Linear Algebra Questions and Answers

Campbell Soup Company is an American processed food and snack company but is known for its canned soups The company provides the followin standard and actual cost relating to material price and labor usage Item to Classify Material Price Labor Usage Standard 8 50 per gallon 30 000 hours Multiple Choice Actual 8 35 per gallon 28 500 hours Based on the above information which statement is correct Both the materials price variance and the labor efficiency variance are favorable

A firm makes three types of wooden cabinets A B C with profit margins of 35 30 24 per unit respectively Process Preparation Assembly Finishing Time in hours per cabinet A B C 225 534 4 423 The manufacturer has 25 men available for preparation 20 men for assembly and 30 men for polishing and all staff work a 40 hour week To remain competitive at least 300 cabinets in all must be produced each week Determine a the number of each model to be manufactured each week in order to maximise the profit b the maximum weekly profit

5 2 point Let F be a smooth vector field with constant curl V x F a b c Let C and C 1 be unit circles in the z 1 and z 1 planes respectively oriented in the same direction See example here Show that F dr fr Hint connect the loops with a surface F dr

9 Part 2 of 2 pints eBook Hint Print References The following information applies to the questions displayed below Megamart provides the following information on its two investment centers Average Assets 17 000 000 13 000 000 Investment Center Electronics Sporting goods Compute profit margin and investment turnover for each center Which center generates more income per dollar of sales Which center has the better investment turnover Profit Margin Complete this question by entering your answers in the tabs below Investment Turnover Sales 40 800 000 17 680 000 Numerator Compute investment turnover for each center Which center has the better investment turnover Sales Income 3 060 000 2 210 000 Investment Turnover Denominator Average assets Investment Center Electronics Sporting Goods Which center has the better investment turnover 1 Investment Turnover Electronics 0 0 Check

4 2 points Let S be the upper hemisphere x y 4 with z 20 Compute the flux of the vector field F x y z r 1 z through S toward the ori

Suppose another drug is administered intravenously The concentration c of the drug in mg L in the bloodstream t hours after it is administered is modeled by the function c t t 4 20t a Determine when the concentration will be 0 5 mg L b Complete the table representing the concentration of the drug in the bloodstream t hours after administration Round to two decimal places as needed 0 2 4 6 10 12 14 16 18 20 t c t c What is a reasonable domain for this function Justify your answer d When must the patient receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg L and below 8 mg L Explain your reasoning e Compare the concentration of the oral drug 1 and the concentration of the intravenous drug 2 over the first 20 hours after it is given

Homework 11 Please give complete well written solutions to the following exercises and submit via Gradescope 1 2 points Consider the vector field F x y 2y x and the domain D x y R 0 x 1 x y x Let C be the counter clockwise oriented boundary of D Compute the integral F dr first directly i e using line integrals and then using Green s theorem 2 2 points Consider a conical paper cup with height h and radius R Parametrize it and compute its surface area 2 ways a as the graph of a function z f x y and b as a surface of revolution

NE ii Compute y o z W Z W W x y 1 The multiplication table above is defined on the set S x y z w i Is S closed under Explain why or why not Z iii Does S have an identity with respect to o If so what is it If not explain why not iv Is S o a group If so write down the inverse of each element If not name th elements that are not invertible y Iso commutative in S Why or why not

According to a sleep foundation in 2013 a certain nation averaged 6 4 hours of sleep each weeknight In 1918 they averaged about 8 hours and 15 minutes of sleep per weeknight Model these data by a linear equation and use it to predict the year when the nation will not be sleeping at all on a weeknight CLE Model these data by a linear equation assuming that the initial year is t 0 y 0t 0 Round to four decimal places as needed Use the equation to predict the year when the nation will not be sleeping at all on a weeknight The nation will not be sleeping at all on a weeknight in the year Round to the nearest year as needed This question 1 point s possible

Let G be a group with G e a b c where e is the identity Construct the multiplication table for G under the following conditions 36 a e and b e 37 a b and b e

blem 4 Cesium 137 is an isotope of cesium that is a common product of fission in a nuclear reactor The rate of change in the amount of any radioactive substance is proportional to the amount present Let C denote the amount of cesium 137 remaining in spent nuclear fuel rods after t years a Using r for the proportionality constant write an equation of change for C b Solve the equation from part a Use Co for the initial value c The half life of cesium 137 is 30 14 years Use this information to find the value of the proportion ality constant r from parts a and b Give the exact value and then round it to three decimal places d How long does it take for the amount of cesium 137 to decay to one tenth of the initial amount Round your answer to the nearest year

3 12 pts A frozen pizza has a temperature of 30 F and is placed into a 72 F room After 15 minutes the temperature of the pizza has risen to 40 F a Use Newton s Law of Cooling to find the function that models the pizza s temperature T as a function of time t

Blood type AB is found in only 3 of the population If 290 people are chosen at random find the probability of the following Use the normal approximation Round your answers to four decimal place a 5 or more will have this blood type b between 5 and 10 will have this blood type

Entries for issuing stock On January 22 Zentric Corporation issued for cash 180 000 shares of no par common stock at 12 On February 14 Zentric issued at par value 50 000 shares of preferred 2 stock 50 par for cash On August 30 Zentric issued for cash 20 000 shares of preferred 2 stock 50 par at 54 Journalize the entries to record the January 22 February 14 and August 30 transactions If an amount box does not require an entry leave it blank Jan 22 Cash V Common Stock Feb 14 Cash Preferred Stock Aug 30 Cash Preferred Stock V 00 00 00 00 00 00

Verity the following identity 1 cos 2x sin 2x tan x Which of the following three statements verifies the given equation 2 sin x O 1 2 sin x 1 2 sin x cos x 2 sin x cos x 1 cos 2x sin 2x 1 cos 2x sin 2x 1 cos 2x sin 2x 1 1 2 sin x 2 sin x cos Xx 1 1 2 cos x 2 sin x cos x 2 sin x 2 sin x cos x 2 cos x 2 sin x cos x tan x tan x tan x

After the 25 years have passed I plan on retiring and will now use the money that has built up as my retirement pay I will make monthly withdrawals every month for 20 years 5 How much money can I withdraw each month from this same account 3 5 compounded monthly for the next 20 years Show all work

Which of the following relations on P are symmetric Select all that apply Be able to explain your answers DA i e the relation of divides OB OC OD DE 2

K Find the linear equation whose graph passes through the given points Write the equation in slope intercept form 13 19 and 7 16 y Type an expression using x as the variable Use integers or fractions for any numbers in the expression Points 0

In 2009 the life expectancy of males in a certain country was 73 years and increasing at a rate of 0 4 year per year Model this situation by a linear equation use this equation to estimate the life expectancy of a male born in the country in 2026 Identify the appropriate problem solving method A The Three Way Principle B Try a Simpler Version of the Problem c Relate a New Problem to an Older One OD Be Systematic Let x be the number of years since 2009 and let y be the life expectancy of males Choose the equation of a line that models this situation A y 0 4x 73 B y 0 4x 73 c y 0 4x 73 OD y 0 4x 73 GEER Estimate the life expectancy of a male born in 2026 y years Type an integer or a decimal

For the given arithmetic sequence find a18 and then find the sum of the terms from a to a 8 inclusive 8 12 5 17 21 5 Find a18 a18 Type an integer or a decimal

K For the following geometric sequence find an 3 6 12 24 find a13 813

9 In still water Maria can paddle at the rate of 7 km h The current in which she paddles has a speed of 4 km h a At what velocity does she travel downstream b Using vectors draw a diagram that illustrates her velocity going downstream c If Maria changes her direction and heads upstream instead what is her speed Using vectors draw a diagram that illustrates her velocity going upstream

Assignment 9 Problem 26 1 point Find the distance of the point 3 3 5 from the line r t 1 4t 1 3t 7 3t Answer

Assignment 9 Problem 30 1 point Find the intersection of the lines r t 1 2t 7 2t 22 8t and R s 6 5s 12 5s s Write your answer as a point a b c where a b and care numbers Answer Note If there is no intersection write none

1 point The plane that passes through the point 0 3 5 and is perpendicular to both 2x y z 9 and 5x 3y 3z 2 has equation as its implicit

1 point Determine whether the points lie on a straight line Answer Yes or No 27 1 A 0 0 0 B 7 1 3 and C 28 4 12 2 D 7 1 3 E 8 1 6 and F 12 9 18 3 G 1 0 1 H 2 7 8 and I 8 21 22 Note You only have two attempts at this problem

A bag of M M s has 7 red 5 green 6 blue and 4 yellow M M s What is the probability of randomly picking give answer as a reduced fraction 1 a yellow 2 a blue or green 3 an orange

Assignment 9 Problem 15 1 point Determine if the pairs of vectors below are parallel orthogonal or neither a 3 1 1 and b 12 4 40 are a 3 1 1 and b 12 4 4 are a 3 1 1 and b 15 5 6 are Note You can earn tial credit on this problem

1 point v 3 5 10 w 8 9 1 Find the cosine of the angle between v and w cos 8

Assignment 9 Problem 12 1 point Let a 10 7 2 and b 2 5 2 be vectors A Find the scalar projection of b onto a Scalar Projection B Decompose the vector b into a component parallel to a and a component orthogonal to a Parallel component 0 Orthogonal Component 00

Assignment 9 Problem 5 1 point Find the scalar and vector projections of b onto a where a 1 1 2 and b 2 8 6 1 comp b 2 proj b

Assignment 9 Problem 2 1 point Find the following expressions if a 3i 5k b i j 5k and c 4i 9j 3k 1 a b 2 a c 3 b c

What is wrong with the following grouped frequency c Grades Frequency 50 55 55 60 60 70 9 70 80 15 80 90 7 90 and above 4 All 2 4 The classes do not all have the same width There are open ended classes The classes overlap

Determine whether the value 15 is a parameter or statistic 15 of College A s students are women Parameter Statistic

16 83 At the instant shown the disk is rotating at w 4 rad s Determine the velocities of points A B and C DO 0 15 m E w 4 rad s B 16

13 Match each equation with its graph Explain your strategy 1 a y x 3 c y 2x 3 Graph A 3 0 2 Graph C y 2 0 2 X 4 2 x b y 3x 2 d y 2x 3 Graph B y 2 0 2 Graph D y N 2

6 4 11 For each equation identify the slope and y intercept of its graph then draw the graph a y 3x 4 3 b y x 2

5 The slope of line FG is given What is the slope of a line that is i parallel to FG ii perpendicular to FG 11 a 3 b d 1 8 6 UITO 5 c

0 10 pts 3299 Details Find the equation of the vertical asymptote f x log x 5

Find the grade point average Assume that the grade point values are 4 points for an A 3 points for a B and 2 points for a C 1 point for a D and 0 points for an F The grade point average is Round to the nearest hundredth as needed Grade Credit Hours B CAC 2 2 3 3

150 Which graph is a solution for A B C D x 2y 24 xZ4

The flight of a cannonball toward a hill is described by the parabola y 2 0 12x 0 002x where x is time in terms of seconds and y is the distance in terms of miles The hill slopes upward along a path given by y 0 15x Where on the hill does the cannonball land

1 State the transformations and then graph the function a y 3x 12 b y 2 x 3 4 8 8 6 6 A 4 4 2 2 18 16 14 12 10 8 6 4 2 ON 199 6 8 10 12 14 16 18 18 16 14 2 12 10 8 6 4 2 0 2 4 6 8 10 12 24 11 14 16 2 2 4

Use the amortization table to determine how much of the 2nd payment is interest Click the icon to view the amortization table The interest amount of the 2nd payment is Type an integer or a decimal

The circle graph shows the percent of the land area of the countries of a region Which country is the largest Choose the correct answer below A Country A OC Country C OE Country G OG Country D O B Country B OD Country F O F Country E COL COL Cou Cou Cour Cour Cour

Restaurant industry food and drink sales y in billions of dollars in a certain country from 2008 through 2017 can be approximated by the equation y 3x 4 1x 541 where x is t number of years since 2008 Assume that this trend continues and predict the year in which the restaurant industry food and drink sales will be 1458 billion The year in which the restaurant industry food and drink sales will be 1458 billion is Round to the nearest whole number as needed

A rocket is launched from the top of a 30 foot cliff with an initial velocity of 170 feet per second The height h of the rocket after t seconds is given by the equation h 16t 170t 30 How long after the rocket is launched will it be 20 feet from the ground ta Simplif feet seconds an integer or decimal rounded to the nearest tenth of a second as needed

B 7 Graph each equation on grid paper Explain the strategy you used a y 2x 7 1 c y x 5 4 e V 100t 6000 f C 10n 95 362 Chapter 6 Linear Functions a O A y y f x 20 2 2 0 b y x 3 5 d y x 4 y y h x 2 4 X b d O 2 6 y 2 N y g x 0 S x y y k x 12 For each graph that follows i Determine its slope and y intercept ii Write an equation to describe the graph then verify the equation iii Use the equation to calculate the value of y when x 10 15 a How can you use the slope intercept form of an equation y mx b to graph the horizontal line y 2 b How can you graph the vertical line x 2 Explain your answers 16 Alun has a part time job working as a bus boy at a local restaurant He earns 34 a night plus 5 of the tips a Write an equation for Alun s total earnings E dollars when the tips are t dollars b What will Alun earn when the tips are 400 Explain your strategy What were the nightly tips when Alun earned

The length of a rectangle is 7 centimeters less than three times its width Its area is 20 square centimeters Find the dimensions of the rectangle The width is and the length is

2 The table below describes features of a rational function Use the information in the table to sketch the graph Ensure to include the asymptotes in your sketch 5 marks y intercept Vertical Asymptote X 4 X Horizontal Asymptote y 3 2 x intercept 1 Im 3 1 8 Domain XER x 4 Positive intervals 4 Negative intervals 00 U 4 00 J A