Complex numbers Questions and Answers

Use a calculator to perform the indicated operations Write the answer in rectangular form 14 cis 96 5 4 cis 13 5 14 cis 96 5 4 cis 13 5 Type your answer in the form a bi Do not round until the final answer Then round to four decimal places as neer

A C 7 19 X 40 Cos 40 x 19 Sin 40 x 40 What equation can be used to solve for x B D Sin 40 x 19 Tan 40 19 x

Find t for the following terminal points 0 t 2 a P 0 1 t b P c P 1 0 t 6 P V 12 2 e P 0 1 t 2 P V2 f P 2 2 2 2 2 t t

KK For the following function find the value of a f 4 and b f 1 if possible y x 5 if x 0 x 3 if x 0 3 a Select he correct choice below and if necessary fill in the answer box to complete your ans A f 4 B There is no solution Simplify your answer b Select the correct choice below and if necessary fill in the answer box to complete your answ OA f 1 OB There is no solution Simplify your answer K For the following function find the value of a f 4 and b f 1 if possible x 5 if xs0 x 3 if x 0 y G a Select the correct choice below and if necessary fill in the answer box to complete your ans A f 4 Simplify your answer B There is no solution b Select the correct choice below and if necessary fill in the answer box to complete your ansv OA f 1 Simplify your answer OB There is no solution

An isosceles trapezoid is shown below Line g intersects two vertices Line h bisects each side it passes through Point X is the center of the isosceles trapezoid 4 X Which transformation s must map the isosceles trapezoid exactly onto itself Choose all that apply Reflection across line h Counterclockwise rotation about X by 180 Reflection across line g O Clockwise rotation about X by 270 None of the above 00 X

ind all integer solutions to the system of equations a bc 8 b ac 8

1 Given d x d t dx dt 4x 0 Initial conditions at t 0 x 1 2 and dx dt 0 Calculate value of x at t 3 2 Given d x d t 6 dx dt 3x 4cos t What will be the function for x when all transients have died away

9 To prove the following assertions modify the argument given in the text a Show that one can compute the Fourier coefficients of a function on Z N when N 3 with at most 6N log N operations b Generalize this to N a where a is an integer 1

A borrower had a loan of 40 000 00 at 6 compounded annually with 15 annual payments Suppose the borrower paid off the loan after 4 years Calculate the amount needed to pay off the l The amount needed to pay off this loan after 4 years is Dut

the following compound inequality Step 2 of 2 Graph the solution set AnswerHow to enter your answer opens in new window 2 Points 12 8 x 9 4 111 10 9 8 7 6 5 4 3 2 1 0 1 26 8 Keyboard Pressing the buttons will create an interval with the indicated endpoint type The interval is graphed by moving the endpoints to the desired v remove graphed intervals use the Clear button To indicate infinity or negative infinity drag an open end point to the end of the number line 2 3 4 5 6 8 9 10 8

Find the equation of the line in slope intercept form that passes through the following point with the given slope Point 7 3 Slope

Tutorial Exercise Plot the point whose polar coordinates are given Then find two other pairs of polar coordinates of this point one with r 0 and one with r 0 a 3 7 b 8 3 c 2 2

Each gallon of stain covers 175 square feet How many gallons of stain should you purchase if you would like to put two coats of stain on your deck that measures 715 square feet 5 gallons 4 gallons 8 gallons 9 gallons

20 A landscape design calls for a stone walkway made of three semi annuli as shown in the figure below One case of stones costs 35 and covers 20 square feet Find the most likely cost of the stones needed to tile the walkway when R 10 feet and r 5 feet R P a 540 Answer

Find the work perfoneed when the given force E applied to an stject whose resulting motion is represented by the displacement vector d Assume the force is is pands and the displacement is measured in feet F 7 14 0 14

The terminal point of the vector is Question Help Message instructor Submit Question Jump to Answer Question 3 A vector has initial point 9 13 and terminal point 11 8 The component form of the vector is Question Help Message instructor Submit Question Jump to Answer 0 1 pt Question 4 0 1 pt

A straight driveway is 74 0 ft long and the top is 11 0 ft above the bottom What angle does it make with the horizontal Round to the nearest tenth as needed

Problems 1 3 Find all numbers for which the rational expression is undefined If the rational expression is defined for all real numbers so state 1 2 3 x 1 2x 9x 3 5x x 3x 1 2x 3x 48

21 sin pt OR 5 a Solve D 4 y sec2x by the method of Variation of parameters b Solve D 1 y e x eCosx

area the lowest angle of elevation of the sun in winter is 24 25 Find the minimum distance x that a needing full sun can be placed from a fence 401 ft high 401 n

Fill in the blank by performing the indicated elementary row operation s Answer 2 Points 4 5R R1 2

Two sides and an angle are given Determine whether the given information results in one triangle two triangles or no triangle at all Solve any triangle s that results a 7 b 9 B 49 O one triangle a 35 94 y 95 06 c 11 88 no triangle O one triangle a 76 01 y 54 99 c 7 60 O two triangles a 76 01 54 99 c 7 60 or 0 103 99 2 27 01 12 14

The vector v has initial position P and terminal point Q Write v in the form ai bj that is find its position vector P 0 0 Q 4 6 Ov 4i 6j Ov 6i 61 Ov 6i 4j Ov 4i 6j

Which term of the expansion of 1 28 Term number 48 contains a 48 contains a

Use the table to compute the probability of the z score less than 1 62 Provide the answer to four decimal places withoi ounding 0 09 0 9441 0 95 45 0 05 0 06 0 07 0 08 0 9394 0 9406 0 9418 0 9420 0 0484 0 9495 0 9505 0 9515 0 9525 0 9535 0 9582 0 9591 0 9599 0 0608 0 9616 0 0625 0 9664 0 9671 0 0678 0 9686 0 9693 0 9699 0 9706 0 9732 0 9738 0 9744 0 9750 0 9756 0 9761 0 9767 0 9633 2 0 01 0 04 0 00 0 02 0 03 1 5 0 0332 0 0345 0 9357 0 9370 0 9382 1 6 0 9452 0 9463 0 9474 1 7 0 9554 0 9564 0 9573 1 8 0 9641 0 9649 0 9656 1 9 0 9713 0 9719 0 9726

A data set is summarized in the frequency table below Using the table determine the number of values greater than or equal to 10 Value 2 3 4 5 6 7 8 9 Frequency 3 4 6 3 2 3 4 5

ind the exact location of all the relative and absolute extrema of the function Order your answers from smallest to largest t h t 60t 90t with domain 2 1 5 0 has an absolute minimum has a relative maximum has a relative minimum at t y at t y at t y 1 30 0 0 X

The endpoints of a diameter of a circle are 2 6 and 8 2 Give the radius of the circle The exact radius is The approximate radius rounded to 1 decimal place is

Given that the probability of a company having a section in the newspaper is 0 43 and the probability of a company having a website given that the company has a section in the newspaper is 0 84 what is the probability of a company having a website and a section in the newspaper Round your answer to three decimal places Provide your answer below

The acts in a talent competition consist of 4 instrumentalists 10 singers and 8 dancers If the acts are ordered randomly what is the probability that a singer performs first Provide the answer as a simplified fraction Provide your answer below

You take a package to the local shipping company They charge a fixed base cost of 3 per package plus an additional 0 63 per pound If P represents the number of pounds of your package and C is the total cost of shipping your package write an equation that represents the relationship between P and C Provide your answer below

Find the smallest possible set that is the set with the least number of elements that contains the given sets as 7 8 9 f c

Form a polynomial f x with real coefficients with leading coefficient 1 having the given degree and zeros Degree 4 zeros 4 3i and 1 of multiplicity 2 Enter the polynomial f x Type an expression using x as the variable Use integers or fractions for any Sinn Simplify your answer

Determine proj u the orthogonal projection of u on a and deduce proj u for 3 1 2 1 3 a 2 1 2

tan 0 24 where 0 0 TT 2 Use the given information about to find the exact value of cos 20

Find the amount that results from the given investment 500 invested at 12 compounded quarterly after a period of 3 years After 3 years the investment results in Round to the nearest cent as needed www

Use any convenient method to determine whether the following system of equations is consistent inconsistent or dependent x 6y 22 3x 18y 66 Answer Only One Solution Inconsistent System Dependent System

Complete the information for the circle x 2 y 2 8x 8y 16 0

One hundred college seniors attending a career fair at a university were categorized according to gender and according to primary career motivation The table below shows the results If one of thes students is to be selected at random find the probability that the student selected is female given that their primary motivation is a sense of giving to society Primary Career Motivation Male Female Total Money 10 6 16 Allowed to be Creative 10 30 40 Sense of Giving to Society 25 19 44 Total 45 55 100 The probability that the student selected is female given that the primary motivation is a sense of giving to society is Simplify your answer Type an integer or a fraction

termine whether the following function is a polynomial function If the function is a polynomial function state its degree If it is not tell why not Write the polynomial in standard form Then idently we leading term and the constant term G x 2x 1 x 4 Determine whether Gix is a polynomial or not Select the correct choice below and if necessary fil in the answer box to complete your choice A it is a polynomial of degree Type an integer or a fraction B It is not a polynomial because the variable x is raised to the power which is not a nonnegative integer Type an integer or a fraction OC It is not a polynomial because the function is the ratio of two distinct polynomials and the polynomial in the denominator is of positive degree Write the polynomial in standard form Then identify the leading term and the constant term Select the correct choice below and if necessary tll in the answer box to complete your choicen OA The polynomial in standard form is Gx with leading terms and constant Simplify your answers Use integers or fractions for any numbers in the expressions

sec B 1 tan p Separate multiple solutions by commas Enter if there is no solution Find all solutions to the equation 1 for which B T

d BC CB given that B 8 0 81 and C 8 6 6 9 If an operation is not defined state the reason

Find the values of x y and z in the triangle to the right p 2x 6 20 2x 6

write equation using point Slope form but in Slope intercept form 0 4 5 en

write equation using point Slope form but end n Slope intercept form 4 3 3 4

Find the area between the x axis and the curve defined by y x 4 x on the interval 5 0

Write the rational expression in lowest terms 7k 21 6 2k O 1 O 12 04 01

Solve the equation 9d 27d 18 0 0 2 1 01 1 1 O 2 1 P

Solve the equation x 9x 22 0 O 11 1 11 2 11 2 11 2

Simplify 2 4y 12 2 3y 18 Oy 2 O E A 4y 12 3y 18 ZT AF ZA 3y 18 O 4y 2 3y 3