Complex numbers Questions and Answers

Plot the point 0 6 in a rectangular coordinate system Plot the point 0 6 on the graph to the right E 12 Ay

Use the order of operations to simplify the expression 6 8 2 6 8 2 Simplify your answer

The graph of a function is shown below Use the graph of the function to find its average rate of change from x 1 to x 7 Simplify your answer as much as possible Nit

Write the expression in power form ax for numbers a and 6 V8x5 2 216 5 8x

Your test scores in one class are 81 and 87 What possible scores can you earn on your next test to have a test average between 84 and 89 inclusive Your score on the third test must be between and inclusive Use ascending order

The total revenue for Jane s Vacation Rentals is given as the function R x 100x 0 5x2 where x is the number of apartments booked What number of apartments booked produces the maximum revenue Answer How to enter your answer opens in new window Keypad Keyboard Shortcuts

Determine the domain and range of each relation Sketch a graph if it will help De Rangemel 1 y 3x 5 2 y x 3 3 y 2x 4 y 3x 2 7 5 y 2 x 3 2 6 y x 2 7 7 14 x 6 3 Domain

2 0 2 Points DETAILS PREVIOUS ANSWERS SCOLALG7 2 FOM 022 10 30 Submissions Used A graphing calculator is recommended In this problem you are asked to find a function that models a real life situation and then use the model to answer questions about the situation Use the guidelines on page 273 to help you A rancher with 850 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle see the figure a Find a function A that models the total area of the four pens Use w to represent the width of the field A w 1700 8w b Find the largest possible total area of the four pens

Convert the angle measure 34 33 18 to decimal degrees O 34 33 18 Type an integ r or decimal rounded to the nearest thousandth as needed

Domain Range

Theorem 1 If lim f x L and lim f x M then L M x p x p IL MI Proof Suppose L M then IL MI 0 Since lim f x L if we take 2 then 38 0 such that x p Ix pl 8 f x LI E Similarly since lim f x M 38 0 such that x p Ix pl 8 If x MI e If we choose 8 min 8 8 then Ix pl 8 will mean that ix pl 8 and lx pl 8 In this case we will have both I f x LI e as well as I f x MI e So that IL MI L f x f x MISI f x LI f x MI E 2 IL MI That is we get L MI IL MI which is a contradiction Therefore our supposition is wrong Hence L M We now state and prove a theorem whose usefulness will be clear to you in Unit 4 Theorem 2 Let f g and h be functions defined on an interval I containing a except possibly at a Suppose i f x g x h x x I a ii lim f x L lim h x X 48 Then lim g x exists and is equal to L 243 Proof By the definition of limit given e 0 38 0 and 8 0 such that If x LI e for 0 ix al 8 and Ih x LI e for 0 lx al 8 Let 8 min 8 8 Then 0 lx al 8 lf x LI e and I h x LI E L ESf x SL E and L esh x SL E We also have f x g x Sh x xE I a Thus we get 0 1x al 8 L ES f x g x h x L In other words 0 lx al 8 Ig x Li e Therefore lim g x L 113 Theorem 2 is also called the sandwich theorem or the squeeze theorem because g is

K Money is borrowed at 7 simple interest After one year 771 47 pays off the originally borrowed The amount of the original loan was an How II

Part 1 of 2 Use the given graph to find each of the following a the zero of the function b the x intercept What is the zero of the function O Points 0 of 1

An airplane that travels 400 mph in still air encounters a 50 mph headwind How long will it take the plane to travel 1050 mi into the wind hours to travel 1050 mi into the wind The airplane takes Type an integer or decimal

a Use the product rule to find the derivative of the given function b Find the derivative by expanding the product first h z 3 2 3z 4 a Use the product rule to find the derivative of the given function Select the correct answer below and fill in the answer box es to complete your choice OA The derivative is 3 z O B The derivative is 3 z z 3z 4 OC The derivative is 3 z z 3z 4 OD The derivative is 2 3z 4 The derivative is 3 z z 3z 4 b Expand the product 3 2 z 3z 4 Using either approach dz TILB Simplify your answer 3 z z 3z 4

a Use the Product Rule to b Find the derivative by expanding the product first f x x 6 x 3 a Use the product rule to find the derivative of the function Select the correct answer below and fill in the answer box es to complete your choice O A The derivative is x 6 x 3 OB The derivative is x 6 x 3 O c The derivative is x 6 1x 3 OD The derivative is x 6 O E The derivative is x 1x 3 b Expand the product x 6 x 3 Simplify your answer Using either approach x 6 x 3 d dx

4 20 pts We learned before that we can find the equation of a line if we are given a point and a degree of elevation or depression a Find the equation of a line that passes through the point 3 7 at an angle of elevation of 35 Degrees

1 Calculate the length of the unknown side for the following right triangle if a 7 and b 63 27 O 4 7 O 7 7 14 b 63

A vector with a magnitude of 12 0 m is directed at an angle of 25 0 above the x axis What is the component of this vector Provide your answer below

The graph of the quadratic function y ax 2x chas x intercepts 2 and 3 and y intercept 12 Find a and c a

et f x 3x 1 be a composite function Which is the correct decomposition of f x Multiple choice A a x 3x 1 b x 3x 1 f x b a x B a x 3x 1 b x x7 f x a b x c a x 3x 1 b x 3x 1 f x a b x D a x 3x7 b x x 1 f x b a x E a x 3x 1 b x x f x a b x F None of these G a x 3x 1 b x x f x b a x H a x 3x7 b x x 1 f x a b x

onsider the graph of the function y f t as drawn below If f x 3 find x lick the image for a larger version H 88 f t H

The perimeter of a square must be greater than 70 inches but less than 106 inches Find the range of possible side lengths that these conditions Hint The perimeter of a square is given by P 4s where s represents the length of a side Express your answer in interval notation Use decimal form for numerical values Answer

Let f x x 4x and g x x 8 Evaluate the following 1 fog x 2 gof x 3 fof x 4 gog x

a Let D Z EC z 1 Prove that for any a ED the map z a f z 1 az maps the unit circle to the unit circle b Determine with proof the image of the line 1 it t R under the map

1 Graph a line with a slope of that contains the point 6 3 4 4 7 6 5 4 3 2 CO C Y 4 3 2 2 3 4 5 6 7 1 2 3 4 5 6 7 I

For x Bx C x a x b x a x b 0 which of the following must be true O ab C and a b B Oa b C and a b B Oab B and a b C Oab Band a b C

For the function find the average rate of change of 1 from 1 to 3 165 HD f x X 4 5 14 07 10 O 7

Answer the question about the given function Given the function f x x 4x 96 list the x intercepts of the graph of t 12 0 1 0 12 0 8 0 12 0 8 0 12 0 8 0

Ak O 14344 even odd neither a function is given Decide whether it is even odd or neither

Graph of a piecewise defined function is given Write a definition for the function O 2 3 7x 4 Nebcam x 4 if 3 x 0

4 12 The local minimum occurs at x

Find the exact value of csc 0 given that cot 0 A Select the correct choice below and if necessary fill in the answer box to complete your choice csc 8 26 5 and 0 is in quadrant IV Rationalize denominators when applicable B The function is undefined Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Find the domain of the function g x 3x 2 4 x x 2 2 all real numbers O x x 4 O x x 0

Espa When Christine had 5 years left in college she took out a student loan for 19 246 The loan has an annual interest rate of 4 2 Christine graduated 5 years after acquiring the loan and began repaying the loan immediately upon graduation According to the terms of the loan Christine will make monthly payments for 5 years after graduation During the 5 years she was in school and not making payments the loan accrued simple interest Answer each part Do not round intermediate computations and round your answers to the nearest cent If necessary refer to the list of financial formulas a If Christine s loan is subsidized find her monthly payment Subsidized loan monthly payment 0 b If Christine s loan is unsubsidized find her monthly payment Unsubsidized loan monthly payment S S E

Determine the signs of the six trigonometric functions of an angle in standard position with the given measure 592 Determine if the value of sin 592 is positive or negative Positive Negative Is the value of cos 592 positive or negative Positive Negative What is the sign of the value of tan 592 Negative Positive Is the sign of the value of csc 592 positive or negative Positive Negative Determine if the value of sec 592 is positive or negative O Negative Positive www

Click here to watch the video Sketch an angle 8 in standard position such that has the least possible positive measure and the point 6 8 is on the terminal side of 0 Then find the exact values of the six trigonometric functi for 0 B The function is undefined sin 8 Simplify your answer Type an integer or a fraction 5 A Select the correct choice below and if necessary fill in the answer box to complete your choice cos 0 A B The function is undefined 35 tan 0 Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an integer or a fraction OA csc 8 413 CXXE Simplify your answer Type an integer or a fraction B The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an integer or a fraction

Find the measure in degrees not equal to the given measure of the least positive angle that is coterminal with A A 8 Points 0 of 1 The measure of the least positive coterminal angle is Simplify your answer

Find the next two positive and two negative angles that are coterminal with the given quadrantal angle A 630 The two positive angles are Use a comma to separate answers as needed Do not include the degree symbol in your answer

Convert the following angle to decimal degrees x 79 39 17 X Points 0 Round to 3 decimal place

Convert the following angle to decimal degree notation 69 54 0 Points 0 of 1 69 54 Round to two decimal places as needed

Find an equation for the plane that is tangent to the given surface at the given point z y x 3 4 1 WA Find the equation for the tangent plane to the surface z y x at the point 3 4 1 Use a coefficient of 1 for

2 A jet and a passenger plane left Nairobi at the same time The planes flew in opposite directions The passenger plane flew 260 mph faster than the jet After four hours they were 2320 mi apart Find the jet s speed A 183 mph B 155 mph C 160 mph D 245 mph

4 5 4 2 5x 3 6 3 8 18 9 A 1 6 x 2 46 B 5 62 x 2 9 C x 5 7 or x 3 7 D 7 48 x 4 6 HO Find each quotient 5 J Tw at inequality and graph its solution A 1 B 39 35 35 5 4 3 2 1 0 1 2 3 4 5 6 7 9 8 7 6 5 4 3 2 1012 10 7 e 6 0

2000 freshmen at State University took a biology test The scores were distributed normally with a mean of 70 and a standard deviation of 5 Label the mean and three standard deviations from the mean 55 60 65 70 75 What percentage of the class scored a 70 or above What percentage of the class scored between a 65 75 What percentage of the class scored between a 60 65 What percentage of the class scored between a 70 80 80 85

4 a Samuel is interested in finding out the favorite video game of other students at his school Part A Samuel decides he is going to conduct a sample survey to answer this question Explain how he could design his survey and how he could randomly choose those who will take the survey BiU FE E EXA

The scores on an Algebra midterm were normally distributed with a mean of 82 If Anthony scored 67 with a z score of 2 5 what is the standard deviation w

the planes 2y 8x 4z 5 and x z 2 y 4 are parallel proof that they are orthogonal proof that its parallel

If sin x 35 and x is in quadrant III find the exact values of the expressions without solving for x 37 sin

Use the half angle formulas to simplify the expression sqrt 1 cos8x 1 cos8x