Linear Algebra Questions and Answers

The frame which is made of Al alloy 6 900 T37 is supporting SON m a point load and a point moment as shown in figure 58 Given the geometry and loads find the internal reactions at point D Note that there are pins at points A B and C To receive full points you must show all your work including appropriate Free Body Diagram used to calculate any external reactions you deem necessary as well as that used for the internal reactions 1 m 1 B Im D 400 N 0 5 m hs 2 m Figure 58 Frame with external loads made from Al a 6 000 TOT

Monthly attendance at financial planning seminars for the past 24 months and forecasts and errors for those months are shown in the following table Determine if the forecast is working by computing a tracking signal beginning with month 10 updating MAD with exponential smoothing Use an alpha value of 0 2 Round all your calculations to three decimal points Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Attend 42 47 51 51 46 43 37 33 26 23 30 34 43 56 62 59 54 53 45 38 36 34 42 46 Forecast 41 43 54 50 55 41 37 27 27 29 32 34 53 57 72 61 58 52 41 33 40 43 36 56 A F lel Cumulative lel MAD Cumulative Error Tracking Signal

1 of 2 S Book Print erences Required information Complete this question by entering your answers in the tabs below c llinn ovnancac and nonoral and administrative Ovnancoc Required 1 Required 2 Required 3 Prepare a single step income statement for the year ended January 31 NELSON COMPANY Income Statement For Year Ended January 31 Expenses Total expenses

18 Change the decimal 0 0112 to a fraction O A 112 100 O B 112 1 000 O C 112 10 000 O D 112 100 000

A rectangular box has the dimensions shown in the diagram The volume of the box is given by the function 3 V x x 4x where x is the height of the box in inches If the volume of the box is 15 in what is its height x 2 in x in x 2 in

1 For each sequence determine whether it is arithmetic geometric or neither If it is arithmetic or geometric write a recursive definition for the sequence A 2 4 8 16 32 B 1 7 5 1 15 3 45 9 137 7 C 8 6 4 2 0

Andover Bank and Lowell Bank each sell one year certificates of deposit CDs The interest rates on these CDs are given in the table below for a three year period 2024 Bank Andover Bank Lowell Bank 99 496 2022 196 496 2023 296 4 Suppose you deposit 2 000 in a CD in each bank at the beginning of 2022 At the end of 2022 you take your 2 000 and any interest eamed and invest it in a CD for the following year You do this again at the end of 2023 At the end of 2024 the interest over this three year period at Andover Bank is Enter your response rounded to the nearest penny

The following table contains data from FRED on the U S population billions of persons and real GDP for April of 2023 and 2018 U S Month Yr Population billions of persons 0 327667595 0 336047315 April 2018 April 2023 Real GDP billions of Month Yr April 2018 chained dollars 18 565 7 20 404 1 Nominal GDP billions of dollars 20 470 2 26 835 0 Real time data provided by Federal Reserve Economic Data FRED Federal Reserve Bank of Saint Louis GDP per capita A relatively simple method of gauging the change in living standards over time within a country is to compute real Complete the following table by computing for each period the per capita real GDP Enter your responses rounded to the nearest dollar Real GDP Per Capita chained dollars

Mechanical engineers often study the movement of damped oscillating objects Studies of this type play an important role in the design of automobile suspensions among other things The horizontal displacement of an object is given as a function of time by the equatior x xoe Bt cos wt B w sin wt The parameters and w depend upon the mass of the object and the dynamic characterisucs of the system a Prepare a table of x versus t over the interval 0 t 30 At 0 5 sec Let xo 8 in 0 10 sec and w 0 50 sec The mua last three values are constant therefore Absolute addresses are needed All variables must be clearly labeled Make sure to add borders to the table and use 2 decimal places 23 b Highlight the first points where x first crosses the t axis Tumainos

In each of the following list three terms that continue the arithmetic or geometric sequences Identify the sequences arithmetic or geometric a 1 5 9 13 17 b 3 9 27 81 243 c 17 26 35 44 53 a The next three terms of 1 5 9 13 17 are Is the sequence arithmetic or geometric OA Arithmetic OB Geometric b The next three terms of 3 9 27 81 243 are Is the sonuence arithmetic or geometric MCC and and Use ascending order Use ascending order

2 a lim Problem 2 Evaluate each limit numerically algebraically and graphically 7 xx 2x x 1 16x 9 112x b lim c lim 418 1 x 7x 3x 25x 5 10 V 0

3 3 Find all complex roots of x 2x 19x 20 0

An international company has 11 400 employees in one country If this represents 28 8 of the company s employees how many employees does it hav total Round your answer to the nearest whole number

1 2 3 Distance 4 Find the distance between K and L on the number line below X 5 K L 12 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 S 6 7

d the missing factors 3 17 x 100 1 700 40 400 1 315 X 4 668 X Complete Example 4 X 300 4 X X 1 000 478 000 35 12 12 X 500 12 X 1 200 466 800 39 700 X 900 700 X 131 500 37 33 3 X 100 X 100 X 100 X 100 320 X X 100 X 100 X 1 000 25 000 320 000 X 1 000 2 662 000 X 100 576 000

Directions Give the first 5 terms of each sequence 1 a 17 a a 13 3 a 1 a 3 a aa 2 7 1 2 6 24 120 11 a Directions Write a recursive rule for each sequence Then find a 5 7 21 63 189 567 15 9 3 2 2 3 13 a This is a 2 page document 4n n 5 2 a Directions Give the first 5 terms of each sequence 9 a 3n 7 n 1 n 2a 2a 5 4 a 3 a 7 a a 2 a 6 13 8 4 8 6 7 12 10 a n 4 12 a 6n sequences 14 a 3n 4 2n 1

Directions Write an explicit rule for each sequence Then find ans 15 4 7 12 19 28 17 4 2 5 3 Explicit 16 23 21 19 17 15 Recursive 18 Directions Write an explicit and recursive rule for each sequence 192 6 18 54 162 1 4 9 16 25 13 5 7 9 11 20 3 2 7 12 17 Explicit Recursive 21 Elan makes time every day at the end of basketball practice to work on his free throws Du one week he makes 11 15 19 23 and 27 throws Assuming this sequence continues find recursive and explicit rules

How Fast to Drive Suppose Duke is driving to a nearby town to attend a dance party and must decide how fast to drive The marginal benefit of speed is the extra dance time he will get by driving faster and the marginal cost is the additional risk of a collision The marginal benefit curve is negatively sloped and the marginal cost curve is positively sloped Suppose Duke s favorite dance partner Daisy is grounded for makeup violations In the absence of Daisy Duke s from speeding

Problem 6 Consider functions u u x t of the form u x t u t uo t uo t a What can you say about us and us if u is a solution of uur 6

Problem 5 3 Algo Hoosier Manufacturing operates a production shop that is designed to have the lowest unit production cost at an output rate of 115 units per hour In the month of July the company operated the production line for a total of 205 hours and produced 21 400 units of output What was its capacity utilization rate for the month Round your answer to 1 decimal place Capacity utilization rate

Calculate the condition number of the matrix A using the infinity norm The condition number is fill in blank SUBMIT Problem Consider the following matrix A and it s inverse A 1 0 1 3 A 1 21 2 3 1 By hand calculate the condition number of A using the infinity norm max b 01 111 13 0 1 3 4 1 2 1 4 2 3 1 6 A 1 21 2 31 11 21 41 15 2 A 1 2 3 3 2 1 1 2 4 5 2 A 1 2 3 3 2 1 2 1 1 2 11A 6 Max 4 4 5 7 A 7 3 3 5

15 Which of the following will conduct electricity OA Base solutions only OB Acid solutions and base solutions OC Acid solutions only OD Neither acid solutions nor base solutions

11 are substances that facilitate the movement of electrons or electrical charge OA Oxidizing agents OB Electrolytes OC Solvents OD Reducing agents

16 Simplify 320 OA 4 2 OB 5 7 O C 14 2 OD 8 5

13 Simplify 32 x 33 0000 OA 36 OB 38 OC 35 OD 3

10 Simplify O 0 A B 10 3m n 3 0 5 m 4 C 8 5 0 1 m n 3m 5n

3 Solve 7 2x 9 O A x 2 O B x 1 O C x 5 2 O D x 1

3 A line in the Cartesian plane passes through the points 2 4 and 2 1 What are the rise and the run of the line OA The rise is 5 the run is 4 B The rise is 4 the run is 5 C The run is 4 the rise is 5 D The run is 5 the rise is 4

1 What is the ordered pair for point H 10 8 6 4 A 0 4 5 B 5 0 O C 0 5 G D 4 5 0 N 10 TO IST 100 TV 14 CO 10 2 A K 12 X H 8 10

ter to the following graph and information An ant is crawling on a straight wire The VELOCITY v t of the ant at time 0 t 8 is given in the graph at right Note The graph on 0 t 2 is a semicircle half circle A 4 T 2 O B 4 O c 4 O D 7 O E 3 5 3 5 6 What is the total distance traveled by the ant over the time interval 0 t 8 Click here for long description

Research online and use the scientific method to show evidence for or against the following statement Earth is no longer in a state of warming Your answer should include your hypothesis information from something in the 1800s 1900s and 2000s and an analysis of your findings Paste the links s to the resources you use BIU

3 of 3 apped Book Print rences Complete this question by entering your answers in the tabs below Required 3 Required 4 Required 5 Compute the amount of stock issuances for Company D during the year Beginning of Year Assets End of Year Assets Equity beginning of year Less Cash dividends Equity end of year 11 Liabilities Liabilities 0 0 S Equity Equity 0 0

Write a script that generates a plot of the first 20 squares vs i Use your function from problem 1 to generate t data to plot Problem 2 required submission Printout of well commented script you coded included in your Gradescope submission Printout of well annotated graph

Linearize f x 5 x for a 1 and use it to approximate the value of 2 5 L x The approximated value of 2 5 is Round to two decimal places as needed

1 4 3 Use the inverse of A 1 3 to decode the following 11 52 8 9 13 39 5 20 12 56 5 20 2 7 9 41 25 10

9 Determine if S 7 4x 4x 6 2x 3x 20 6x 5x is linearly independent or depender

10 Given A a AB b A A c 5A d A B and B 2 1 find

8 Given ui 2j 3k and v a u X v the cross product i 3j 2k find

7 Determine the polynomial function that passes through 0 42 1 0 2 40 3 72

4 Find the Wronskian for ex e ex

a u b v C uzv the dot product d a unit vector in the direction of u

6 Let T R R be a linear transformation such that T 1 1 1 2 0 1 T 0 1 2 3 2 1 and T 1 0 1 1 1 0 find T 2 1 1

A 35 2 8 3 1 2 m MC A 12 m A 35 2 4m 9 11 9 c Find worksheets games lessons more at e

h B 30 12 212 1 3 A 1 3 8 2 cm D 11 1 cm 7 5 cm A 3 A 8 3 1 2 m 3

3 Consider the following assumptions for implementing heap memory a Explicit free list b 4 byte pred and succ pointers in each free block c Zero size payloads not allowed d Headers and footers are stored in 4 byte words Determine the minimum block size for each of the following combinations of alignment requirements block formats Alignment Allocated block Free block Minimum block size bytes

Which of the following is a graph of a single variable OA Graph A B Graph B OC Graph C Sales millions of automobiles 6 5 6 0 5 5 5 0 Graph A 4 5 2005 2007 2009 2011 2013 2015 Q 50 40 30 20 10 Graph B U S firms Japanese firms European firms Korean firms Graph C European firms 9 496 Japanese firms 37 99 U S firms 45 5 Korean firms 7 2

Let R be the region 1 y x False y x X By taking the order of integration as dyde over R we can solve the integral using one region of integration only True

P and B 42 3 and R A 3 and 3 50 36 17

Divide the following numbers in scientific notation a express the result in scientific notation 1 x 1016 2 x 105 Round your answer to one decimal place Provide your answer below x 10 FEEDBACK

3 10 Given the linear transformation T defined by T x Ax where A 9 2 6 find the kernel of T