later A second train leaves the same station on the same route in 5 hours The first train is traveling 42 mph faster than the second train Find the rates of the both trains Set up a table and solve using an algebraic equation Please write a complete sentence

olve for x 8 8x 15 x 7 Write the exact answer using

Question 12 3x 12 Given f x 9x 20 asymptotes Determine the de domain all real numbers except x 5 vertical asymptote x 4 and x 5 domain all real numbers except x 4 and vertical asymptote x 4

Consider the following product to sum formulas sin x sin x costx1 x2 cos x1 x cos x x cos x x sin x x sin x1 x eBook cos x cos x sin x cos x Use one of the formulas above to write the given product as a sum of cosines of a sum of sines sin cos 4 1 Points DETAILS ZILLPRECALC6 4 7 007 Consider the following product to sum formulas sin x sin x cos x x cost

value zo days after The graph shows the amount of a m injection The amount of the medici the 8 6 150 100 Find the decay factor for each 3 In the first 3 hours increased by a fac 4 In the first 0 5 ho increased by a fac

Click the icon to see the 5 Complete the ratio table for Car A Miles Driven Gallons of Gas 150 225 375 5 10 20 50

ind the exact value of the following cos 1 1 2

12 Which function best represents the values in the table below f x 27 1 0 8 125 A f x x B f x x C f x X D f x x X 3 1 0 25 5

A C 3x y 10 4x 4y 8 4 2 1 3 4 3 1 q 4 2 0 2 4 4 2 0 2 4 y y 2 2 4 4 X X B D 1 3 3 1 4 2 4 4 2 O 2 4 2 2 O 2 4 y 2 2 4 4 X X

13 Find the domain of the following function x A x x is any real number B x x 0 C x x 7 D x x 7 x 7

15 For f x 5x 1 find f 4 A 19 B 1 C 21 D 21

A C 11 1 4 x 1 4 2 4 2 0 2 4 4 2 O 2 4 2 2 4 4 x X B D 4 4 2 4 2 O 2 4 4 2 O 2 4 a 2 4 X

6 Graph the equation 3x y 6 A C 12 8 12 8 8 4 40 4 8 12 12 8 4 4 0 4 8 12 4 8 8 12 x 12 x B D 12 8 12 8 4 12 8 4 b 4 do 8 12 12 do 8 4 0 4 8 2 8 12 x 12 x

8 8 4 b 3 00 8 6 CH kto do do 6 Oy x 3 3 Oy x 3 3 O y 3 x 3 3 N St 6 8 co X graph

Which expression is equivalent to 16x8y 12 O 4x y6 O 8x y6 4 O 1 2 4x4 y6 8x4

The equation 7 4 shows the relationship between a planet s orbital period T and the planet s mean distance from the sun A in astronomical units AU If planet Y is k times the mean distance from the sun as planet X by what factor is the orbital period increased O 19 O O 112 213 K

O Which expression is equivalent to X Y Z 12 112 z N 112 1 2 xz 2

Tyna simplified the expression 3x to 12x 2 4 What was Tyna s mistake O She divided the coefficients incorrectly O She added the exponents instead of subtracting them O She divided the coefficients instead of subtracting them She subtracted the exponents instead of dividing them

20 What is the purpose of liability coverage A Liability coverage will pay for injuries to persons within a client s vehicle B Financially protects the client for injuries or property damage that is caused to them C Financially protects the client for injuries or property damage they cause to others D None of the above

17 is the cost imposed by the court on a judgement in a suit defended by the insurance company after the judgement has been entered and before the insurance company offers to pay A Supplementary Payment B Bail Bond C Post Judgement Interest D None of the above

D None of the above 13 Liability Coverage Part A states that the limits which are shown on the Declaration Page are the minimum amount that will be paid in any one accident regardless of the number of people or cars involved in the loss A True B False

Which expression is equivalent to 8 O 325 C 10 325 32

Which of the following is equivalent to 133 O132 O 1315 O 13 13 513

7 Which of these is not a Group A Exclusions A The Personal Auto Policy won t provide liability coverage B There is coverage for damage to property owned by that insured C This exclusion takes away coverage for damage to a rental vehicle the insured may be driving D All of the above

Which of the following is equivalent to 05 4 54 O O 57 73 5 3

1 The Personal Auto Policy provides owned auto per the Other Insurance provision for an A Limited Liability Coverage B Financial Responsibility C Primary Liability Coverage D None of the above

A Recommending protection that meets the needs of each clients exposures B Understanding the clients asset profiles C Knowing the defense coverage provided D A B only E B C only F All of the above G None of the above

coverage for bodily injury has two separate limits per person and per accident ntal 3 With A Combined single limits B Split limits C Stacking limits ed ar D None of the above red for liability cover

16 To understand when these endorsements can provide coverage there are three phases you need to know about A Driver is logged into the mobile app and is available to accept passengers B Driver has accepted a request from a passenger and is on the way to pick up C Starts when the passenger fully exits the vehicle and ends when the new passenger enters the vehicle D A B only E B C only F All of the above

10 Important factors to consider when discussing liability limits A The frequency and severity of damage caused by a distracted driver B The reaction time of a sleepy driver C The cost of medical care D A B only E B C only F All of the above G None of the above

2 It is in the best interest of your client to select the highest limits of coverage they can comfortably afford A True B False

9 Prejudgement interest is an accumulation of interest on money awarded by the court had the injured party received the money on the first day of their injury rather than having to wait on legal proceedings A True B False

Solve the equation 1 2 r r 6 2 5r 1 2 5r

12 6400 1 6 22 2 x 3x 21 22 21 21 9 2 x 3x 1 2 1 2 13 42 x 1 8028 X 2 X 1 5 1 8029 16 1 5 1 5 1 1076 0 3 49

Simplify 10 2i 2i O 5 i i O1 5i O 1 5i 0 1 O

What is the complex conjugate of 2 i O 1 2i O2 i O 2 i O 2 i

Multiply and simplify 2 i 7 3i O 14 i 3i O 17 i 09 2i O 17

Simplify and write your answer in the form a bi 5 2 i O 2 i O 10 5i 5 10 i O 2 i

expression 8 2i 2 4i 5 4i O 11 2i O 1 6i O 1 2i O 11 6i

How would the imaginary number i be writte as a complex number O 7 2i O zi O 7 2 0 1 2 i

Which of the following shows 49 simplified and written as a complex number O 49i O 7 i O 7i O 0 7i

For each of the following rational expressions determine the values for which the expression is undefined 14m 13n A The expression B The expression C The expression is undefined when 6y 5 20y 18 b 19 h 81 is undefined when is undefined when

Rationalize the denominator and simplify 2 6 6 6 O O O O 2 6 3 2 6 2 3 2 6 6 2 2 6