Functions Questions and Answers

3 Evaluate the integral by converting to polar coordinates 7 points 1 1 x lou pawens 00 cos x y dy dx

5 Use spherical coordinates to integrate f x y z x y2 z over the solid between the spheres x y z 1 and x y2 z 4 7 points

Purchases transactions Bowers Company purchased merchandise on account from Saunders Corp for 10 200 terms 1 10 n 30 Bowers returned merchandise with an invoice amount of 1 500 and received full credi a If Bowers Company pays the invoice within the discount period what is the amount of cash required for the payment If required round the answer to the nearest dollar b What account is debited by Bowers Company to record the return Accounts Payable Saunders Corp Accounts Receivable Cash Merchandise Inventory Purchases Sales Sales Returns and Allowances

bok int int ences Express the following comparative income statements in common size percents Using the common size percents which item is most responsible for the decline in net income Complete this question by entering your answers in the tabs below Income Statement Reason for Decline in Net Income Express the following comparative income statements in common size percents Note Round your percentage answers to 1 decimal place Sales Cost of goods sold Gross profit Operating expenses Net income GOMEZ CORPORATION Comparative Income Statements For Years Ended December 31 Current Year Current Year 740 000 565 400 100 0 174 600 129 200 45 400 Income Statement Prior Year 640 000 280 000 360 000 258 800 101 200 Prior Year Reason for Decline in Net Income Check my

Book Hint rint rences Common size and trend percents for Roxi Company s sales cost of goods sold and expenses follow Sales Cost of goods sold Operating expenses Change in Net Income Net Income Common Size Percents Sales Cost of Goods Sold Operating Expenses Net Income Current Year 100 0 63 2 14 3 Determine the net income for the following years Did the net income increase decrease or remain unchanged in this three year period Complete this question by entering your answers in the tabs below Trend Percents 1 Year 2 Years Current 1 Year 2 Years Year Ago 104 78 103 5 116 3 111 0 106 3 101 3 Ago 100 0 61 0 13 8 Current Year 104 700 66 284 15 033 23 383 Determine the net income for the following years Assuming sales were 100 000 2 yrs ago what is net income in each year Note Enter all amounts as positive values Ago 100 0 56 9 14 1 1 Year Ago 101 159 61 780 13 979 25 400 no In Net Ingeme Ago 100 0 100 0 100 0 2 Years Ago 100 000 56 900 14 100 29 000

3 The height h in meters of a springboard diver above the surface of the water t seconds after the leave the board is given by h t 4 9t 8 8t 3 Determine the diver s maximum height above the springboard

Write the following functions in vertex form State if the vertex is a minimum or maximum 1 y x 10x 6 2 y 2x 12x 16

md Starting with the 3 scores 10 20 and 30 what 2 additional scores must be included to create a set of 5 scores that has a median of 28 and one mode Write your answers joined by the word and such as 100 and 150 A

K Use the given graph to find the mean median and mode of the distribution Find the mean Select the correct choice below and fill in any answer boxes in your choice A The mean is 8 3 Type an integer or a decimal B There is no mean for this distribution Find the median Select the correct choice below and fill in any answer boxes in your choice OA The median is Type an integer or a decimal B There is no median for this distribution C

The manager at a coffee shop counted the customers once each hour over a few busy weekends The results she obtained are summarized in the bar graph to the right use it to answer parts a through d a What was the largest number of customers in the coffee shop and how often did it occur The largest number of customers was 12 It occurred 2 time s b What was the most frequently occurring nonzero customer count The most frequently occurring nonzero customer count was 6 c For how many hours were the customers counted hours C Frequency 11 11 0 1 2 3 4 5 6 7 8 9 10 Number of Customers

If the mean median and mode are all equal for the set 40 80 70 90 x find the value of x X Simplify your answer Type an integer or a decimal

How many ways can you get exactly 1 tail Construct a tree diagram Choose the correct diagram below OA Begin Quarter Dime Nickel H H H H Penny H T T T H T H H T There is are exactly Type a whole number H H H PNDQ HHHH HHHT HHTH HTTH HTTT THHH THHT THTH THTT TTHH H H TTHT T H TTTH TTTT way s to get 1 tail HHTT HTHH HTHT OB Begin Nickel H Penny H T T Dime H T H H Quarter H V V V V V V H T H HTH H T PNDQ HHHH THHH HTHH HHTT HHTH THTH HTTH HTTT HHHH HTTH THTH THTT TTHH THTT TTTH TTTT O C Begin Nickel H Penny H H Dime T T H T Quarter H V V V V V V V V H 7 T H T H T H H T PNDQ HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT

4 16 Two soybeans are impacted against a steel surface Assume the impact is elastic and obeys the Hertz equations for contact between two solids This assumption is not valid Nevertheless insight can be gained by doing the analysis The equivalent radius of the first soybean is 0 251 cm and during the impact the maximum force reached is 22 1 N The equivalent radius is the radius of a sphere which has the same volume as the soybean The second soybean has an equivalent radius of 0 325 cm and during impact the maximum force reached is 37 0 N Assume the soybeans have the same modulus of elasticity 18 54 MPa and a Poisson s ratio of 0 35 For each soybean calculate the maximum normal stress developed during impact on the steel surface The maximum stress will develop at the point on the soybean where contact is first made between the soybean and the steel wall Compare the stresses experienced by the two soybeans Solution hints Assuming the soybeans are spherical calculate the radius of the contact circle a b from the force F and radius of the soybeans Then calculate the maximum contact stress Repeat the procedure for both small and large soybeans You will find that the stresses imposed on small and large soybeans are almost identical

Consider the strategy we introduced about adaptive error control which uses two different methods of different order with the same step size Assume we use Euler s method to get w and midpoint rule to get u to approximate y that solves y y t 1 with y 0 0 5 and h 1 simultaneously a Compute w and by the two methods b Assuming the desired local truncation error is 0 1 compute the largest q so that qh for Euler s method can approximately ensure that the local truncation error is smaller than 0 1 Point out whether the current step size is acceptable or not You do not need to consider the case that there is an extra factor 2 in the definition of q hint recall the expression for q in Lec 7 and choose n 1

Farmers wishing to avoid the use of purchased seeds are increasingly concerned about inadvertently growing hybrid plants as a result of pollen drifting from nearby farms Assuming that these farmers raise their own seeds the fractional portion of their crop that remains fr hybrid plants t years later can be approximated by P t 0 98 a Using this model predict the fractional portion of the crop that will be free of hybrid plants 5 yr after a neighboring farm begins to use purchased seeds b Find P 5 and explain its meaning c When will half of the crop be hybrid plants a After 5 yr 90 of the crop will be free of hybrid plants Round to the nearest integer as needed b P 5 Round to one decimal place as needed

Find the derivative of the following function A 870 1 620 Type an exact answer

Differentiate g x 3 7x 2

1 5 pts Graph one continuous function f x such that all of the following hold a f x is increasing on 2 f x is constant on 2 4 C f x is decreasing on 4 6 d f x is increasing on 6 0

12 Consider f x x 4x and g x x 2 a 3 pts Find f g x Simply your answer b 3 pts Find g x f x c 4 pts What is the domain of Use interval notation

11 Consider the function f x 881 x 6265 x 549 x 22196 x 268 a 3 pts The degree of f x is b 3 pts List the zeros of f x MIDDLESEX Fill in the blanks with either co or 00 c 2 pts As x o f x d 2 pts Ax 100 f x EGE

3 Given f x 2x 3 x 5 x 2 answer the following questions a List the zeros of the function b What is the degree of f x c As x o f x d As x o f x IDDLESEX

11 Consider the function f x 881 x 6265 x 549 x 22196 x 268 a 3 pts The degree of f x is b 3 pts List the zeros of f x MIDDLESEX Fill in the blanks with either co or 00 c 2 pts As x o f x d 2 pts Ax 100 f x EGE

Ing functions in vertex form State if the vertex is a minimum or maximum 1 y x 10x 6 2 y 2x 12x 16 520 3 y 3x 6x 5 5 y x 2x 3 7 y 4x 24x 15 4 y x 12x 15 6 y 2x 16x 11 8 y 5x 100x 300

6 A bullet fired vertically and will have its height h in meters after t time in seconds given by h t 80t 5t a At what time did the bullet reach the maximum height b What is the maximum height the bullet will reach c What is the height of the bullet after 5 seconds d After how many seconds will the bullet hit the ground el When is the bullet at a height of 240m

1 For the following functions state the domain a b d 7 5 2 6 3 9 6 8 8 8 f 04 i g j C 00 02367 on or not e 1 2 8 2 1 5 7 8 2 8 h k

8 A robotic submarine is programmed to quickly film a small area of the ocean floor The program a course set to follow the equation d t 5t 75t 70 where d represents the depth belov the surface in meters and t is the time in minutes a Find the depth of the submarine after 10 seconds b How long will the submarine be under water c At what time s is the robotic submarine at 100m Round to 1 decimal place d At what time does the submarine reach the maximum depth e Find the maximum depth the sub is programmed to reach

P 1 91 0 51 where I is the current in amperes a What value of the current will produce the maximum power b What is the maximum power by a battery is given by the formula 5 A computer software program is sold to students for 20 each A formula that represents the aliment revenue R dollars for an x dollar increase in price is R x 6x 180x 6000 a Calculate the increase in the price of the computer software that produces the maximum revenue DY What is the maximum revenue

9x 8 3x 2 8 pts f x 2 pts f 0 7 Consider f x a b and find e

5 Consider the function f x 6x5 5x 4x 3x 2x 1 and answer the following questions a 1 pt State the Remainder Theorem b 4 pts Use the Remainder Theorem to determine the remain when f x is divided by x 1 Don t forget to show your w

5 5 pts Find all zeros of the function f x 16x 48x 25x 7 factoring Algebraic solutions only

4 10 pts Let f x 5x 4x 2 Find f x h f x h

2 Consider f x x 2 x 5 a 2 pts Find the domain of f x Give your answer in interval notation 2 pts State any vertical asymptotes Remember vertical asymptotes should be written as an equation of a line e 2 pts State any horizontal asymptotes Remember horizontal asymptotes should be written as an equation of a line OLLEGE d 2 pts Find any x intercepts algebraically 2 pts Find any y intercepts algebraically

1 point Consider the digraph of a relation R shown below a How many ordered pairs are in the relation R b Which of the following ordered pairs are in the relation R Select Yes if the order pair is in R and No if it is not 2 2 1 3 3 2 3 1 3 5 2 4 2 5 5 5 5 6 4 3 7 5 1 8 4 4 9 4 2 10 4 1 11 1 1 12 2 2 5 3

Consider the data from the table showing the heights of 15 people at a family gathering 55 Create a stem and leaf plot using the first digit as the stem and the second digit as the leaf for each number Stems 3 4 5 6 17 I Leaves 8 27 0012458 2 56 How many people had a height under 5 feet 7 people had a bright under 60 inches 5 1 57 If we let A represent the set of names of all people at this gathering whose height is under 5 feet write that set using the roster method A Hannah Manuel Luigi Ava John Braxton Entensit 58 Give a verbal description of what would be meant by A in this situation A would be the complement of A This would be the people whose height is 60 mches or more Name Bob Bill Lisa Manuel Hannah Braxton Ava Jake Charlotte Nate Emmett John Mario Ben Luigi Height inches 72 65 60 42 38 55 51 64 62 68 57 54 60 61 47

The average monthly temperature changes from month to month Suppose that for a given city we can model the average temperature in a month with th following function f t 59 25 sin 70 6 In this equation f t is the average temperature in a month in degrees Fahrenheit and t is the month of the year January 1 February 2 Find the following If necessary round to the nearest hundredth Maximum average temperature in a month Fahrenheit Period off months Frequency of fcycles per month X S

ppose that a household s monthly water bill in dollars is a linear function of the amount of water the household uses in hundreds of cubic feet HCF When aphed the function gives a line with a slope of 1 55 See the figure below the monthly cost for 16 HCF is 46 17 what is the monthly cost for 13 HCF Monthly cost 46 17 in dollars 16 Water usage in HCF s X

fight pairs of species 16 species in all from Alabama Mississippi Tennessee Kentucky South Carolina and North Carolina and brought them all back to the lab In some species pairs the color patterns were very similar and in some they were very different For each species pair he put five males of both species and five females of both species in the same fish tank and observed their behavior for five hours He did this eight times once for each species pair for a total of 1 280 fish During the five hour observation period he recorded 1 how many times females mated with males of their own species or of a different species and 2 how many times males were aggressive towards males of their own species or of a different species He used these data to calculate an index of bias for each behavior to show whether individuals had stronger reactions towards members of their own species He used the following equation where A and B represent two different species and AxA represents how individuals in species A acted towards other members of species A index of bias AxA BxB AxB BxA AXA AxB BxA BxB Another way to write the same equation is index of bias events within species events across species total of events If the index of bias value is positive greater than zero this means that the behavior happened more often with members of the same species If the index of bias value is negative less than zero this means that the behavior happened more often with members from a different species Michael also measured color differences between each pair using digital pictures The larger the color difference score the more different the color pattern is between the two species Scientific Question In what ways do color pattern differences between different darter species influence female mating decisions and male aggression What is the hypothesis State Dr Martin s alternative hypothesis from the above text I

What is the rate of change 1 B X y 2 3 4 5 4 6 8 10

What is the rate of change 1 A Your answer 10 7 5 3 2 1 0 1 2 3 4 5 6 7 8 9 10 X

1 Determine the value of the function a f x x 11 at f 4 b g x 3x 2x 1 at g 5 2 Determine the value of x for each function a k x 5x 4 when k x 19 c h x 2 x 4 at h 3 b p x 7 3x when p x 9

5 Emma hits a golf ball off a tee The height of the ball is given by y 0 01x 0 5x 0 2 where y is the vertical height in yards above the ground and x is the horizontal distance from the tee in yards Round all answers to one decimal place a How far does Emma hit the golf ball

4 Solve the following quadratics using the quadratic formula Round to the nearest hundredths a 2m 7m 13 10 b 8x 4x 16 x c 2a 36a 0 Bird 3 d 8n 7n 15 7

Which of the following propositions over R are tautologies over R Select all that apply OA q x x B q z x 7 x 7 x 49 OC q z x 1 2 1 OD q z x 1 x 2x 1 OE q z x 0 Be able to justify your answers using truth sets

2 1 point Which relation best describes this graph ES

Use the following to answer questions 24 25 Figure The Supply of DVD Rentals Rental price of DVDs Rental price of DVDs 0 0 A K C Quantity per period S S Quantity per period A to o in panel A B p to q in panel B C s tot in panel D to v in panel D Rental price of DVDs A 7 to o in panel A B p to q in panel B C s to fin panel C Rental price of DVDs 0 0 B D Quantity per period S1 S 24 Figure The Supply of DVD Rentals Look at the figure The Supply of DVD Rentals A decrease in the price of DVD rentals would result in a change illustrated by the move from Quantity per period 25 Figure The Supply of DVD Rentals Look at the figure The Supply of DVD Rentals A decrease in the price of DVDs sold by movie producers to rental stores would result in a change illustrated by the move from

27 Important factors that can cause supply curves to shift include input prices technology and A consumer preferences B imports C taxes D demand

Correct The revenue function is given by R x x p x dollars where x is the number of units sold and p x is the unit price If p x 41 4 find the revenue if 16 units are sold Round to two decimal places

find the future value of the following 500 deposited two times year for 20 years interest is 6 per year compounded monthly

8 4 cm 3 cm 10 cm 7 cm

14 For each given domain and range draw one relation that is a function and one that is not a Domain x E R Range y E Rly 1 y X y X