Linear Algebra Questions and Answers

When you were a baby your parents started a college fund for you Now that you attend college you are able to use those funds to reduce your tuition however you are on your own in terms of books and food By the end of Fall Quarter you have charged 1 300 worth of food and school supplies on your credit card which has an annual interest rate of 16 99 Assume that you only pay the minimum payment of 3 per month or 25 whichever is greater and also that you make no other purchases with your credit card a Set up an amortization table to show the month by month history of your balance Paste the first five months of the table into the pace below 3 points b How many months will it take you to pay off your balance Type your answer in the space below 1 point c How much interest will you pay Type your answer in the space below 1 point

Solve the given initial value problem X t X 1 2 1 N H X X 0 N6 2

What is the truth value of the compound proposition below FV FOT O True False

Please state your Question 2 6 points Consider the series 3k k 1 reasoning along with all tests that you are using to answer the following questions a Does the series converge

1 10 points Compute the derivative Here In t log t de SMG2 4 1 dx cos 2y 1 Vy cos 3y 3 dy

Solve for x t i t x 7 3 0 x 7 x 1 2 1 3 x 2

Assume n is a positive integer Our goal is to find a power function g n n such that the algorithm below is O n x 6 for i 1 to n for j 3 to 3i x x i j next j next i 1 Start by counting the number of operations performed in the inner loop This total will depend on i In each iteration of the inner loop The inner loop runs operations are performed times so the total number of operations performed in this loop is 2 With the information above we can count the number of operations the overall algorithm computes In ith iteration of the outer loop operations are performed This total depends on the value of i To get the total number of operations we need to add up the number of operations performed for each value of the total number of operations performed in this loop is That is

A selection rule takes three inputs i the number of reserved seats R and unreserved seats U ii the set of applicants and a list of which are eligible for reserved seats and iii a priority ordering of applicants From this it must output a set of applicants to select Say that two selection rules are equivalent if for every possible inputs they produce the same output Say that two selection rules are equivalent under condition C if for every inputs satisfying C they produce the same output Consider the selection rule defined by the following procedure similar to that used in Chile 1 Tentatively accept the R U highest ranked applicants 2 If the set of tentatively accepted applicants includes fewer than R reserve eligible applicants replace the lowest priority tentatively selected applicant who i NOT reserve eligible with the highest priority reserve eligible applicant who is NOT tentatively selected 3 Repeat step 2 until at least R reserve eligible applicants are tentatively selected Call this the minimum guarantee rule as it ensures that at least R reserve eligible candidates will be selected while having no effect if more than R reserve eligible candidates would have been selected naturally Let condition C be the condition that i there are more total applicants than total seats and ii there are more reserve eligible applicants than reserved seats Which of the following is correct The minimum guarantee rule is equivalent under condition C to the over and above rule The minimum guarantee rule is equivalent under condition C to the exemptions first rule The minimum guarantee rule is equivalent under condition C to both the over and above rule and the exemptions first rule The minimum guarantee rule is equivalent under condition C to neither the over and above rule nor the exemptions first rule

Consider the following function 1 y 24 What is the domain of the function O Domain is all real numbers except 1 Domain is all real numbers except 4 O Domain is all real numbers except 4 Domain is all real numbers except 0

ght of 64 feet Use the interactive figure to find your answer Use the left and right arrow keys to move along a slider as needed Click here to launch the interactive figure t seconds Type integers or decimals Use a comma to separate answers as needed Domain and Range Height of a Baseball 120 height 110 100 90 80 70 60 50 40 A baseball is hit from a height of 36 feet at 64 feet per second Find the height function the maximum height and the domain 30 f t 16 64

Write the quadratic equation in standard form 32 32 9 2

Find the slope and the y intercept of the line with the given equation 5 y x 2 The slope is m The y intercept is 5 9 Type an integer or a simplified fraction Type an integer or a simplified fraction

Begin by solving the linear equation for y This will put the equation in slope intercept form Then find the slope and the y intercept of the line with this equatio 2x y 7 The slope is m Simplify your answer Type an integer or a fraction ELLERN

etermine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at 3 2 1 6 7 5 and 6 2 5 Volume 0

6 Recall the defining rules for elements x y and z in a Boolean Algebra B i e that a Identity There exist elements 0 1 B such that for every x E B we have x 0 x xo1 x b Complement For every x E B there is a unique element EB such that x x 1 xox 0 c Commutativity For every x y E B we have x y y x xoy yox d Distributivity For every x y z E B we have xo y z xoytroz x y o x 2 x yoz Use these rules to show the Idempotent Rules for any x E B i e

Question 40 The quadratic function y f z has the graph shown 63 k 5 m N 1 3 4 3 16 M 6 1 23 456 Which of the following is true about the discriminant of f x The discriminant is undefined The discriminant is zero The discriminant is negative The discriminant is positive Next Question

Exam circle graph to answer the question A library clas he the number of science fiction DVDs

The fractional reserve characteristic of the banking system allows banks to create money and also create wealth from bank deposits Describe why this statement is or is not true

Solving Quadratic Equations with Complex Solutions Solve the quadratic equation 5x 60 260 0 by using the Quadratic Formula Steps 1 Write the equation in Standard Form 2 Identify the coefficients a b and c 3 Substitute the values into the quadratic equation b b 4ac 2a 4 Solve the equation for an and 54 b b 4ac 2a 3 Exact Form b b 4ac 2a 5 Write your answers in Exact Form 6 Note If only one solution exists I will equal DNE or 60 260 0 22 Exact Form

5 M A 3 2 1 TH 5 5 4 3 2 1 P 2 3 4 5 64 1 CO 2 3 456 apn shown Which of the following is true about the discriminant of f x The discriminant is positive The discriminant is zero The discriminant is negative The discriminant is undefined

2 13x 40 0

y 6x 3 and y 10x 5 the overall solution set

A coin sold for 259 in 1979 and was sold again in 1986 for 434 Assume that the growth in the value V of the collector s item was expon a Find the value k of the exponential growth rate Assume V 259 k Round to the nearest thousandth b Find the exponential growth function in terms of t where t is the number of years since 1979 V t c Estimate the value of the coin in 2012 Round to the nearest dollar d What is the doubling time for the value of the coin to the nearest tenth of a year years Round to the nearest tenth e Find the amount of time after which the value of the coin will be 3451 years

A wooden artifact from an ancient tomb contains 45 percent of the carbon 14 that is present in living trees How long ago was the artifact made The half life of carbon 14 is 5730 years Round your answer to the nearest year The artifact was made years

5 860 6 33 000ft 300 and 33 000 ft 6 25 mi so l 62 65mi 6 Graph the approach path if the conditions stated in Problem 5 are satisfied P x 1U 2 33 000 x 3 33 000 62 65

Extra Practice X and Y intercepts Find the x and y intercepts and graph the line Your x and y intercepts MUST be written as a point 1 4x 5y 20 3 2x y 4 AM Name 44 2 2x y 2 4 x 2y 8 2

A certain field is a rectangle with a perimeter of 868 feet The length is 170 feet more than the width Find the width and length of the rectangular field The width is The length is DERECH

25 27 23 21 16 18 12 2 10 5 45 50 37 16 20 22 24 26 20 28 28 46 27 28 M 27 44 35 13 12

ar 3 9 864 24 24 11 14 M J ALKJ 2x 17 A 11 2 K ASRO 2 17x 28 40 10 22 65 N 12 S E 30 B 54

A street light is at the top of a 14 ft tall pole A woman 6 ft tall walks away from the pole with a speed of 5 ft sec along a straight path How fast is the tip of her shadow moving when she is 35 ft from the base of the pole ft

ework 10 3 A rectangular field is two times as long as it is wide If the perimeter of the field is 330 yards what are the field s dimensions The width of the rectangular field is 55 yd The length of the rectangular field is yd yd yd Part 2 of 2 yd

Evaluate the expression for x 2 6 x 3 6 x 3

Question 19 2 2 57 equation of the line satisfying the given conditio 3 4 and parallel to 6x 2y 3 ation of the line is y your answer C

3 Write the following in a b form 27x 27x 81 8 256 2 16x4 24x

Answer the following questions 1 Simplify the function below using a three variable K Map F A B C 0 2 3 4 5 6 2 Simplify the function below using a four variable K Map F w x y z 0 2 8 9 10 12 13

Problem 4 Graph the Quadratic Fur 5 4 3 2 1 3 2 O 2

The factorial form of multiplying the natural numbers 9x8x7x 6 is A C 1 71 B E 8 B 91 D 5 9

a inve A PIL ater company charges homeowners based on how much water se in thousands of gallons The company progressively charges at gher rate the more water that is used 2000 gallons of water costs onal Radiost 7000 gallons of water costs Based on the graph at the right how much does the city charged when a home owner uses the following number of gallons of water 1700 gallons of water costs Cost of Water Bill dollars Gravity Hol

L Complete ordered pairs fo the equation 3x 5y 15

Find f x and g x such that h x fog x x 7 7 h x

Solve for x by writing the equation in exponential log 3x 10 2 X

Convert the given unit of weight to the unit indicated 5 dg to mg

Use a calculator to convert the angle to a decimal in degrees 44 27 13

To go with the animals sold you want to include a trivia booklet about each animal One interesting bit of information you want to include with the polar bear stuffed animal is how fast their fur grows You know that it grows at a rate of 1 x 10 miles per hour 7 How much longer will the fur be after 100 hours Don t forget units 3 points a Length in scientific notation in miles b Length in decimal notation in miles 8 How much longer will the fur be after 1 week Don t forget units 3 points a Length in scientific notation in miles b Length in decimal notation in miles

Espa ol Suppose we want to choose 7 letters without replacement from 9 distinct letters a How many ways can this be done if the order of the choices is taken into consideration 0 b How many ways can this be done if the order of the choices is not taken into consideration 0 X

1 point Let x 6 2 and y 1 3 Find the following vectors

2 Determine the exact equation for the graph below 2 0 0 8 1 0 2 0 Zero order 1 Zero order 2 Zero order 3 Degree of f x Point on f x Family of f x Function is Even Odd

A fifteen 15 year 8000 CD through Bank X pays 4 96 interest compounded weekly A fifteen 15 year CD that pays 5 interest compounded annually is available at Bank Y Explain which bank maximizes your investment

A physician orders 9 teaspoons daily of a certain drug in three equally divided doses Refer to the appropriate entries in the table of English and Metric Equivalents for Capacity to convert given units to the unit indicated Complete parts a through d K Click to check the table of English and Metric Equivalents for Capacity a How many milliliters of the drug should be administered daily 45 Round to two decimal places as needed b How many cc of the drug should be administered daily Round to two decimal places as needed CIB

Use the unit fractions 5280 ft 1 mi Convert 25 mi to km 12 in 1 ft and 2 54 cm 1 in 25 mi km Type an integer or decimal rounded to five decimal places as needed