Application of derivatives Questions and Answers

Suppose 7 4 7 4 and 7 6 6 and let g x f x cosx Find g 6 6 080 2 54 02 3 3 0 5 10 O 0 3 2 2 3 3 bo 7 6 g 6

value of x where the minimum occurs Use a comma to separate answer

Consider the Harris Todaro model applied to the Monocentric Model that we studied in Module 6 The urban income is y 15 000 The land rent is 3 000 r 3 000 commuting cost is 100 per mile 1 100 The city offers 30 000 jobs J 30 000 After solving the quadratic equation you learn that in equilibrium the population is 109 808 a In equilibrium what is the chance of getting an urban job b What is the implied unemployment rate in the city

A simple random sample of size n 1 080 is obtained from a population whose size is N 1 100 000 and whose population proportion with a specified characteristic is p 0 51 Describe the sampling distribution of p Round the standard deviation of the sampling distribution to three decimal places O A Exactly normal Hp 0 51 p 0 015 OB Approximately normal p 0 51 p 0 015 OC Approximately normal p 0 51 op 0 151 D Exactly normal p 0 51 p 0 151

A 22 ft ladder leans against a building so that the angle between the ground and the ladder is 81 How high does the ladder reach on the building ft

Find the absolute extrema if they exist as well as all

The number of cups of coffee sold at Lauren s Coffee House for each w shown in the graph at the right Consider the closed interval 1 5 and g absolute extrema for the interval a Identify each point as a relative minimum a relative maximum or ne At week 1 27 is a relative minimum At week 2 176 is a neither At wook 2 227 in a relativo maximum

3 The combined age and daughter is 55 age Give an examp

48 107 9844 D how much police tape is needed to tape off the entire area The search party is able to cover 200ft per hr If the sun goes down in 8 hrs do the police have en enough time to conclude their search

Curriculum 2 0 Honors Precalculus Unit 4 Topic 2 REVIEW Formative Assessment CALCULATOR REQUIRED 5 x t y 3t 1 y 3t 4 1 3t S 1 0 Name Emily Goncalves Date 3 23 2623 Period Graph the parametric equation Include an arrow to show the direction of motion x 5 3 cost y 4 3 sin t where 0 ts Circle radius 3 Center S x 5 2 cost y 1 4 sint where 0 t n circles ORadius Erite t 2 4

ucture com courses 676833 quizzes 10 Google Docs myMCPS Classroom Quiz Instructions Question 4 M

1 3 refer to the following scell A golfer hits the ball from the ground on one side of a 10 foot long pond at a 30 degree angle with an initial velocity of 110 feet per second He needs the ball to land on the green on the opposite side of the pond or else it will go into a lake on the other side of the green The green is 300 feet long before it ends at the lake 1 Write a set of parametric equations that represent the horizontal distance traveled by the ball and its height above the ground in feet as functions of the time in seconds since it is hit 4 16 1lo sin 30 Ho X 11 0 COS 30 t 3 Parame 2 To the nearest foot what is the maximum height of the golf ball 57ft Y 16 11o Sin 36 ttlo 3 Does the ball land on the green Justify your answer 110c03 30 t n 4 5 eliminate the parameter to write the set of parametric equations in rectangular form x 5t 3 y 6t 7 4 7 64 7 2023 Period 4 7 2

Barry and his wife Mary have accumulated over 3 million during their 42 years of marriage They have two children and four grandchildren How much will Barry and Mary remove from their estate if they gift the maximum amount possible in 2013 to their children and grandchildren without incurring any gift tax liability Total amount removed without any gift tax liability

3 Given the function a Find all critical points b Find all horizontal and vertical c Find all local max and local m d Find the intervals of increase a

Verify the following function satisfies the Mean Value Theorem and then find all values of c for f x x x 1 on 0 2 fe f 0 2 2 1 07 c 1 15 20 2 O F x 3x 1 0 3x 1 kembatan X 3 3 3

1 AGS Mux Find the absolute max min for F f 0 27 in for x 6x 5 on 3 5 F 5 2 20 F1 01 667 15 5 3 3 6 37 5 76

Attempts Average 3 1 Financial institutions in the U S economy Suppose Derrick decides to use 8 000 currently held as savings to make a financial investment One method of making a financial investment is the purchase of stock or bonds from a private company Suppose Arcadia a biomedical research firm is selling stocks to raise money for a new lab This practice is called finance Buying a share of Arcadia stock would give Derrick the firm In the event that Arcadia runs into financial difficulty will be paid first Suppose Derrick chooses to buy 250 shares of Arcadia stock Which of the following statements are correct Check all that apply The price of his shares will rise if Arcadia issues additional shares of stock Expectations of a recession that will reduce economywide corporate profits will likely cause the value of Derrick s shares to decline An increase in the perceived profitability of Arcadia will likely cause the value of Derrick s shares to rise Alternatively Derrick could undertake their financial investment by purchasing bonds issued by the U S government Assuming that everything else is equal a municipal bond issued by a state most likely pays a by an electronics manufacturer interest rate than a corporate bond issued

Score on last try 0 5 of 1 pts See Details for more Next question You can retry this question below Select all the residual plots that violate the conditions for li a b

I A 0 10 What is the minimum value of 0 on the interval 0 2 Hint After finding 0 make sure to write your trigonometric functions in terms of sin and cos 0 B 20 C 20 2 D 10 20 2 E None of the above

ohamed Salad Attempt 1 Question 4 0 833 points Listen Determine the area of the region bounde y cos x y sin 3x x 4

Determine the oblique asymptote of the graph of the function h x 4x 1 3 2x 9 The equation of the oblique asymptote is

any vertical al or oblique tes in the graph of State the domain of 12 8 T EID 17 11 I 4 U n I I I I I I T T 16 DO 12 16 20 Identify any vertical asymptotes Select the correct choice below and if necessary fill in the answer boxes to complete your choice A There is only one vertical asymptote Its equation is Type an equatic OB There are two vertical

es d Attempt 1 1 0 833 points n ine the area bounded by y x 2 to x 2

Consider the closed curve in the xy plane given by x 2x y 4y 5 Is it possible for this curve to have a horizontal tangent at points where it intersects the x axis Explain your reasoning

lad Attempt 1 on 6 0 833 points mine the area of the region bounded by the this parabola at 1 1 and the x axis 3

Salad Attempt 1 ion 3 0 833 points isten ch the region enclosed by the curves x 2 y 9 x x 2 an n correct to two decimal places

amed Salad Attempt 1 Question 7 1 point Listen Determine the number b such the curves y x and y C 2 3 that the lin 5 into t

S Attempt 1 2 0 833 points e the area bounded by y x to x 1

Consider the closed curve in the xy plane given by 2x y 4y 5 Write an equation for the line tangent to the curve at the point 2 1

Question 4 Instructor created question A Estimate the population at the beginning of the year 2019 ROUND TO THE NEAREST PERSON The population at the beginning of 2019 will be about 60 Points 0 of 1 At the beginning of the year 1995 the population of Townsville was 3983 By the beginning of ne year 2010 the population had reached 5331 Assume that the population is growing exponen ollowing 3 How long from the beginning of 1995 will it take for the population to reach 9000 ROUND TO 2 DECIMAL PLACES The population will reach 9000 about C In what year will did the population reach 9000 The population will or did hit 9000 in the year years after the beginning of 1995 5 points

For the function f x 2x 3x 3x 4 find f x Then find f 0 and To find f x first find f x f x Find f x Find f 0 Select the correct choice below and if necessary fill in the a OA f 0 OB f 0 is undefined Simplify your answer

Write the equation of a sine function that has the given characteristics The graph of y xl shifted 9 units to the left Oy kx 91 Oy kxl 9 Oy kxl 9 Oy x 91

The graph of y x2 shifted 9 units downward Oy 9x Oy x 9 Oy x 9 Oy

You are selecting an advisory board of four people to oversee Hennepin County s management of services to support people experiencing homelessness You have interviewed each candidate and based on this have ranked them based on whom you would most like to see on the board However in addition to your feelings about individual candidates would like to ensure that the board has at least two women on it and at least one person with lived experience meaning that they have been homeless themselves at some point in their life You may assume that among your applicant pool there are at least two women and at least one person with lived experience so that your goal is achievable You are considering the following method of selecting candidates 1 Select the highest ranked woman with lived experience if one exists 2 a If you selected a candidate in step 1 select the highest ranked woman remaining 2 b If you did not select a candidate in step 1 select the highest ranked person with lived experience AND the two highest ranked women 3 Select the highest ranking remaining applicants until you have a total of four committee members Is this choice function guaranteed to be substitutable no matter who applies and how you rank them Explain your answer using examples if needed Your explanation should demonstrate a clear understanding of the meaning of substitutability in this context

main abc func a ab n N sin If tan 0 COS tan a sin 0 equals B cos 0 equals TU 24 0 7 9 7 8 1 0 DEG 0 0 5 I 2 9 6 2 3 ans then X clea

What is the annual growth rate of P t 50 1 62 t where t is given in years as a percent Be sure to show all your work

At the beginning of an experiment a scientist has 300 grams of radioactive goo After 90 minutes her sample has decayed to 9 375 grams What is the half life of the goo in minutes Round to one decimal place The half life of the goo is 0 039 Find a formula for G t the amount of goo remaining at time t G t X How many grams of goo will remain after 80 minutes Round to one decimal places There will be 13 25 minutes X grams of goo after 80

26 arginal Revenus of a Commuter Air Service Will he following function where R x is measured in dollars ar R x 6 400x 80x a Find the marginal revenue R x

Use a numerical integration routine to evaluate the definite integral below to three decimal places 1 1 1 8 4 3x dx 10 8 dx 4 3x 1 Round to three decimal places as needed

Rule Salad Attempt 1 tion 4 0 5 points Listen company has set up a production line to manufacture a new dx 5700 dt duction of these calculators after t weeks is culators per week Production approaches 5 700 per week initial production is lower because of the workers unfamili chniques Determine the number of calculators produced fro e third week to the end of the fouth week 8677 SER

A virus is spreading across an animal shelter The percentage of animals infected after t days 100 is given by V t 1 99e 0 139t A What percentage of animals will be infected after 13 days ROUND YOUR ANSWER TO 2 DECIMAL PLACES i e 12 34 About of the animals will be infected after 13 days B How long will it take until exactly 90 of the animals are infected ROUND YOUR ANSWER TO 2 DECIMAL PLACES 90 of the animals will be infected after about days

Answer the following questions about F x x 35x 202 A Calculate the change in F x from x 10 to x 15 The change is

Salad Attempt 1 stion 5 0 5 points Listen e acceleration function in m s and the initial velocity ar ving along a line Determine the velocity at time t and the di ring the given time interval UUTI U U TU v t 5 m s 616 m

te Integrals Salad Attempt 1 tion 3 0 5 points Listen 6 uate sin x 0 943 1 057 2 d 0557

A population of bacteria follows the continuous exponential growth model P t Poekt where t is in days The relative daily growth rate is 4 4 The current population is 752 A Find the growth model the function that represents the population after t days P t B Find the population exactly 3 weeks from now Round to the nearest bacterium The population in 3 weeks will be C Find the rate of change in the population exactly 3 weeks from now Round to the nearest unit The population will be increasing by about bacteria per day exactly 3 weeks from now D When will the popualtion reach 6256 ROUND TO 2 DECIMAL PLACES 6056

relative maximum of relative minimum of at x at x and a relative maximum of at x

h ed in Connect ad Attempt 1 on 4 0 5 points ten So f x 6 f x dx 15 and f

if necessary fill in the answer box to complete your choice numbers in the expression Use a comma to separate answers as needed

Determine an equation for the pictured graph Writ leading coefficient is either 1 or 1 If you have trouble seeing the behavior at the roots 9 3 5 3

K For the following function find a the critical numbers b the open inte y 5x 14 a Identify the critical numbers of the function Select the correct choi