Application of derivatives Questions and Answers

ans F t 1 An object with initial temperature 200 F is submerged in large tank of water whose temperature is 40 F Find a formula for F t the temperature of the object after t minutes if the cooling constant is k 0 2

R TU sin COS tan 4 1 0 CT 5 6 2 3 ans X 1 x t The fox population in a certain region has a continuous growth rate of 5 percent per year It is estimated that the population in the year 2000 was 14900 a Find a function that models the population t years after 2000 t 0 for 2000 Hint Use an exponential function with base e Your answer is P t b Use the function from part a to estimate the fox population in the year 2008 Your answer is the answer must be an integer

sin N COS tan TU 5 4 3 2 1 5 3 2 1 2 4 3 4 1 0 ST 5 6 2 3 1 2 3 4 5 ans Write an equation for the transformed logarithm shown below Your answer should include a vertical scaling and will be in the form f x a log x c X I 1 X

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Find the exact value of the expression Do not use a calculator csc 28 sec 62 tan 62 cot 28 csc 28 sec 62 tan 62 cot 28

Find the derivative of the function dy dx y 8 x 7x 3 IN 7

Convert the angle in radians to degrees 4 9 radians

Find the first partial derivatives of f x y 4x y6 5x y 1 af of 36 42 16x y 25x y

Expand the binomial y 2 4 O4 8y 24y2 32y 16 JA 8y 16 8y 12y2 OA 8y 24y2 32y 16 O4 2y 8y2 32y 16

rite a system of equations that can be used to solve the fol afar owns a total of 60 shares of stock some in stock A ar 85 per share If Jaafar s stock for these companies was wo

Dave wants to purchase per pound How many po

3 5 f x 4 x 8x 6 f x 5x 8ln 2x e

Find the equation of the tangent line to the curve y 6 sec a 12 cos a at the point 7 6 Find the exact trig values for your answers no decimals allowed The equation of this tangent line has a slope of The equation of the tangent line is

1 sin x a What are the restrictions on the domain of p x on the interval 0 2 Let p x csc x and recall that csc x domain a b Use the quotient rule to develop a formula for p x that is expressed completely in terms of sin x and cos x p x c Now simplify p x using other relationships among trigonometric functions to write p x only in terms of cot x and csc x p x d What are the restrictions on the domain of p x on the interval 0 2 domain Question Ho FA

What is 4 radians converted to degrees If necessary round your answer to the nearest degre O 13 O 45 229 720

Graph the solution set of the inequality where x is a X 24

vvich grapn represents the system or inequalttes y 3 4 x 2 y 1 2x

lestion 13 Match the equation wit the s x 2 9 y 2 36 z 2 9 1

tor out the greatest commo lynomial 30s 5 t 3 10t 8 10t 3

Graph the solution set of the inequality wh x28 ph below

22 Here is a histogram of T cell velocities in vitro in microns per minute Count 350 300 250 200 150 100 50 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Velocity microns min The data represent a random sample of T cells grown in lab conditions Is it appropriate to compute a 95 for the mean T cell velocity a Yes despite the clearly skewed data because the sample size is large enoug b No because the data are clearly skewed c Yes because the population of T cell velocities is most likely approximate Normal d No because the population of T cell velocities is most likely not Normal

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Graph the solution set of the inequality where x is an in 0 7 x 5 10 0 9 Choose the correct graph of the solution set below

Suppose that f 1 2 and that f x 3 cos 3x Find f 4

Determine whether the integral J1 x ln x convergent divergent conditionally convergent O None of the answer choices onverges of diverges

Problem 4 5 points Consider the function f x y z x yz Consider the curve parametrized by r t 1 cost sint i cost sint j tk where 0 t 2 For each t calculate the directional derivative of f at the point with positional vector r t in the direction of the tangent vector to the curve at r t

orm the following operation and express in simplest x 2 16 2x 18 x 2 2x 8 x 2

A 8 6 4 2 4 2 0 2 4 6 6 2 4 6 X E

Please find the value of the unknown in the following formula C nE R nr Find C if n 6 E 4 r 6 R 12

Please find the value of the requested unknown Hint You may wish to re arrange the formula first and then insert the numbers or you may insert the numbers first and then re arrange the formula H S F 550t Find F if H 5 S 5 5 t 2

Please solve the following equation 3 3 X 4

Please solve the following equation 7c 8 15 22

Please solve the following equation 2 x 6 3 A

Solve for x 23 5x 18

Reattempt last question below or select another question What is the coefficient of x12 in the expansion of x 2 8 x x 3 2

27 bring 7 points possible Question 5 Write an equation for the 3 2 1 0 7 answe 5 4 3 2 1 1 2 3

For a standard normal distribution which of the following expressions must always be equal to 1 O P z a P asz a P z a O P z a P asz a P z a OP z a P asz a P z a O P zs a P aszsa P z a

In Juneau Alaska the 30 year annual snowfall average is 86 7 inches with a standard deviation of 40 4 inches The last four years saw an average annual snowfall of 115 7 inches 62 9 inches 168 5 inches and 135 7 inches Hia performs a hypothesis test on this data to determine if the next 30 year norm will have a different average if the trend from the last four years continues She uses a significance level of 5 Which of the following is a conclusion that she may make O The z statistic is 1 44 so the null hypothesis cannot be rejected O The z statistic is 1 68 so the null hypothesis cannot be rejected O The z statistic is 1 85 so the null hypothesis should be rejected O The z statistic is 4 6 so the null hypothesis should be rejected

You are challenged to a lucky draw game If you draw a face card K Q J from a standard deck of cards you earn points If you draw any other card you lose 2 points What is the expected value of a draw O 0 77 1 69 1 85 2 31

Question 7 Find all real zeros of the fu

A local weather enthusiast wants to see if the last five summers have been warmer than normal for Eloy Arizona From the National Oceanic and Atmospheric Administration NOAA he knows the 30 year average for July was 90 with a standard deviation of 2 1 The last five summers recorded have an average of 93 5 If he uses a 5 which of the following would be valid based on the data he has gathered He can conclude that the summers have been warmer than the 30 year average He can conclude that the summers will continue to be warmer for the next 10 years O He does not have enough information to make a decision O The average for the last five years fits with the 30 year average

The resting heart rates for 80 women aged 46 55 in a simple random sample are normally distributed with a mean 71 beats per minute and a standard deviation of 6 beats per minute Assuming a 90 confidence level 90 confidence level z score of 1 645 what is the margin of error for the population mean Remember the margin of error ME can be determined using the formula ME 0 66 O 1 10 O 1 31 O 1 73 Z S

Dwayne and Alisha both correctly graphed a standard normal curve Which of the following statements is true ONeither the means nor the standard deviations of Dwayne s and Alisha s graphs must be the same The means of Dwayne s and Alisha s graphs must be the same but not the standard deviations The standard deviations of Dwayne s and Alisha s graphs must be the same but not the means O Both the means and the standard deviations of Dwayne s and Alisha s graphs must be the same

A manager of a grocery store wants to determine if consumers are spending more than the national average The national average is 150 00 with a standard deviation of 30 20 The manager collects 40 random receipts and fir that the average is 160 Complete a hypothesis test with a significance level of 2 5 to determine if the average customer spends more in his store than the national average Which of the following is a valid conclusion for the manager based on this test O The customers spend more than the national average in his store O The manager should decrease prices in his store O The customers do not spend more than the national average in his store O The customers in his store just come from a rich neighborhood

The human resources manager at a company records the length in hours of one shift at work X He creates the probability distribution below What is the probability that a worker chosen at random works at least 8 hours Px x 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 62 0 78 6 hours Probability Distribution 7 hours Shours X 9 hours 10 hours

9x 5x 45 c 9 Show that the given value of c is a zero of P x P 9 0 P x x Score 0 11 out of 0 11 Comment Find all other rores of

Use the Factor Theorem to show if x c is a factor of P x for the given value of c P x x 2x 6x 72 c 4 X 4 Select a factor of P x

Question 10 5 2 47 BE points Points 0 of 2 erson wants to invest 13 000 for 3 years and is considering two different investments The first inv hey market fund pays a guaranteed 5 1 interest compounded daily The second investment a trea annual interest Which investment pays the most interest over the 3 year period ct the correct choice below and if necessary fill in any answer box es to complete your choice not round until the final answer Then round to the nearest cent as needed A The treasury note is the better investment since the market fund produces in interest and note pays in interest 8 The market fund is the better investment since the market fund produces in interest and note pays in interest C Both the market fund and the treasury note produce the same interest with S

18 Compute lim x y 0 0 3x y x x y along lines of the form y mx for m 0 What can you co clude

Calculate the average rate of change of the given function over the given interva Interval 0 2 X f x 0 G 1 2 3 4 5