Complex numbers Questions and Answers

0 1 1 0 20 2 Use the graph to find a The numbers if any at which f has a local maximum What are these local maxima b The numbers if any at which f has a local minimum What are these local minima

Write Matlab function Use Heun s method with 10 subintervals to approximate the solution to the initial alue problem y 12e for the interval of 0 x 5 by using initial value of y 0 1

Simplify Do not use a calculator or round to a decimal 2 8 6

3 An asteroid is going to make a near Earth hyperbolic flyby If the center of the Earth is located at the focus of the hyperbola the asteroid is seen to be 100 000 km away when directly overhead and the asteroid approaches from 45 degrees above the horizontal how close will the asteroid be from the center of Earth in the middle of its flyby neglect the radius of the Earth Think of what 45 degrees means for a special case right triangle 545 d ch 545 Asteroid 100 000 km

Consider the line that passes through the point P 2 5 and has slope 2 Write the slope intercept form of the equation of the line Use exact values

Complete the ordered pair so that it is a solution for the given linear equation x 4y 11 0 1 4 Enter answers as integers or reduced fractions no decimals

Find the exact value of tan 2 sin 1 C 12 12 13

Consider the graph of the function f x loga 4 2 1 A B C 2 D 14 1 2 0 Which is a feature of function g if g x 1 2 f 13 3 4 horizontal asymptote of y 2 range of y 2 vertical asymptote of x 2 domain of 2 5 log x 2 X

Rotate the given triangle 90 clockwise about the origin 3 51 1791 2 TO 0

Subtract the matrices What number fills in B 4 6 5 9 A 2 9 3 5 1 A B 2 15 3 8 14 1 4 Enter

Draw the graph of f x 2 7 6 S 4 3 2 Clear All Draw 1 7 6 5 4 3 2 1 VS SAN L 2 4 5 1 2 3 4 5 6 7

Find the center and radius of the circle x y 10x 18y 70 0 Center Radius Enter

Find the explicit definition of this sequence 6 12 24 48 an 2n 1 6 B an 2n 6 an 2n 6

Solve the system using addition elimination method If there is exactly one solution write as an ordered pair Otherwise choose one of the other options 2x 3x 4y 22 6y 37 No solution

550 are deposited in an account with 8 5 interest rate compounded continuously What is the balance after 6 years F Round to the nearest cent

A Identify the graph for the equation y 24 4 x 120 96 NG 73 48 24 2 Y 2 4 B 96 72 48 24 4 N N C 120 96 9890 72 48 24 2 N

A 8 6 HAVAMAK 2 K AN y 2 x 4 B Identify the equation for the graph y 2 x 4 y 2 x 4

Solve the equation Check for extraneous solutions Show your work using the Equation Editor tool logs x 5 log x 2

Suppose that 500 is invested at an annual interest rate of 6 8 Part A Find the final amount of the investment after 10 years if the interest is compounded continuously Part B Determine how many years it would take the investment to triple

A helicopter is rising straight upward Its distance from the ground t seconds after takeoff is s t feet where s t t t What is the average rate of change in height of the helicopter during the first 5 seconds

4 2 4 72 2 4 101 2 A A y x 1 x 1 x 3 C y x 1 x 1 x 3 Identify the equation for the graph B y x 1 x 1 x 3 D y x 1 x 1 x 3

Solve for x 3x 2x 27x 18 0 8 Enter the smallest answer first X X Enter

Graph the function with a graphing utility y 0 2 x 6x 27 10 19 5 y 15 10 5 5 5 X X 10 5 5 20 40 40 20 20 40 20 60 y y 5 X MY

Consider the following equation 1 30 y a Find the vertex of the graph of the equation x y X b Determine whether the vertex is a maximum or minimum point maximum minimum c Determine what value of x gives the optimal value of the function X d Determine the optimal maximum or minimum value of the function

Evaluate the expression when x 5 and y 1 x 1 y 3 x y

The table below represents the total number of bracelets Jaqueline has created at the end of ea week before she sells them at the county carnival Which of the equations below could be used determine how many bracelets she would have ready to sell at the end of week four X O 1 2 3 Y 2 8 32 128 Oy 2 4 O y 4x 2 O y 2x 4

Where is each point located on the graph 3 8i is 4i is 6 is 5 2i is

3 Prove in Euclidean geometry Suppose that in quadrilateral ABCD E and Fare points on BC and AD respectively and BGD E B and EGF are drawn such that ZABG ZCDG AB CD and CE AF Then FG EG A F G D C

Mr Hilton plans to invest some money on the birth of his granddaughter so that there will be 15 000 on her 16th birthday He will invest his money at 8 per year compounded semi annually How much does he have to invest today

The amount of money a bank investment has in the account each year is represented in the table below Identify the initial amount of the investment the decay rate the decay factor and the amount of money in the bank after 5 years Select all that apply X 0 1 2 3 f x 14 500 10 585 7727 05 5640 75 O The amount in the bank after 5 years is 3005 95 The initial amount is 10 585 O The amount in the bank after 5 years is 2194 35 The decay factor is 0 27 O The decay factor is 0 73 The decay rate is 73 O The initial amount is 14 500 0704

3 The following sets are given 3 1 S 1 0 21 ER CR II S 1 1 R CR III S 2 x2 1 and 2 22 R CR Choose the correct answer I II and III are subspaces e subspac I and II subspaces III is not subspace I is subspace II and III are not subspaces I and III are subspaces II is not subspace

A factory began producing new parts Data were collected on the number of defective parts per 10 000 parts produced The graph shown displays some of the data for the first 10 weeks of production Based on the graph during which week was approximately 110 defective parts per 10 000 produced Defective Parts per 10 000 450 400 350 300 250 200 150 100 50 0 O Week 8 O Week 5 1 O Week 3 2 3 4 5 6 7 8 9 10 This image cannot be easily described If you need an explanation of this image please ask your teacher for help 11 12 of Weeks

A basketball is dropped from a height of 10 feet The table below represents the rebound height after each bounce Which of the following statements are correct Select all that apply n O 1 2 3 t n 10 CO 2 2 226 27 The decay factor is The initial height is 6 feet The decay rate is The decay rate is The decay factor is The initial height is 10 feet

A tennis tournament begins with 64 players At the end of round one there will be 32 players There are 16 players at the end of round 2 and 8 players remaining at the end of round 3 Which equation best models this situation O y 0 5x 64 O y 32x 64 O y 64 0 5 O y 64 2 2

A population of 12 bunnies is released into the forest The population triples every year for four years Which equation below could be used to find the population of the bunnies in four years Let P represent the population and let t represent the number of years O P 12 3t OP 12 3t OP 12 3t OP 12t 3

Enter the equation g x 2 5 and f x 5 How does the graph g x differ from the graph of f x The graph stretched vertically by a scale factor of 2 O The graph stretched horizontally by a scale factor of 2 O The graph compressed horizontally by a scale factor of 2 O The graph compressed vertically by a scale factor of 2

Enter the equation g x 2 and f x 3 2 How does the graph g x differ from the 3 graph of f x Select all that apply The graph reflected across the y axis The graph compressed horizontally by a scale factor of O The graph reflected across the x axis The graph compressed vertically by a scale factor of

Enter the equation f x 2 and g x 2 1 in the Desmos Graphing Cal g x differ from the graph of f x O The graph translates up 1 unit O The graph translates to the left 1 unit The graph translates to the right 1 unit The graph translates down 1 unit

Given the vector field F x y y 4x2 2 i 3xy 2y 2 j Evaluate the line integral F dr from 1 0 to 0 1 along the curve 3x 3 y y2 y3 a 2 b 3 C 0 d 1 e 1

Find the dimension and a basis for the general solution W of the following homogenous ystem x 2x 3x 2x 0 2x 4x 5x3 x 0 5x 10x 13x3 4x 0

For the function f solve f x 0 analytically over the interval 0 2 and give solutions in exact forms Graph y f x in the window 0 2 by 4 4 use the results to find the solution to f x 0 and f x 0 over the interval 0 21 2 f x tan x www 1

7 Determinants of market interest rates Some characteristics of the determinants of nominal interest rates are listed as follows Identify the components determinants and the symbols associated with each characteristic Characteristic This is the premium added to the risk free rate that reflects the average sustained increase in the general level of prices for goods and services expected over the security s entire life This is the premium added to the equilibrium interest rate on a security that cannot be bought or sold quickly enough to prevent or minimize loss As interest rates rise bond prices fall and as interest rates fall bond prices rise Because interest rate changes are uncertain this premium is added as a compensation for this uncertainty It changes over time depending on the expected rate of return on productive assets exchanged among market participants and people s time preferences for consumption It is calculated by adding the inflation premium to r It is based on the bond s rating the higher the rating the lower the premium added thus lowering the interest rate Component Symbol

2 A circle has the equation x y x 6y 9 0 a Find the center h k and radius r of the circle b Graph the circle c Find the intercepts if any of the graph a The center of the circle is 2 Type an ordered pair using integers or fractions The radius of the circle is 1 Click to enlarge 3 1 2 Type an integer or a fraction b Use the graphing tool to graph the circle

Channa was asked to write an expression equivalent to i 2 3i 4i 1 in the form a bi Here is her work First I simplified i 2 3i Channa s Work 2 3i i 2i 3i Then I simplified 2i 31 4i 1 and combined like terms 4i 1 2i 81 21 My final answer is 121 5i 2i 31 121 3i 1 Identify one portion of Channa s work that is correct 2 Write an expression equivalent to i 2 3i 4i 1 in the form a bi Show your thinking Note i 1

Draw a complete graph so that it has symmetry with respect to the origin 2x 3 Ay 2 0 0 2 K 3 O 2x 3 U Choose the correct graph below O A 2x 3 O C 2x N 2x 3 2x 3 Q B 2x 3 D n 2 X 2x 3 G 2 3 G O O

Find the ends of the major axis and foci x y2 1 81 16 Major axis 0 Foci 1 0 Enter

The eccentricity of the conic section graphed is a Zero b Between 0 and 1 c One d Greater than 1 Enter

32 Identify the expression for the volume of a rectangular prism if the length is 3 feet longer than some a amount the width is 6 feet shorter than a and the height is a feet OV a 3 a 6 a feet OV a 3 a 6 a feet OV 3 a 6 a a feet OV 3 a 6 a a feet

Verify the identity 2 cos 3x sin x 2 sin x cos x 8 cos x sin x Working with the left hand side use a Product to Sum Identity and then simplify LHS 2 cos 3x sin x 2 LHS 2 1 sin 3x x Use a Double Angle Identity for the first term and then simplify by grouping like terms LHS 2 1 II sin 2x sin 2x Use the Double Angle Identities as needed and then simplify by finding the product 1 2 1 2 sin x 1 1 sin 2x 8 cos x sin x 2 sin x cos x 8 cos x sin x

20 What could this graph represent spider population trend after 3 years of long continuous droughts O spider population trend after a new spider predator has been introduced into the population O spider population trend after much of the spiders food source has died off