Linear Algebra Questions and Answers

g x et powered by desmos X 5 5 0 5 5 t e shown in red and blue respectively in the graph above By zooming in and out view the Compare the functions f x x7 and g x functions using several viewing scales When does the graph of g finally surpass the graph of f The graphs intersect for the last time at Round your answer to four significant figures Hints You can manually adjust the axes of the graph by clicking on the settings tool in the top right To get this much accuracy you may need to zoom in very close to the intersection point You must round your answer or it will be marked wrong

Solution The required numbers are 1 2 3 4 5 6 So the given set in the roster form is 1 2 3 4 5 6 Example 3 Write the set A 1 4 9 16 25 in set builder form Solution We may write the set A as A x x is the square of a natural number Alternatively we can write A x x n where n N Example 4 Write the set 1 2 3 4 5 6 2 3 4 5 6 7 in the set builder form Solution We see that each member in the given set has the numerator one less than the denominator Also the numerator begin from 1 and do not exceed 6 Hence in the set builder form the given set is n Isns6 where n is a natural number and 1 n 6 n 1 ed Example 5 Match each of the set on the left described in the roster form with the same set on the right described in the set builder form 1 P R I N C A L a x x is a positive integer and is a divisor of 18 b x x is an integer and x 9 0 ii 0 ii 1 2 3 6 9 18 c x x is an integer and x 1 1 iv 3 3 d xx is a letter of the word PRINCIPAL Solution Since in d there are 9 letters in the word PRINCIPAL and two letters P and I are repeated so i matches d Similarly ii matches c as x 1 1 implies x 0 Also 1 2 3 6 9 18 are all divisors of 18 and so iii matches a Finally x 9 0 implies x 3 3 and so iv matches b EXERCISE 1 1 1 Which of the following are sets Justify your answer i The collection of all the months of a year beginning with the letter J ii The collection of ten most talented writers of India in A team of eleven best cricket batsmen of the world iv The collection of all boys in your class v The collection of all natural numbers less than 100 vi A collection of novels written by the writer Munshi Prem Chand vii The collection of all even integers

Write the number given below as a binary numeral 53

Change the number to base ten 326 5 eight

ntiate the function 5 x 8 x

6 15 a Show that the differential equation 3x ydx x y dy 0 is exact h Obtain an implicit solution

5 10 Use an integrating factor to solve the differential equation x x y 2x dy dx Give an explicit solution

A regression forecasting model has an intercept of 1 459 a slope of 21 6 and a correlation coefficient of 0 92 Compute the forecast for period 12 That is F12 Your Answer 718 3

blem 5 The table lists the concentration of E coli bacteria P in billions per liter after x hours 3 5 6 2 33 3 X P x 0 0 5 8 414 a Find an exponential function of the form P x Poa that models the data in the table b Use your function from part a to evaluate P 6 2 c Interpret the meaning of your answer to P 6 2 and include appropriate units d Sketch the graph of P x Label and appropriately scale the axes to include the entire graph

How do personal savings create capital Banks use the money saved to Oborrow against deposits to pay interest on the funds held Funds are used to pay down debt owed by the financial institution on bad loans which helps create capital Funds accumulated in financial institutions are matched by the Federal Reserve which increases the amount of capital available Funds deposited by individuals into financial institutions are used to make loans for large or

Write a function that gives the balance B of the given investment in terms of the time t in years Use Bo for the initial balance APR of 2 compounded continuously Express numbers in exact form Use symbolic notation and fractions where needed

A family invests 2500 to convert to solar power The conversion saves 220 per month on energy costs Find a formula that gives the net savings N in dollars on energy after r months where 20 Express numbers in exact form Use symbolic notation and fractions where needed Give the formula in terms of N and r formula

Find the equation of the secant line for the given function for the given interval x 1 x 1 f x for the interval 2 8 Express numbers in exact form Use symbolic notation and fractions where needed Let y f x and give the equation in terms of y and x

Consider the following sets contained in the universe U 0 1 2 3 4 5 6 7 8 A 0 4 7 8 B 0 2 7 C 0 2 3 8 Compute the following a AUBUC b An BnC c AUB nC d AU BOC e A BOC f A B

1 Using limits find the slope of the tangent to the curve f x x 3 at the point where x 7

Is the following statement true Explain why or why not Provide an example to support your claim The limit of a function limx a f x may not exist even if f a exists

3 What transformations of the parent graph of f x x produce the graph of k x 4x 12 12

Write 2 4 3a 3 8b in reduced radical form

5 What is the reduced radical form of 250 54 72

In a High School a survey was taken of 130 students to find out which sports they liked The survey showed all the students who liked wrestling also liked football Of those who like wrestling 12 also liked baseball There were 43 students who liked basketball of those 29 liked football None of the students who liked basketball liked wrestling or baseball There were 87 students who liked football and 28 of them only liked football There were 49 students who liked baseball and 29 of them only liked baseball Use the information from the survey above to match the letters in the venn diagram with the sports A B Sports by Baseball d Wrestling av Basketball Football C Diagram Letter a A b B c C d D D

Let f x sinx X 0 0 SXS T g x cos x 0 x x and h x tan x Find the exact value of the composite function fractions for any numbers in the E

1 1 Two cm of runoff result from a storm on a drainage area of 100 km Convert this amount to cubic meters and acre feet 1 acre 43 560 square feet

Find an explicit solution of the given initial value problem 2 V1 y dx 1 dy 0 y 0 1 y sin y sin x 7 4

1 6 If the mean annual runoff of a drainage basin of 10 000 km is 140 m and the average an nual precipitation is 105 cm estimate the ET losses for the area in 1 year What are your assumptions How reliable do you think this estimate is

For each of the following series 1 decide if the series is arithmetic or geometric and 2 use the partial sum formulas to calculate the indicated sum 5 8 10 12 14 16 S23 6 3 6 12 24 48 Sas

13 Test Practice Which pattern shows 100 more Explain how you know A 1 456 1 556 1 656 1 756 5 832 5 833 5 834 5 835 B 4 987 4 887 4 787 4 687 6 001 7 001 8 001 9 001

1 8 The storage in a reach of river is 20 000 m at a given time Determine the storage 1 hr later if the average rates of inflow and outflow during the hour are 20 and 18 m s respectively

2 Find the quotient and the domain 2 9 x 3x x 6x 9 3x

The graph below illustrates the demand and supply for pizza The demand curve shows that some customers are willing to pay more for a pizza than others and the supply curve shows that some producers are willing to sell pizzas for less than others At what price is total surplus maximized Part 2 2 points Price 15 14 13 12 11 10 9 8 Pizza Market 8 5 8 8 8 8 6 3 3 3 3 3 3 3 5 8 Quantity transcript When total surplus is maximized consumer surplus is and producer surplus is See Hint

1 point Find the quadratic polynomial whose graph goes through the points 2 5 0 1 and 2 13

Write the number given below as a binary numeral 57 two

Find a polynomial of the form f x ax bx cx d such that f 0 3 f 2 3 f 3 7 and f 5 3 Answer f x

1 of the questions remains unanswered Let k h be unknown constants and consider the linear system 7x 6 31 6y 4z 7 5y 4z 3 26y hz k Note You can earn partial credit on this problem This system has a unique solution whenever h If h is the correct value entered above then the above system will be consistent for how many value s of k O A a unique value B no values C infinitely many values

18 What would you have to do to change 10 cubic feet into cubic inches OA Multiply by 1 728 OB Multiply by 46 656 OC Divide by 1 728 D Divide by 46 656

20 41 F equals how many degrees Celsius OA 5 C OB 9 C OC 56 C OD 5 C

7 What s the sum of 6 feet 10 inches and 8 feet 9 inches OA 15 ft 7 in OB 14 ft 7 in O C 15 ft 19 in OD 13 ft 19 in

9 Why does GDP underestimate the actual amount of output produced in an economy Percent 14 12 10 8 0 4 2 0 2 Year to Year Percentage Change in Nominal and Real GDP 1960 1980 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 Years Change Real GDP Change Nominal GDP

1 20 pts Graphically solve the equation and inequality below Sketch the graph s that you used and round your answers to two decimal places hundredths place a 6x 2x x 5x 1 y 2 0 0 142 0 0 5 D arithmetic when there is work to show Simplify and circle your final answers olve problems unless otherwise instructed Show the calculations lead Ana Her D 0 S 10 b 6x 2x x 5x 1 1 5 V value x axis 1 321 0 2 341 0 2 5 x 0 162 1 321 2 3 the solution given equation on y 0 142 X 1 321 x 2 341 C The solution given equati aut x 0 16 1 3

nal homogeneity The one dimensional Navier Stokes eqn takes the form dw dw w dz t Cop dz 4 PO where w p P H g are the velocity pressure density viscosity and gravitational acceleration respectively t z are time and z coordinate which is chosen in the opposite direction of gravity Dimensional homogeneity of an equation requires each term in an equation having the same dimension 2 1 Express dimension of the coefficient C in terms of M L T 2 2 Verify that dimensional homogeneity is satisfied by the equation check each term and make sure they all have the same dimension

A car recently sold for 32 345 If there s a 6 sales tax on automobile sales how much tax will be added to the price of the car A 941 07 OB 34 285 70 OC 1 940 70 OD 194 70

10 What is 36 39 in simplest form O A 12 13 O B 36 39 O C 1 3 O D 13 12

Sketch the graph of the equation below 2 1 2 4 7 6 5 4 3 2 Clear All Draw 6 S 4 3 2 1 7 2 3 1 2 3 4 5 6 7 AVO 4 5 6 7

Task 2 Taylor Series Expansion Order for a Constant Step Size For the following function f x 0 5x 2x 2x 1 Calculate an approximation of the function at x 1 using the value of the function and its derivatives at x 0 for increasing orders of the expansion Fill out Table 3 by hand by calculating the approximation of the function the true error truncation error and the approximate error Table 3 Increasing order of Taylor series approximation Order n 0 1 2 f 1 1 000 0 500 0 0 500 Et 0 500 E a Undefined

Q 3 Using a method of this section or separating variables find the general solution If an initial condition is given find also the particular solution and sketch or graph it 1 y y x y 2 2xyy x 1 y x ex set y z 3 y 1 6ey 2x

ts eBook Hint Print eferences Required information Specific Identification Date January 11 Determine the cost assigned to ending inventory and to cost of goods sold using FIFO Perpetual FIFO Cost of Goods Sold Cost per unit January 10 January 20 Total January 20 January 25 Weighted Average Total January 25 FIFO Goods Purchased of units LIFO Cost per unit of units sold Cost of Goods Sold of units 155 at Inventory Balance Cost per unit 8 00 Inventory Balance 1 240 00

Problem 3 47 LO 1 3 7 Terri age 16 is a dependent of her parents During 2023 Terri earned 5 200 in interest income and 3 000 from part time jobs Click here to access the 2023 tax rate schedule a What is Terri s taxable income b How much of Terri s income is taxed at her parent s rate At her rate c Can the parental election be made Why or why not The parental election be made because Terri s income solely from interest and dividends

i need help with determining the formula to get the values for x and y to plot the graph 4 You ve decided to start saving money for the down payment on a car In doing so you decide to save 20 10 every week Each week you record the amount that you deposit see table below Week 1 2 3 4 5 6 7 Amount S 19 87 25 77 12 30 15 89 27 88 23 10 19 55 Total S 19 87 45 64 57 94 73 83 101 71 124 81 144 36 Week 8 9 10 11 12 13 14 Amount S 12 66 29 33 26 10 24 15 15 85 23 14 20 10 Total S 157 02 186 35 212 45 236 60 252 45 275 59 295 69 Using Excel construct a plot days on the x axis and total savings on the y axis Right click on one of the data points in your plot left click on add trend line and check the box that says display equation on chart Using this y mx b equation that is displayed on your plot estimate how much money you will have saved after two years three years and four years Assume 365 days per year i e non leap years Approximately how much money per day will be saved based on this projection Approximately how many days will it take for you to save 1 000

when compared to the interest on 5 000 over 10 years at 2 compounded semiannually Your answer How much interest would 2 000 earn compounded annually in two years at the rate of 1 2 Your answer Kings Park Bank is advertising a special 1 66 APR for CDs Kevin takes out a one year CD for 24 000 The interest is compounded daily Find the APY for Kevin s account Your answer 1 pol 1 poin

Find the numeral preceding and succeeding each of the following numerals Use T as the digit for 10 a 530 b 100000

Factor out the GCF from the given polynomial 36x 2