Complex numbers Questions and Answers

1 point Use the mixed partials check to see if the following differential equation is exact 2e sin y y dx 4x 3e cos y dy 0 not exact Use the exact differential method to find a function F x y whose level curves are solutions to the given differential equation F x y

2 Find the natural cubic spline for x 21 1 3 5 2 5 8

et p be a prime p 2 and e 1 Find all solutions of x 1 mod p

All of the following statements about the Domain and Range of a function are true except the false statement O The domain must include all real numbers O The domain is associated with the input variable O The domain of a function is the set of all possible values for the input quantity O The range of a function is the set of all possible values for the output variable O The range is associated with the vertical axis Submit Question

Use the graph of the function f given below to answer the questions 40 tipt X A Q CITIE Points 0 of 1 List the values of x at which f has a local maximum Select the correct choice below and fill in any answer boxes within your choice OB There are no local maxima A x 9 3 Type an integer Use a comma to separate answers as needed points OA The local maxima are What are these local maxima if they exist Select the correct choice below and in any answer boxes within your choice Save Type an integer Use a comma to separate answers as needed OB There are no local maxima

The function P y 0 034y 3 642y 252 560 represents the population P in millions of people in 2005 that were y years of age or older The dependent variable is P and the independent variable is y b Evaluate P 20 P 20 193 32 Round to three decimal places as needed Choose the answer below that explains the meaning of P 20 The value of P 20 is equal to the number of people in millions O A who were 20 years of age or older in 2005 OB in 2025 OC born in 2025 D who were 20 years of age in 2005

Find the average rate of change of f x 3x 5 over each of the following intervals a From 1 to 3 b From 3 to 5 c From 3 to 6 a The average rate of change from 1 to 3 is 12 b The average rate of change from 3 to 5 is 24 c The average rate of change from 3 to 6 is

Which of the following equations will have an extraneous solution O x 2 O x X 2 O 0 x 2 X 03 x 2 X N

What is the solution to 40 4 17n 2 On 9 and n 6 On 6 On 6 O No real solution

What is the domain of 5x 2 V V 80 30

Solve the inequality 5 x 4 11 X

A snail is trying to get to the top of a drain pipe that is 50 inches tall Every hour the snail goes up 7 inches but falls back 2 inches At this rate how many hours will it take the snail to reach the top of the drain pipe

L 3 1 3 Quiz Graphing Relations Mastery Test Rosalie is training for a marathon She jogs for 30 minutes at a rate of 5 miles per hour then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour What is the range of this relation 10 9 9 Speed miles per hour 18 5 3 2 1

Let n N Prove that if Q x is a polynomial of degree less than or equal n such that Q x o x as x 0 then Q x is the 0 polynomial

Use the graph of f x x to graph g x 2x y

Solve 5 3x 41 11 14 Give your answer as an interval If no solutions exists enter No solutions

Solve equation by using the quadratic formula 4m 3m 3 0 Entry Tip to type 4 7 3 Type 4 sqrt 7 3 be careful with parenthesis and use the preview button

Write an equation for a line perpendicular to y 2x 2 and passing through the point 2 4 Be sure to write your answer in slope intercept form y mx b y

Perform the indicated operations simplify Add 8 11i 18 20i sum Subtract 8 11i 18 20i difference

Perform the indicated operation simplify Express the answer in terms of i as a complex number 6 24

1 point Note In this problem scalars are in Z3 the field of integers modulo 3 Solve the system of equations represented by the following augmented matrix with scalars in Z3 If the solution involve parameters use the provided spaces If you need fewer parameters than there are spaces leave the spaces for the unused parameters blank The general solution to the system is x y 2 W t t t t 1 1 1 2 1 1 2 00 0 1 0 2 1 2 s s s s T T T T

4 Each row follows the same rule Fill in the blanks 6 12 9 18 15 16 13 26 11 12 9 22 15 30 21 38 35 29 46 94 Magic squares Fill in the numbers 2 to 10 so that every row column and diagonal adds up to 18 You can use each number only once

ation Write the intercepts as ordered pairs z y The x intercept is The y intercept is Use the intercepts to graph 3x y 9 tist 12 10 9 8 13 12 11 10 9 8 7 6 5 6

Find a so that the point 1 4 is a Simplify your answer on the graph of f x ax 5 ww

Complete the sentence the below If the point 4 1 is a point on the graph of f then f If the point 4 1 is a point on the graph of f then f

A power outage occurs 6 min after the ride started Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride Sine function model h 82 5 cos 3x t 97 5 where h is the height of the last passenger above the ground measured in feet and f is the time of operation of the ride in minutes a What is the height of the last passenger at the moment of the power outage Verify your answer by evaluating the sine function model b Will the last passenger to board the ride need to wait in order to exit the ride Explain Answer

Homework HW 2 3 Linear Functions and Slopes 4 4 1 Use the given conditions to write an equation for the line in point slope form and slope intercept form Slope 5 passing through 3 0 Type the point slope form of the line y 5 x 3 Simplify your answer Use integers or fractions for any numbers in the equation Type the slope intercept form of the line Simplify your answer Use integers or fractions for any numbers in the equation

1 Find all the roots and sketch them as vectors 16 7 2 2 3 1 233

2 A rectangle that is x feet wide is inscribed in a circle of radius 27 feet Express the area of the rectangle as a function of x

Find the domain of the function f x 3x 15 The domain is Type your answer in interval not

E 16400 Knowing that n N and a a an are positive numbers such tha a a a n show that 1 a 1 1 a 1 1 an 1 V SIN n 2

x 3x 4 x 2x 3 33 Which is the simplified form of the expression x 2x 8 x2 5x 6 A x 57 7 x 3x 2 A x 3 or x 7 34 Which is the solution for Ix 21 5 2 x 2715 2715 C 7 x 7 B x 4 x 4 A f x 35 Which is f x if f x 3x B f x WIX C x 3 x 2 x 717 X413 B 3 x 7 D x 3 or x 7 C f x 3x D x 1 x 4 x 2 x 4 D f x 3x

he graph of a piecewise defined function is given Write a definition for the function that best describes this graph x if sxs Type the left piece of the function Type the right piece of the function 3 F 2 3 N A 0 0 21

Which of the following dot plots would most likely have the highest standard deviation 6 8 10 12 14 bui 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Question 14 3 3 points Consider the data set 23 1 5 14 17 The data set has a standard deviation of 8 If you were to add 3 to every number in the data set and recalculate the standard deviation what would it be 8 10 12 5

Consider the following Basic Box Whisker Plot HC H 10 What is the Interquartile Range IQR of the data set shown in the graph 0 1 6 10 Question 16 3 3 points Which data set graphed below would most likely consider the MEDIAN as the best measure of central tendency measure just based on the data points 10 10

1 For each of the following functions f 2 find out where if anywhere it is analytic and for those z where it is analytic compute df z dz a 32 22 c 22 3i 3 d z 2z

12 In the previous question how did you decide if the given points were on the given equation s graph For all of them I looked at the graph and decided if the point was there For some of them I looked at the graph and decided if the point was there For some of them I substituted the x value into the equation and matched the y value I just guessed until I got it correct There were 32 different options so it took a LONG TIME

Basis Find a basis of W and its dimensions below a V R and W x y z t x y 0 and x 2y t 0 b V P R and W f x P R f x 0 c V M2x2 R and W X I M2x2 R 1 x x

Simplify 0 x 1 2 where x 1 2 If the given expression is undefined ent

Factor out the GCF if possible 6r 2 12r 24

9 Solve the following equation x 1 2 x 4

Four functions are given below Perform the indicated compositions to determine which functions are inverse to each other Be sure to simplify the results f x g x h x j x f g x Conclusion f and g f h x Conclusion f and h g x g f x inverses h f x 1 inverses g j x 13x 10 10 10 13 I 13 I 13 13x 130

7 Find the 9th term of the geometric sequence whose initial term is a 4 and the common ratio is 2

B E In the figure above which of the following would allow you to prove A CBA similar to A EDA Select one O DA CB O No more information is needed they are already similar CB EA A O O ZDEA ZA LC LA

A scientist mixes water containing no salt with a solution that contains 35 salt She wants to obtain 210 ounces of a mixture that is 20 salt How many ounces of water and how many ounces of the 35 salt solution should she use Note that the ALEKS graphing calculator can be used to make computations easier Water ounces

my homework is suggesting that y 3 1 4 7 but every time i type in this equation my calculator says that it only equals 5 any tips

for the following exerc de 3 2824 range of the quadratic function f x 2x 4x 2 Answers Domain Range 3 2 M40 For the following exeroses solve the equations over the complex numbers 52 82 5 0

T i 1 2 T j 3 1 T k 5 2 Find T 2 1 3 1 20 20 1 3 2 5 2

Show that the function f R R defined via is measurable f x 1 when x EQ 0 when Q

2 of 6 Enlarge shape A by scale factor 2 with centre of enlargement 3 3 What are the coordinates of the vertices of the image