Complex numbers Questions and Answers

Convert 3 j into polar form and then evaluate 3 j giving the answer in polar and exponential form

The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB as indicated in the diagram So the distance from P 2 4 to the line through the points A 2 4 and B 3 3 is

COMPARE Which One Doesn t Belong Study the tables below to identify patterns similarities and differences Then answer the question X 3 7 1 5 15 Table 1 y 8 16 24 32 64 X O 1 2 3 4 Table 2 y 1 4 16 64 256 X O 1 2 3 4 Table 3 2 Which table doesn t belong Explain your reasoning y O 16 32 48 64 X O 1 2 3 4 Table 4 y 32 40 48 56 64 1 What do you notice about the tables Identify 3 similarities or differences between them

Use the first derivative test and the second derivative test to determine where each function is increasing decreasing concave up and concave down y 4x 2 x2 GLIDE Select the correct choice below and if necessary fill in the answer box within your choice OA The function is increasing on Type your answer in interval notation Use integers or fractions for any numbers in the expression Simplify your answer B The function is not increasing on any interval

It has been estimated that a certain stream can support 73 000 fish if it is pollution free It has further been estimated that for each ton of pollutants in the stream 1600 fewer fish can be supported Assuming that the relationship is linear write the equation that gives the population of fish p in terms of the tons of pollutants x Need Help Read It DETAILS HARMATHAP12 1 5 025 MY NOTES ASK YOUR TEACHER 7 1 Points Use a graphing calculator or Excel to find the solution of the system of equations If the system is dependent enter DEPENDENT If there is no solution enter NO SOLUTION

For each of the graphs below create a function of the form a cos k x d cor f x a sin k x d c Show all of your calculations b n n 2 0 5 2 1 5 0 5 n 2 n 2 in 3 2 2n

1 6pts Calculate the missing values and write the values in the blank spaces provided Disease Present Absent Total Test Results Positive Negative Total 43 567 600 650 2 Using the results in the two way frequency table from question answer the following questions in the proper format a 3pts What percent of the participants tested positive and absent answer to the nearest 1000ths auilly they b 3pts What percent of the participants tested negative and ish house absent answer to the nearest 100ths c 3pts What percent of the participants were present answer to be in simplest fractional form d 3pts What is the probability the participants were present or positive answer to be in fractional format in simplest form

Question 1 Two friends Nick and Tim are running a race Nick runs at 8 mph and Tim at 4 5 mph If the run has a staggered start and Tim starts first with Nick starting 14 minutes later how long will it take before Nick catches up with Tim Solve the problem by going through the following steps Create a variable ii Set up an equation i iii Solve the equation iv State the Answer Question 2 Simplify the quotient Write the answer in standard form a bi 4 3i 4 3i

Rationalize the denominator of each radical expression Assume all variables represent nonnegative numbers and that no denominators are 0 2 x 5 x y 2 x 5 x y Simplify your answer Tyne an exact answer uning

Find the product or quotient 2 z 12 2 11z 18 2 2z 15 z 3z 10 2 z 12 2 11z 18 z 2z 15 z 3z 10 Simi 11

Find the product or quotient n 9 4n 12 2n 16 n 4n 32 4n 12 2n 16 n 9 2 n 4n 32 0

2x 3 5x 2 x 2 if its one factor in x 1 find the prodect

State the domain vertical asymptote and end behavior of the function g x ln 4x 12 1 2 Enter the domain in interval notation To enter 00 type infinity Bh The vertical asymptote is As a approaches the vertical asymptote As a approaches 00 g x g x BB Which of the following graphs best represents the graph of g z BL

Consider the graph below y f x Use the graph of the function to find the domain of f Enter your answer using interval notation Use the graph of the function to find the range of f Enter your answer using interval notation Find f 0

Find the distance between the points 2 10 and 9 4 Round decimals to the nearest tenth units

Use the remainder theorem to evaluate the polynomial for the given values of x h x 7x 3x 49x 21 O C O C O S

A Little League baseball diamond is actually a square 60 feet on a side see the figure What is the distance directly from first base to third base the diagonal of the square 3rd base feet The distance directly from first base to third base is approximately Type an integer or decimal rounded to two decimal places as needed 60 ft 60 ft 2nd base Pitching rubber 1st base Home plate

The U S Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels since 1959 At that time there were 320 parts per million of carbon dioxide in the atmosphere In 2005 the figure was 381 parts per million Find the increase in carbon dioxide levels and the percent of increase Round to the nearest tenth of a percent Increase carbon dioxide levels Percent increase parts per million

reserved Write the slope intercept form of the equation of each line

Example Solve z5 4 4i and express the answer in exp form

Which two triangles are congruent by the SSS Theorem Complete the congruence statement D A X HHHH A HH E C V Q W HHHH P H

1 a Show algebraically that the following is 1 1 and then find a formula for its inverse function Please show all work f x x 1 2x 5

Graph the image of square STUV after a rotation 270 counterclockwise around the origin 8 6 4 2 V 10 8 6 4 2 S 2 4 6 y 8 2 4 6 T 8

Evaluate the Cauchy principal value of 2x 1 10 x4 5x 4 dx I need detail explanation

Find the value of z that corresponds to the given area See Example 1 4 3 2 2 1 0 Area of the shaded curve is 0 8554 1 2 3 4 a

87 6x 47 27 5 4 3 2 1 T 2 3 4 5 211 41 61 81 100 127 147 167 187 201

Simplify by reducing the index of the radical 6 x18

5 Apply the inverse property of addition 16

Write as a single fraction 5c 2d 8c 3d 2c 3c Simplify your answer as much as possible 3

Find approximate in standard form graph the 8th roots of z 6401 1440i Show your work for zo and z then either continue OR use symmetry ideas

x y Answer Answered 2 Points 2x 4y 8 4x 8y 14 Indicate the number of solutions to this system State the solution if one exists and if there are infinitely many solutions express the solution set in terms of one of the variables Selecting an option will display any text boxes needed to complete your answer O One Solution No Solution Keypad Keyboard Shortcuts O Infinitely Many Solutions

33 Given a 3 and ag 17 the first and fifth numbers in an arithmetic sequence find a20 O A 51 B 100 O C 97 D 92 34 All of the following are even functions except O A f x 3x 5 B f x lx 21 C f x cos x 7 O D None they are all even functions

find the domain range slope y intercept and x intercept of the linear equation 2x 30 Sketch its graph

Consider the following piecewise defined function 2 x 5 5 36 X 9 Step 3 of 3 Evaluate this function at x 0 Write the exact answer Do not round If the answer is undefined write Und as your answer answer 2 Points F x f 0 11 5 if x 5 if x 5 Keyboar

Admission to a baseball game is 2 00 for general admission and 4 50 for reserved seats The receipts were 2903 50 for 968 paid admission How many of each ticket were sold Round to nearest integer if necessary AnswerHow to enter your answer opens in new window 2 Points general admission tickets sold reserved seating tickets sold Ke Keyboard Sh

Graph the rational function 2x 2 x 4 f x Start by drawing the vertical and horizontal asymptotes Then plot two points on each piece of the graph Finally click on the graph a function button 1 6 2 1 3 44 5 X

Use synthetic division to determine p c for the given value of c and the given polynomial p x 2x4 14x 9 c 2 Answer 2 Points p c

Consider the following polynomial inequality x x 6 x 7 0 Step 1 of 2 Write the polynomial inequality in the form p x 0 p x 0 p x 0 or p x 0 then find the real zeros of p x Answer 2 Points Separate multiple answers with a comma 67 O Keyboard

12 x Step 3 of 3 Identify the correct graph of this piecewise defined function Answer 2 Points R 4 4 8 4 4 8 Enable Zoom Pan y u x 0 0 of O 4 O 8 X an if x 3 8 4 4 4 Enable Zoom Pan A 8 O 00 O 4 O X Keypad Keyboard Shortcuts Enable Zoom Pan

Answer 2 Points Step 2 of 3 Identify the general shape and direction of the graph of this function on the interval 3 00 X 2 x X if x 3 X X Keypad Keyboard Shortcuts X X

2 x Step 1 of 3 Identify the general shape and direction of the graph of this function on the interval 3 Answer 2 Points y Ay X if x 3 Ay X X Ay Keypad Keyboard Shortcut X

If a sample of a certain solution is determined to have a H3O concentration of 9 33 x 10 moles liter what is its pH Round off your answer to one decimal place AnswerHow to enter your answer opens in new window 2 Points 3 0 Keypad Keyboard Shortcuts

Step 2 of 3 Use the following information to find g f x Answer 2 Points g f x f x x 1 and g x x 1

Answer 2 Points awkes Learning A 000 f g x f x x 1 and g x x 1 MacBook Pro

rev Step 1 of 2 Find the constant of proportionality k rounded to two decimal places if necessary and use it to write an equation that mod relationship Let x represent the number of gallons purchased and let y represent the total price Answer 2 Points Keybo

V f x 3x x 1 if x 3 Step 1 of 3 Evaluate this function at x 3 Express your answer as an integer or simplified fraction If the function is undefined at the given value indicate Undefined Answer 2 Points Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is used f 3 Keypad Keyboard Shortcuts O Undefined

K rev f x x 2 and g x x Step 1 of 2 Find the formula for f g x and simplify your answer Then find the domain for f g x Round your answer to two decimal places if necessary Answer 2 Points f g x Domain Keypac Keyboard Shortcu

The kinetic energy K of a moving object varies jointly with its mass m and the square of the velocity v If an object weighing 9 kilograms and moving with a velocity of 10 meters per second has a kinetic energy of 450 joules find its kinetic energy when the velocity is 19 meters per second Type an integer or decimal rounded to one decimal place as needed

Write an equation that relates the quantities 11 E varies jointly with m and w The constant of proportionality is DEE

Write a general formula to describe the variation F varies inversely with d F 20 when d 5 F