Functions Questions and Answers

K The exponential model A 98 8e0 018 describes the population A of a country in millions t years after 2003 Use the model to determine the population of the country in 2003 The population of the country in 2003 was million

6 5x 42 1x 934 The function f x models the pH level f x of a mouth x minutes after 144 eating food containing sugar The graph of this function is shown to the right Complete parts a through e 4 64 12 36 48 Number of Minutes after Eating 60 Question View e Use the graph to describe what happens to the pH level during the first hour OA The pH level starts at 6 5 then decreases rapidly for 12 minutes For the remainder of the hour the pH level gradually increases back toward 6 5 OB The pH level starts at 4 7 then decreases rapidly for 12 minutes For the remainder of the hour the pH level gradually increases back toward 4 7

A bacteria culture grows with constant relative growth rate The bacteria count was 784 after 2 hours and 117649 after 6 hours Answer the following questions 1 What is the relative growth rate Answer k 2 What was the initial size of the culture Answer Po 3 Find an expression for the number of bacteria after t hours Answer P t 4 Find the number of cells after 5 hours Answer 5 When will the population reach 1000000 0 Answer in hours t

Points 0 of 1 Suppose that v and w are unit vectors If the angle between v and i is a and the angle between w and i is use the idea of the dot product v w to prove the following equation cos B cos acos sin asin cos 0 V W Let 0 represent the angle between v and w Write an equation which relates this angle to the vectors Since these are unit vectors the v and w factors can be omitted from this equation Save Write the i and j components of v in terms of a Since it is a unit vector the v factor has been omitted V

Part 1 of 2 A minivan with a gross weight of 5100 pounds is parked on a street with a slope of 6 Find the magnitude of the force required to keep the vehicle from rolling down the hill What is the magnitude of the force perpendicular to the hill SELES Points 0 of 1 What is the magnitude of the force required to keep the vehicle from rolling down the hill pounds Round to one decimal place as needed Save Weight 5100 lbs

Given the right triangle below which of the following is equal to A A sin A B sin B C tan A D tan B b B 2

Part 1 of 3 a v w Simplify your answer For the following vectors a find the dot product vw b find the angle between v and w c state whether the vectors are parallel orthogonal or neither v 5i 2j w 21 5j Points 0 of 1 Sa

Let u 9i 4j v 3i j and w 7i Find 3u 2v w point s poss

Let v 5i 3j Find 3v point s possible

swer 2 Points f x 2x 4 3 and g x O No O Yes 3x 4 2

If the annual demand is 40 000 computers ordering cost is 1000 order and inventory holding carrying cost is 5 computer what is optimal order quantity based on EOQ Model Show your solution

Solve for Y s the Laplace transform of the solution y t to the initial value problem below y 4y 4y cos 6t sin 6t y 0 3 y 0 5 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms Y s

Let u 8i 4j v 6i j and w 8i Find 3u 2v w point s p

Find the Fourier series of fon the given interval 1 x 0 0 x 1 f x f1 F x 1 34 n 1 Give the number to which the Fourier series converges at a point of discontinuity of f If f is continuous on the given interval enter CO

Use the dot product to determine whether v and w are orthogonal v 2i 2j w i j Select the correct choice below and fill in the answer box to complete your choice O A The vectors v and w are orthogonal because their dot product is B The vectors v and w are not orthogonal because their dot product is

Solving A Pet for P we obtain P Ae rt which is the present value of the amount A due in t years if money earns interest at an annual nominal rate r compounded continuously For the function P 19 000e 0 04t in how many years will the 19 000 be due in order for its present value to be 17 000 In years the 19 000 will be due in order for its present value to be 17 000 Type an integer or decimal rounded to the nearest hundredth as needed

Given the vectors 2 5 and t 8 3 find 5s and s t Write your answers in component form 5s 0 0 s t 00 X

5 The yearly budget for a family of four living in Austin Texas is shown below Yearly Budget Family of 4 Austin 11 500 6 750 4 800 9 250 6 150 5 500 4 375 1 950 Rent Mortgage Transportation Childcare Food Mon Utility Bills Insurance Taxes Clothing Which equation can be used to determine m the money a family must earn to meet the requirements of this budget for one bolesc cea feric month F m 50 275 8H m 50 275 12

A town has 13 police officers to be apportioned among 3 precincts based on the population of each precinct The populations for the years 1998 and 1999 are given in the following table Precinct 1 2 3 1998 Population 930 738 415 1999 Population 975 750 421 Does the population paradox occur using Hamilton s method of apportionment OYes O No

Irvine Valley College is hiring a new public relations director The hiring committee ranks the four candidates A B C and D according to the preference table below Suppose the Borda count method is used to determine the winner Determine whether the majority criterion is satisfied Number of Votes First Second Third Fourth 2ABCD Yes TBCDA Is the majority criterion satisfied 3 B D C A 3ABDO

RoldGold pretzels are sold in bags of 16 ounces Actual weights vary slightly from bag to bag and are normally distributed with mean A consumer advocacy group wants to see if there is any evidence that the mean weight is less than the advertised and so intend to test the hypotheses Ho 16 H 16 A Type I error in this situation would mean O concluding that the bags are not being underfilled when they actually aren t concluding that the bags are being underfilled when they actually aren t O concluding that the bags are not being underfilled when they actually are concluding that the bags are being underfilled when they actually are Page 9 of 10

Suppose a closed economy has an intended investment of 150 and an aggregate consumption function given by C 200 0 75Yd Suppose also that the government spends 150 but collects no taxes What is equilibrium output and income round your answer to the nearest whole value Your Answer

Submit cosx 7 sinx If the curve passes through the point pi 6 2

1 point The pressure P in pounds per square foot in a pipe varies over time Two times an hour the pressure oscillates from a low of 90 to a high of 280 and then back to a low of 90 The pressure at time t 0 is 90 Let the function P f t denote the pressure in pipe at time minutes Find a possible formula for the function P f t described above f 1 help formulas

3 Consider the function f x e 1 2 2 2 Show that x 0 is a zero of f What is the multiplicity Implement the modified Newton s method to calculate the root with tolerance 10 10 Now use the usual Newton s method and try to compute the root with same tolerance Describe your results do you have convergence Why You can use as initial point xo 1

7 9 59 19AM the quadratic equation in standard form x 6 3x 2

1 Implement the secant method Apply the secant method to f x 2 cos x 0 for at least 30 iterations What do you get Explain your with Po 1 and pi results

What Amendment made it illegal to charge a poll tax to vote O 15th Amendment O 22nd Amendment O 24th Amendment 36th On at

apportionment using Webster s method with the standard divisor Hotel C Number of rooms 163 A 306 Hotel Number of apportioned surfboards Type a whole number Hotel Number of apportioned surfboards Type a whole number Hotel Number of apportioned surfboards B 213 A 10 B 7 Total 682

A large hotel chain needs to apportion 22 new surfboards for its visitors to rent among three hotels based on the numbers of rooms in each hotel as shown below Determine each hotel s apportionment using Webster s method with the standard divisor Hotel Number of rooms A 306 Hotel Number of apportioned surfboards Type a whole number B 213 A C 163 Total 682

A gas station stores its gasoline in a tank under the ground The tank is a cylinder lying horizontally on its side In other words the tank is not standing vertically on one of its flat ends If the radius of the cylinder is 2 5 meters its length is 6 meters and its top is 3 meters under the ground find the total amount of work needed to pump the gasoline out of the tank The density of gasoline is 673 kilograms per cubic meter use g 9 8 m s Work include units

Scores on the GRE Graduate Record Examination are normally distributed with a mean of 506 and a standard deviation of 134 Use the 68 95 99 7 Rule to find the percentage of people taking the te who score between 238 and 774 The percentage of people taking the test who score between 238 and 774 is This

Find the range of the data set represented by the graph O 70 75 80 85 The range of the data set is 90 95 100 e Simplify your answer

Find the system of linear inequalities that corresponds to the system shown 12x 7y Select 3x 9y Select 9x 2y Select x y x y Additi 10 12x 7 y 20 10 8 6 4 20 8 6 20 63 44 N 2 4 4 6 8 10 3x 9y 3 4 X 9x 2y 44 8 10 Find all the corner points of the feasible region Order your answers from smallest to largest x then from smallest to larg x y smallest x value largest x value 6

Graph the solution set 3x 2y 18 No Solution Help 2 1 A 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 2 1 2 3 4 5 6 7 8 9 10 11 12 12 13 14 15 16 17 18 13 14 15 S Fill WebAssign Graphing Tool Graph Layers After you add an object to the gra can use Graph Layers to view an properties

Consider the equation and identify the center and radius 2 y 3 14 Center Radius

3r 2 Find the arc length of the bold arc O 84 1 37 9 75 4 16 ft 55 8

8 Determine the factors of 2x 11x 14 a 2x 7 x 2 b 2x 7 x 4 c 2x 4 2x 2 d 2x 11 x 14

4 The x intercepts and vertex of the quadratic relation y x 3 x 5 are a x intercepts are 3 and 5 vertex is 4 63 b x intercepts are 3 and 5 vertex is 4 1 C x intercepts are 3 and 5 vertex is 4 0 d x intercepts are 3 and 5 vertex is 4 9

Which equation below has an phase shift of 23 Oy 2 sin x O y sin x 2 y sin x x O y sin x 2

Select the answer for each question below 88 cos 64 isin 64 4 cos 45 isin 45 15 A22 cos161 isin 161 11 352 cos 109 isin 109 C 22 cos19in 19 D 22 cos 19 isin 19 E 84 cos19 1sin 19

6 A firefighter is standing on top of a building 19 m high holding a firehose 1 m above the top of the building She finds that if she holds the hose horizontally the water flows from it at 15m s As this happens the water hits an adjacent burning building at a height of 14 m above the ground The gravitational acceleration constant is 9 8 m s What is the horizontal distance from the firefighter to the building The additional parts on the next page guides you through one possible way of solving this problem Firefighter problem a Do we need to use a vector valued function that is 2 D or 3 D b What is the acceleration function for the stream of water t e Find the initial velocity the velocity function the initial position and the position function for the stream of water t d How long does it take the water to travel from one building to the other

Which wave will cancel out the wave shown in the graph Select one a D amplitude mm O amplitude mm amplitude mm A stance mm estance hm K

From the list below select all universal generalizations of the statement a 1 then a 1 for all a ER VxER x 1 x 1 0x 1 Let P x x 1 Q x x 1 Domain of x is a set of all real numbers Vx P x Q x vx x 1 x 3 3 1

cos 40 miles Question 7 8 33 points Law of Sines Determine the approximate measure of segment h H 6 cm T 7 81 cm 7 37 cm 7 42 cm 8 12 cm I 5 cm 54

Basic Trigonometry Determine the approximate value of e D 8 20 6 22 0 68 0 4

y 4 sin 3x 3 Find the period and the amplitude of the graph of the function 2x 3 period amplitude 4 x y Excellent job Consider one cycle beginning on the y axis Divide the cycle into four equal parts to obtain the five distinct key points over the interval see this example State these five key pain smallest x value in l That s right x

Find f 4 for the recursive function if f n is defined recursively by f n 1 f n 2f n 1 f 0 1 1 3

Choose a recursive definition of the following sequence an n 1 2 3 An 5n an 1 an for n 1 and a 5 an 1 an 5 for n 1 anda 6 Oan 1 5an for n 1 and a 5 an 1 an 5 for n 1 and a 1 5

Given the following vectors Perform the indicated operations u 3 1 v 3 2 U VE U V 2u 3v 3u v