Complex numbers Questions and Answers

GRAPHING A LINEAR EQUATION Graph the linear equatio 10 y 5x 11 y 9x 12 y 5 15 y 7x 1 14 y x 3 18 y 2 3 19 y 6 75 16 y 4 3 20 x 0 5 13 x 6 17 y 0 75x 21 x 4

Find the isogonal path to 60 of the family of circles of radius 4 and center on the x axis

d Find all solutions of the equation Leave your solutions in the exponential form 647

a Let x be a positive real number Show that x 1 x 1 b Let x and y be real numbers such that both x and y are either positive or negative Show that x y y x 2

Build the Taylor series for f x ex centered at x 2

The substitution zwy 2 transforms the non linear DE y a x y b x y 0 to the lin Oz 4a x z 4b x Oz 5a x z 5b x None of these Oz 2a x z 2b x Oz a x z b x changes to this answer e substitution z y 1 transforms the non linear DE y a x y b x y 0 to the linear DE z 2a x z 2b x None of these z 5a x z 5b x z a x z b x

Utilize the information provided to determine your answer Note that day the necessary steps including appropriate formula substitutions diagrams graph Answer the question in this part A correct answer will receive 6 credits only 1 credit All answers should be written in pen except for graphs and dra necessarily drawn to scale A correct numerical answer with no work sho should be done in pencil s 37 A recreation center ordered a total of 15 tricycles and bicycles from a sporting The number of wheels for all the tricycles and bicycles totaled 38 Write a linear system of equations that models this scenario where t represents e tricycles and b represents the number of bicycles ordered On the set of axes below graph this system of equations 4 2 6 16 10 18 14 12 8 b 12 Part IV 4 6 8 10 12

28 The graph of f t models the height in feet that a bee is flying above the ground with respect to the time it traveled in t seconds f t Height feet 4 N 2 4 6 Time seconds 8 10 12 14 State all time intervals when the bee s rate of change is zero feet reasoning per second Explain your

12 Fred earns 16 50 an hour for overtime He worked overtime on Monday and Thursday this week On Monday he worked 4 hours of overtime His total overtime pay for the week was 123 75 Write and solve an equation to find the number of overtime hours Fred worked on Thursday

2 4 Identify the equation for the graph A y x 1 x 2 x 4 B y x 1 x 2 x 4 C y x 1 x 2 x 4 D y x 1 x 2 x 4

200 to invest in stocks You purchase shares for 11 87 sh You decide to sell the stock at 11 95 sh How much did you net with this transaction 0 00 0 15 Hint C A 1 Subtract the purchase price per share from the sale price per share 2 Divide the Investment by the purchase price per share 3 Multiply your answer in step 1 by the answer in step 2 11 87 Speed 1x B 30 71 Paused

If you bought 28 shares of stock at 30 sh and sold them at 25 sh How much did you net after selling the shares CA 0 00 0 10 A 840 Speed 1x

You spent 529 on several shares of stock When you sold the stock you received 725 What was your net profit or loss CA 0 00 0 12 Hint Subtract the sale price by the purchase price A 196 1196 Speed 1x Paused

C 0 00 0 31 Drive your self Fill your gas tank at 60 week car insurance at 475 yr oil changes at 50 every 3 months quarter Speed 1x Public Transportation Bus P You take the bus to and from work A ticket to ride the bus is 7 25 one way remember you ne to get to and from work each day so you will need two tickets per day

You are planning to rent a condo Your monthly rent will be 750 and your renter s Insur ance will be 1 800 per year What is the adjusted monthly cost for renting this condo CA 0 00 0 12 Speed 1x Paused

of 50 43 Joel has a Personal Auto Policy with Collision and Other Than Collision Coverages He bought a new Ford F 150 and has added 5 000 in body customizations and furnishings to his truck What coverage if any is provided by Joel s policy and what if anything i needed to improve Joel s coverage for custom equipment and furnishings The Policy provides up to 1 500 for custom equipment and furnishings The Excess Custom Equipment endorsement can be used to increase coverage Custom equipment and furnishings are automatically covered by the Personal Auto Policy without a limitation Custom equipment and furnishings are uninsurable The policy does not cover any custom equipment and furnishings The Custom Equipment endorsement must be added

32 of 50 Cathy has a Personal Auto Policy with Medical Payments Coverage included Which one of the following would NOT be a covered Medical Payments claim injuries to Cathy s daughter who lives with Cathy while riding in a friend s car injuries to Cathy s friend Sarah while she is riding in Cathy s covered auto injuries to Cathy sustained while she is riding an owned three wheel all terrain vehicle injuries Cathy receives as a result of an accident while driving her covered auto

of 39 Jessa has a Personal Auto Policy with Liability Coverage and Part D Coverage For Damage To Your Auto During heavy rain she drove into floodwaters causing damage to her vehicle What coverage if any would apply under Jessa s policy 50 Other Than Collision Coverage less the deductible Liability Coverage since Jessa was negligent Damage caused by flood is not covered Collirion Coverage less the deductible

34 Coverage provided by the Uninsured Underinsured Motorists of Coverage endorsement for injuries to an insured caused by someone who does not have any automobile insurance is known a 50 Underinsured Motorists Coverage Uninsured Motorists Coverage Medical Payments Coverage

of Which one of the following is a non owned auto by definition in Part D Coverage for Damage to Your Auto of a Personal Auto Policy 1 a car owned by the named insured s boss and assigned to the named insured for business a car owned by the named insured but insured under another policy a pickup the named insured borrowed from a neighbor because her car would not start a trailer owned by the named insured s resident son and borrowed by the named insured

36 of 50 Ophelia is hit by another motor vehicle and is injured She has a Personal Auto Policy with Underinsured Motorists UIM Coverage limits of 100 300 Assuming the other party is at fault and underinsured if Ophelia s policy defines an underinsured motor vehicle with a limits trigger which one of the following is TRUE The at fault vehicle has liability limits equal to Ophelia s UIM limits The at fault vehicle s Liability Coverage is not enough to cover Ophelia s bodily injury damages The fault vehicle must be unidentified

27 of 50 George is in an at fault accident where he injures five pedestrians The bodily injury damages suffered by the pedestrians are as follows one at 200 000 and four at 50 000 each George also did 8 000 damage to a parked car The limits on George s Personal Auto Policy are 100 000 300 000 50 000 How much should George s Personal Auto Policy pay for these claims 358 000 308 000

26 The following description summarizes which Liability Coverage of provision 50 When an auto accident occurs outside of the state where your covered auto is primarily garaged the Personal Auto Policy will provide coverage in compliance with financial responsibility and other compulsory laws in that state where the accident occurs Other States Insurance Limit of Liability

A pharmaceutical company is testing the effectiveness of a new drug for asthma patients The drug is given to 100 volunteers who suffer from asthma while a placebo is given to 100 other volunteers who also suffer from asthma After 4 weeks the volunteers are asked if they noticed improvement in their asthma symptoms The results of the survey are shown in the contingency table below What is the probability that a volunteer received the placebo given that he did not report a noticeable improvement in symptoms Received the Drug Received the Placebo Totals Select one O a 0 7333 O b 0 32 OC 0 88 O d 0 2667 Improved 68 12 80 Did not Improve 32 88 120 Totals 100 100 200

22 Which arc lengths on the unit circle have central angles with measures less than 180 3A 4 3A C 2 5

17 An angle has a measure of 120 What is the radian measure of the angle A B D 5T 6 3T 4 3 2 2 3

14 In the first quadrant if sin 0 1 2 then cos 0 5 2 B None of these answer choices are correct A D E 2 5 2 3 2 3 2

5 What is log 36 5 in exponential form 5 36 x5 36 B D 10 36 5 365 x

What is log x y in exponential form A B D 3 x y 3

Suppose you are a salaried employee paid semi monthly You currently receive 52 000 gross income per year The 20 60 20 budget model has been working well for you so far so you plan to continue using this model Suppose you would like to build up an 8 month emergency fund over a 15 month period of time How much do you need to save each month to accomplish your goal 4 333 33x0 70 3 033 33 month 52 000 12 4 333 33 month 1 820 month X 8 months 15 months Monthly gross income 970 67 month 3 033 33x0 6 1 820 month

CH 0 00 0 06 Rent Mortgage Insurance Gas Electricity 850 kwh month Water and Sewage Garbage Amenities A Speed 1x 1 275 00 mo Current 900 mo 75 quarter none 150 mo 55 mo 45 quarter 130 mo Reminder Get every value to a monthly value before adding it There are 3 months in a quarter of a year and 12 months every year Paus

Match each type of life insurance to its definition term life whole life universal life a b Provides an individual lifetime pro tection and offers a savings compo nent with cash value and has no ex piration date More flexible permanent life insur ance with protection that is low cost but it also has a savings element which is invested to build the cash value C Provides a pre determined amount upon the death of the policy owner provided that the death occurs within a specific time period

Identify the examples of discretionary and essential expenses Press on an item in the answer box then press on the box under the correspondin category To remove an item you can press on the box and the trash can icon to the right of the item you want to remove Discretionary Add an answer item Essential Add an answer item

You need new shoes for work which cost 75 You earn 500 after taxes each week and you have other expenses totaling 480 each week If you set aside the difference between your income and expenses each week how many pay periods will it take for you to save enough money to buy the shoes A B C 6 weeks 3 weeks 4 weeks

File Paste Home Cut E Copy Clipboard Insert Draw Page Layout Format Painter Calibri BIU 11 67 Formulas Data A A A M Review ab Alignment

Joe is building a rectangular pool in his yard He knows that the perimeter of the pool must be 88 feet but he wants the surface of the pool to have the largest possible area What length and width should Joe choose for the pool 30 ft x 14 ft 20 ft x 24 ft 9 ft x 35 ft 22 ft x 22 ft

A 32 Michelle invested 10 000 in an account that earns 8 5 interest that is compounded monthly Write an exponential model for the balance of the account then determine the amount of money in the account in 15 years 5 Simplify the expression below 24p P 10 24 p 10 P 14 p 40 3p 18p 24 16p 2p 4p D Equation 4 P 10 24p 1 24p p 10 A 5x 6 Simplify the expression below 17 x 9 2x 3 3x 6 B 5 x 2 3 r Answer Wood TODEUDS 3x 6 C 5x 2 x 2 D 5x 4 x 2

Directions Give each degree measure in radians and radian measure in degrees 8 165 9 54 10 243 11 9 A 5 bahet 12 Coterminal 2 s 13 20 Reference Z 13 TT Directions Give two coterminal s one positive and one negative and a reference for each 14 305 7x 15 10 4x 45 based on 180 180 04x0180 45 1 1807018 126 360 Coterminal 2 s 16 486 Reference 54

3 Simplify the expression below A B 2 18 32 8 3 3w 2 2 w 7 3m 2 w 7 C D 3w 7w 6 12m2 80w 28 E 3w 2 2 w 7 2 3w 2 w 7 15 Solve the equation below a 2 6 5 a a 5 9 Which graph represents the function f x B 4 Simplify the expression below 1 x 3 A B 2c 1 c 7 C 1 c 7 2c 5c 3 c 4c 21 S C 17 Solve the equation below c 3 c 7 c 3 D c 7 2c 1 1 2 n 4 n 2 Z D 2 6n 8 7

Plot the inverse of the function shown You must plot the points and the segments both 5 5 3 2 3 2 1 3 4 1 5 Clear All Draw Dot Line Segment 2 3 4 5

4 Grant has 75 to spend on gifts for his daughter He buys dolls for 15 each and toys for 8 each Which inequality to represent this situation where d is the number of dolls and t is the number of toys OB 8d 15tz 75 C 15d 8tz 75 A 15d 8t 75 OD 8d 15t 75

13 The height of a ball Doreen tossed into the air can be modeled by the function h x 4 9x 6x 5 where x is the time elapsed in seconds and h x is the height in meters The number 5 in the function represents 1 the initial height of the ball 2 the time at which the ball reaches the ground 3 the time at which the ball was at its highest point 4 the maximum height the ball attained when thrown in the air

11 If C 2a 5 and D 3 a then C 2D equals 1 2a a 8 2 2a a 8 3 2a 2a 11 4 2a a 11

6 5 3 A Q Find a function of the form y a sec bx cor y a csc br c whose graph matches the function shown above

Resuelve 10 puntos Hallar los extremos de la funci n f x y e restricci n x y2 1 Representar gr ficamente sujeta a la find the extremes of the function f x y e x y 4 subject to the constraint x 2 y 2 less than or equal to 1 graph

et Mn M 9 6 ind formulas for the entries of M where n is a positive integer Your formulas should not contain complex numbers 10n 8 6

Integrate by series A 9x 1 x y 12y 4y 0 B y xy y 0

13 If the matrix M transforms the point A 3 5 onto B 7 11 and the point C 1 1 onto D 1 1 find M 43 3 23 14 The dot product is not useful in a calculating the area of a triangle b determining perpendicular vector c determining the linearity between two vectors di Ginding the angle betu

If a 6 7 foot arch has the dimensions and a pool noodle has the dimensions 7 in x 4 in x 55 in How 80 7 in x 78 7 in x 3 in many pool noodles will William need to buy for the arch

Answer 6 Points lane below 4 cos 57 isin 5 2 cos isin 4 Keyboard Points can be moved by dragging or using the arrow keys If using the arrow keys note that the right left arrow will increase decrease the ra the up down arrow will increase decrease the angle AY Enable Zoom Pan