Complex numbers Questions and Answers

possible log d log d 3 xy 76 3 xy 6 Z Simplify your answer

K Let log 5 J and log 2 D Write the expressic log 25 log 25

expr Use properties of logarithms to expand the logarithm Where possible evaluate logarithmic expressions without using a log y 10 000 log x y 000

Begin by graphing f x log 5x Then use transformations of this graph to graph the given function What is the vertical asymptote Use the graphs to determine the given function s domain and range g x log5 x 7 Graph the function g x log5 x 7 Graph the asymptote of g x as a dashed line Use the graphing tool to graph the functions Click to enlarge 108 84 2 8 6 Ay 10 G

Give a third degree polynomial that has zeros of 13 5i and 5i and has a value of 680 when x 3 Write the polynor in standard form ax bx 1

Simplify the expression by using a double angle formula 0 2 sin cos 0 3 3 010 sin cot B cos sec

Write the equation in its equivalent exponential form 2 log M What is the equivalent exponential form of the equation

2 If the relation between x and y is as shown in Table AQ 3 2 then which among the following lines is the best fit O O O x y 0 1 1 3 2 4 y 2x with SSE 143 y x with SSE 40 Table AQ 3 2 y 3x with SSE 428 Oy 4x with SSE 895 3 2 4 5 6 5 0 8

x YEN x y 31 A 200 x y C 240ING D 215 B 205 E 22

K Use transformations of the graph of f x 2 to graph the function g x given below Graph and give the equation of the asymptote Use the graph to determine the domain and range of g x g x 2x 3 Graph the function g x 2x 3 and its asymptote Graph the asymptote as a dashed line Use the graphing tool to graph the function Click to enlarge graph C L 10

You have 12 000 to invest One bank pays 8 interest compounded semiannually and a second bank pays 3 9 interest compounded monthly Complete parts a and b a Use the formula for compound interest to write a function for the balance in each bank at any time t Write a function for the balance in the first bank at any time t Choose the correct answer below OA A 12 000 1 0133 2t OC A 12 000 0 96 OE A 12 000 1 04 2t BOCOD OB A 12 480 OD A 12 000 1 08 OF A 12 000 0 04

Solve the inequality and graph the solution set on a real number line Express the solution set in interval notation x x 11 9 The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression

a compute the power in rectangular form by using binomial multiplication b write the complex number in trigonometric form and compute the power using the De Moivres theorum writing your final answer in rectangular 2 2 2i 2 6

Include the dollar symbol round to two decimal places and add a comma if needed If no name soda costs 1 a six pack and increases 4 5 each year what will be the new price in 7 years

Write the contrapositive and converse of the following statements 1 If x is a prime number then x is odd ii It the two lines are parallel then they do not intersect in the same plane iii Something is cold implies that it has low temperature iv You cannot comprehend geometry if you do not know how to reason deductively v x is an even number implies that x is divisible by 4

The tangent line to 2x2 6x 6 at x 2 is y 14x 2 y 2x 14 y 2x 14 OY 2x 18

Graph the rational function Answer parts 1 through 7 below 2x X 2 f x 1 Select the symmetry of the function The function is symmetric about the y axis O The function is symmetric about the origin The function has no symmetry about the y axis or the origin

Find the values of tan sin 3 cot 12 2

Find the values of Answer sin sin 2 3 sin sin 2T 3

Write the function in the simplest form tan

The graph of a polynomial function is given What is the smallest degree that the polynomial could have The smallest degree the polynomial could have is Simplify your answer the

Find all zeros of the polynomial function Use the Rational Zero Theorem Descartes s Rule of Signs and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root f x x 4x x 14x 10 Find the zeros of the polynomial function Simplify your answer Type an exact answer using radicals and ias needed Use a comma to separate answers as needed Type each answer only once

Consider the functions f x x 7 and g x x 7 3 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other

For the quadratic function f x 2x 2x 3 answer parts a through f e Determine where the quadratic function is increasing and where it is decreasing The function is increasing on the interval Type your answer in interval notation Use integers or fractions for any numbers in the expression The function is decreasing on the interval Type your answer in interval notation Use integers or fractions for any numbers in the expression f Determine where f x 0 and where f x 0 Select the correct choice below and fill in the answer box es within your choice Type your answer in interval notation Use integers or fractions for any numbers in the expression 5 d Y

Examine the table of f x O 0 75 O 1 95 O 0 50 f x 0 2 1 89 3 3 75 4 30 4 90 5 13 4 5 68 6 6 288 Which is the average rate of change for the function f x over the interval 0 x 5 GeoGebra Graphing Calculator O 0 45 I 3 1 0 1 2 3 5 6

f x x x 2 x 6 The graph touches the x axis and turns around What does the graph do at the rightmost zero The graph crosses the x axis The graph touches the x axis and turns around What does the graph do at the leftmost zero The graph crosses the x axis The graph touches the x axis and turns around c Find the y intercept y 0 d Determine whether the graph has y axis symmetry origin symmetry or neither OY axis symmetry O Origin symmetry Neither e If necessary find a few additional points and graph the function Use the maximum number of turning points to check whether it is drawn correctly Choose the most accurate sketch of the function O A OB Ay Q Q O C Q tfria 8 4 4 OD F

the second polynomial by the first polynomial i 3 2r 3r 27 97 12 x 3x 1 3x 5x 7x 2x 2 iii x 3x 1 x 4x x 3x 1

Find the magnitude of sin z dz 4z 8iz C where C consists of the boundaries of the square with vertices 3 counterclockwise and 1 i clockwise to 3 decimal places 3 3i 92i 3 x

A typical Social Security number is 555 47 5593 How many Social Security numbers are possible if the first two digits cannot be 0 Social Security numbers

A certain lock has five tumblers and each tumbler can assume six positions How many different possibilities are there Xpossibilities Enter an exact number Need Help Read It

Write in exponential form log 6 1296 4 Write the equivalent exponential equation Tun Tupo your power using exponential notation Do no

Use the properties of logarithms to rewrite the following expression Assume all variables represent positive real numbers 3 log 2x 4 log 2y 3 log2x 4 log y

Graph the solution set of the system of inequalities 2x 3y 6 x y 4 y 2 Use the graphing tool on the right to graph the system Click to enlarge graph 10 8 6 4 2 10 8 6 4 12 2 Ay 4 6

Find both the positive and negative angles in standard position given that the reference angle in the diagram to the right is 54 80 1 mark each The positive angle is 0 The negative angle is 0 Pay Type an integer or a decimal number rouned to one deomul place the nedenst 0 11 3 mark une

b Use the models from part a to approximate the population on January 1 2020 for each country Round to the nearest hundred thousand Thailand had fewer people than Ethiopia in the year 2000 yet from the result of part b Thailand would have more people in the year 2020 Why The population of Thailand on January 1 2020 would reach million million The population of Ethiopia on January 1 2020 would reach Thailand would have more people than Ethiopia in the year 2020 because the Choose one is Choose one for Thailand than for Ethiopia 3

4 Sketch the graph of a polynomial function f x that has a zero of order 3 a zero of order 2 two zeros of order 1 and a negative leading coefficient 12 marks a Determine a possible equation for f x in factored form

A study of urban density shows that the population density B in persons mi2 is related to the distance m in mi from the city center by log B log d um cm u and c are positive constants Solve for B as a function of m B Simplify your answer

A plane has an airspeed of 125 km h It is flying on a bearing of 85 while there is a 29 km h wind out of the northeast bearing 225 What are the ground speed and the bearing of the plane The ground speed is 104 5 km h Round to the nearest tenth as needed The bearing is Round to the nearest tenth as needed

1 Match the A P s given in column A with suitable common differences given in column B Column A A 2 2 6 10 A a 18 n 10 an 0 A3 a 0 a10 6 A4 a 13 a4 3 Column B B 2 3 B 5 B3 4 B4 4 B5 2 B6 1 2 B7 5

7 In which of the following situations do the lists of numbers involved form an A P Give reasons for your answers i The fee charged from a student every month by a school for the whole session when the monthly fee is Rs 400 ii The fee charged every month by a school from classes I to XII when the monthly fee for class I is Rs 250 and it increase by Rs 50 for the next higher class iii The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10 per annum

1 Which of the following form an A P Justify your answer i 1 1 1 1 ii 0 2 0 2 iii 1 1 2 2 3 3 iv 11 22 33

A pizza pan is removed at 9 00 PM from an oven whose temperature is fixed at 400 F into a room that is a cons 74 F After 5 minutes the pizza pan is at 300 F a At what time is the temperature of the pan 135 F b Determine the time that needs to elapse before the pan is 150 c What do you notice about the temperature as time passes a The temperature of the pan is 135 F at PM Do not round until the final answer Then round to the nearest minute as needed

let lim Sinza tasinn 1270 3 h hew

1 Then x 2 x Bigger no 2 x 15 30

3 The weight of cell phones is normally distributed The mean weight of a sample of 300 cell phones is 112 grams with a standard deviation of 2 grams With a 95 confidence level determine the maxi error of estimate 22 63 29 73 18 99 O 1 31

E OA B Examination Figure III BD OB OC a 6 FC D 4 Which one of the following proportions is true for the segments in Examination Figure III if the lines a b and c are parallel to ea CT

Consider a triangle ABC like the one below Suppose that 4 27 C 104 and c 17 The figure is not drawn to scale Solve the triangle Round your answers to the nearest tenth If there is more than one solution use the button labeled or 8 0 a 0 b 0 D O No solution

N15 10 30 E FIND THE INTERIOR ANGLES N51 00 00 E N 2 S67 02 05 E S47 58 22 W

Part 2 Verify each identity Use trigonometric identities to verify each expression is equal a 1 tan2 x sec2 x cos 2x 3 points

Complete the statement below If z 256 cos 120 isin 120 then any fourth root of z has r has 8 and the fourth root with least positive argum