Complex numbers Questions and Answers

Given x 3x 7 x answer the following Part 0 3 Part 1 of 3 a Find f x f x 79

Fill the exact values of the function values of a given in the table below X 0 6 K 4 K30 5 T 6 3 4 2 T 3 2 3 4 2 6 Y Y cos x for each cos x 100

6 Suppose f and g are inverse functions Consider the table below X f x f x 5 12 4 1 10 1 2 0 9 2 Write an equation for the line tangent to g x at x 4 1 4 2 2 0 1 4 2 5 5 7 0

a varies directly as the square of b and inversely as the square of c If a 172 when b 10 and c 5 find a if b 9 and c 3 Round your answer to two decimal places if necessary Answer a Keypad Keyboard Shortcuts

Instructions For the given scenario identify the labels of x and y axis A cab company charges a 3 flat rate in addition to 1 50 per mile x Axis y Axis

The variable a is jointly proportional to the square of b and the cube of c If a 189 when b 5 and c 4 what is the value of a when b 4 and c 3 Round your answer to two decimal places if necessary Answer Keypad Keyboard Shortcuts

12 Solve for x O 12 24 O 42 O 17 O 3 43 2 12 7 x

Solve for x 2 7 7 x Another way of writing this question is 7 X 19 0 Solve the following proportion for x 32 X 1 Solve 36 96 30 160

The electrical resistance varies directly as the square of the voltage V and inversely as the electric power P If the voltage is 10 volts and the electric power is 2 watts then the electrical resistance is 50 ohms Express the electrical resistance as a function of voltage and electric power Answer R V P Keypad Keyboard Shortcuts

have 75 for the day The entrance fee is 49 95 and lunch is 11 You want to be able to join your friends and play in the arcade Each game is 1 75 a Write an inequality to express the number of games you can play b How many games can you play Graph the solution interval on a number line on a sheet of paper Describe how your graph looks c After you have played in the arcade have you spent all your money If not how much is left over Explain your answer d If you want to play 2 more games to beat your record how much less will your lunch need to cost

7 Given the formula V Ah solve for h O O 3VA O VA 0 31

Differentiate the given series expansion of f term by term to obtain the corresponding series expansion for the derivative of f If f x f x 1 1 2x 00 n 1 1 2 x n 0

4 Simplify completely m 2 m 7 O m 9 O m 14 O m 9 O m 14 5 Simplify 11 21 1 6 Simplify 3 6y

10 Graph the following system on a sheet of paper or graphing utility 5 and y 3 Determine which of the following points if any satisfy the system More than one answer may be correct check all correct answers 1 3 0 2 0 7 1 8 0 6 10 7 5 6 None of these points satisfy the system

4 Suppose you own a toy company square The packaging for boxed toy dogs involves 2 5 feet of cardboard and boxed toy ponies require 3 7 square feet of cardboard To meet sales goals you need to put at least 328 toys into stores by tomorrow Is 800 square feet of cardboard enough to package the toys O yes O no

inequality that matches the following graph y

the diagram below a rectangle has its base on the x axis One upper vertex is a point x y in the first quadrant which lies on the parabola y 5 x and the other is its reflection in the second quadrant wer the following Express the length of the base of the rectangle as a function of x Base Express the area of the rectangle as a function of x Area base x y

What is the degree measure of the angle A 15m 2 Select one Ob 1350 4789

A function is defined by f x x 2 x where x 0 Find f1 x Select one O a 2 x 1 O b 2 x 1 O c 1 x 1 O d 2x x 1

The function f x 3 demonstrates linear degression linear growth exponential growth quadratic increase exponential decay

of Which equation is represented by the graph 301 Select one or more Da ye Ob y 2 Oc yas Od y 3 2

1 If Z 2 i and Z 3 i a Find Z Z using rectangular form b Find Z 5 c Find the second roots of Z Z

15 Solve the linear systems of equations using the elimination or addition multiplication method Express your answers as fractions Write none in both blanks if there is no solution 5a 11b 1 a 116 2 b

Suppose you want to have 500 000 for retirement in 20 years Your account earns 8 interest How much would you need to deposit in the account each month

4 Use substitution to solve If the system has no solution write parallel in both answer boxes If the system has an infinite set of solutions write infinite in both answer boxes If one solution is found show the answers for x and y in the respective answer boxes For more analysis graph the equations in your calculator or graphing program or a sheet of paper The equations are x y 4 4x 80 20y x y

he scale diagram below shows the end of a gable roof for the shed The roof is to project 00mm from the front and back of the shed Find the number of sheets of aluminium needed fo he roof if the sheets can be supplied cut to length have a width of 1 2m and must be overlapp y 10 cm Justify your response with mathematical reasoning Scale 1 100 11 2 m

4 10 points Find the two square roots of 1 i 3 and write the roots in rectangular form

paper Ine equa y 21x 14 5y 28x 26 x 21 x

Which function is graphed below CHI 2 Ch 1 1 5 N I Of x cos x Of x cos x Of x sin x flx sin x

Given that sec 58 23 5 8 O O O O 12 01 12 01 12 2 37 T what is the value of cot for 7

A carpenter is building a rectangular table He wants the perimeter of the tabletop to be no more than 28 feet He also wants the length of th tabletop to be greater than or equal to the square of 2 feet less than its width Create a system of inequalities to model the situation where x represents the width of the tabletop and y represents the length of the tablete Then use this system of inequalities to determine the viable solutions OA Part of the solution region includes a negative width therefore not all solutions are viable for the given situation OB Part of the solution region includes a negative length therefore not all solutions are viable for the given situation OC The entire solution region is viable OD No part of the solution region is viable because the length and width cannot be negative

What is the range of f x sin x O the set of all real numbers 2x y 2 O the set of all real numbers 1 y 1 O the set of all real numbers 0 y 2 Othe set of all real numbers

On the unit circle where 0 e 2 when is tan undefined O e and e 2 O sin cos e O XT 2 and 8 O sin e 1 cos e 370

Which of the following best explains why cos cos 3 O The angles do not have the same reference angle O Cosine is negative in the second quadrant and positive in the fourth quadra O Cosine is positive in the second quadrant and negative in the fourth quadra O The angles do not have the same reference angle or the same sign

What is 5x 6 radians converted to degrees If necessary round your answer to the nearest degree O 30 O 90 O 150 O 900

Use the horizontal line test to determine if the inverse of the function graphed below is a function Then determine whether the function is one to one 10x 3

paration for designing a new line of business wear a clothing manufacturer asked a large sample of department store customers What is your favorite of dress shirt The pie chart below summarizes their responses Grey Pink Other White Black Blue a Which color was chosen by approximately one fourth of the customers b Approximately what percentage of the customers chose Blue or Black Select One Write your answer as a multiple of 10 that is 10 20 30 0 c If 5 of the customers chose Other approximately what percentage chose Grey 2 15 30 X 300 P

Destiny performs a hypothesis test on a population with 115 and o 30 Her sample size is 25 with a mean of 120 4 Which of the following correctly depicts the z statistic for this data O 0 04 O 0 90 O 3 53 O 3 93

3 Graph the function State the period amplitude equation of axis and range for the final graph Use a vertical scale of 1 and a horizontal scale of 6 marks Period Equation of Axis x 7 1 f x 3sin x Amplitude Range

a 6 ky h 2 4 6 8 7 Identify a and b for the ellipse with equation X b k x h a y k 6 1

Let A 1 2 1 3 and Q 9 Q 3 67 6 5 5 We obtained the column vectors of Q by applying the Gram Schmid process to the column vectors of A Find a QR decomposition of the matrix A NOTE Enter exact answers

Do not round off anything until you obtain the final answer Round your answers to the nearest dollar Bert receives an inheritance of 58 000 and decides to invest his money into an account that will pay 5 9 if the money is not withdrawn for 5 years Round your answers to the nearest dollar a Complete the table depicting Bert s money and interest earned after the 5 year period round all dollar amounts to 2 decimal places Compounding Quarterly Daily Number Amount in Account Interest Earned Number Number Number Continuously Number Number b Find the difference between his money compounded quarterly versus compounded continuously

2 Find an orthogonal basis for the column space of A 1 process N 5 3 using the Gram Schmid I

17 Find an equation for the graph below AAAA 2m HIN 2 2m

The point a b is in quadrant IV of the unit circle as shown An arc of length s is shown as the darkened arc draw clockwise from 1 0 to a b Select each of the following tangent functions that are equal to Select all answers that apply O O tan s tan s tan s a b tan 8

Question 20 15 3 2 5 4 3 2 1 y 2345A 2 1 2 3 4 5 5 Write an equation for the function graphed above

2 Find an equation of the form y A sin wx B or y A cos wx B for each graph a 2x 2 R 2x b ol

Divide the complex number 3 4i 2i 2 31 2

a COS X 1 2 where 0 x 2 2 marks

1 Equation of Midline Amplitude Period Equation of the function 20 40 60 100 120