Application of derivatives Questions and Answers

Question Part 2 homes are located 8 miles apart on a straight stretch of beach each a our along the road but only 4 miles per hour in the sand Because of a nue on the road and then jog on the sand to get from one house to the

Assume the annual rate of change in the national debt of a country in billions of dollars per year can be modeled by function D t 842 62 828 46t 190 35t 19 6t where t is the number of years since 1995 By how much did the debt increase between 1996 and 2007 The debt increased by billion Round to two decimal places as needed

Suppose that in a memory experiment the rate of memorizing is given by M t 0 006t 0 2t where M t is the memory rate in words per minute How many words are memorized in the first 30 min from t 0 t 30 In the first 30 minutes words are memorized

Evaluate Then interpret the result in terms of the area above and or below the x axis 2 INST 1 2 1 1 4 0 x 4x dx Type an integer or a simplified fraction x 4x dx Interpret the result Choose the correct answer below O A All of the area is below the x axis OB There is more area below the x axis than above it OC The area above the x axis is the same as the area below it O D There is more area above the x axis than below it OE All of the area is above the x axis 3 1 5 2 1 5

Evaluate e 1 5x X e x 1 a 5x X 1 dx dx Type an exact answer in terms of

223 Suppose that a particle moves along a straight line with velocity v t 42t where 0 t 2 in meters per second Find the displacement at time t and the total distance traveled up to t 2

Find Ln Rn and their average value for the definite integral using the indicated value of n 7 2 x 2 dx n 8 Round to three decimal places as needed R 0 Round to three decimal places as needed The average of Ln and Rn is Round to three decimal places as needed

My courses SC N signments Assign

Evaluate 7 7 Sx x 36 6 x x 36 dx dx 2197 6

Find the minimum distance from the parabola to the point 0 3 Minimum distance 11 2 x y 0

Suppose that A List all critical numbers of f If there are no critical values enter NONE 1 6 Critical numbers f x 12x2ln x x 0 B Use interval notation to indicate where f x is increasing Note Use INF for oo INF for o and use U for the union symbol Increasing 00 C Use interval notation to indicate where f x is decreasing Decreasing D List the x coordinates of all local maxima of f If there are no local maxima enter NONE I values of local maxima NONE E List the x coordinates of all local minima of f If there are no local minima enter NONE 1 6 values of local minima F Use interval notation to indicate where f x is concave up Concave up 0 00

13 Write the factored form of the quadratic function shown at the right 16 8 8 4 Q 8 16 y 4 X 8

10 15 dx f x dx f x dx f x f x dx

Consider the integral 2x 4x 4 dax a Find the Riemann sum for this integral using right endpoints and n 3 R3 b Find the Riemann sum for this same integral using left endpoints and n 3 L3

A box is to be made out of a 6 cm by 16 cm piece of cardboard Squares of side length x cm will be cut out of each corner and then the ends and sides will be folded up to form a box with an open top a Express the volume V of the box as a function of V cm b Give the domain of V in interval notation Use the fact that length width and volume must be positive c Find the length L width W and height H of the resulting box that maximizes the volume Assume that W L L W H cm cm cm d The maximum volume of the box is cm

f x 12x2ln x x 0 A List all critical numbers of f If there are no critical values enter NONE Critical numbers B Use interval notation to indicate where f x is increasing Note Use INF for oo INF for oo and use U for the union symbol Increasing C Use interval notation to indicate where f x is decreasing Decreasing D List the x coordinates of all local maxima of f If there are no local maxima enter NONE values of local maxima E List the x coordinates of all local minima of f If there are no local minima enter NONE I values of local minima F Use interval notation to indicate where f x is concave up Concave up G List the values of all inflection points of f If there are no inflection points enter NONE values of inflection points H Use all of the preceding information to sketch a graph of f When you re finished enter a 1 in the box be

Find two numbers A and B with A B whose difference is 44 and whose product is minimized A B

5 f x 2 16 A List all critical numbers of f If there are no critical numbers enter NONE Critical numbers B Use interval notation to indicate where f x is increasing Note Use Inf for oo Inf for oo and use U for the union symbol Increasing C Use interval notation to indicate where f x is decreasing Decreasing D List the x coordinates of all local maxima of f If there are no local maxima enter NONE z values of local maxima E List the x coordinates of all local minima of f If there are no local minima enter NONE values of local minima F Use interval notation to indicate where f z is concave up Concave up G Use interval notation to indicate where f x is concave down Concave down

Find two positive numbers whose product is 121 and whose sum is a minimum

Find the exact area below the curve y x 2 x and above the x axis area

In the following exercises use the Fundamental Theorem of Calculus Part 1 to find each derivative 148 fe da 149 150 152 153 fest dz 151 F dt 9 y dy ds 16 s e cost dt 2x ft to tdt x 1 S dz tdt

Find the function f x described by the given initial value problem f x 7x 1 f 0 2 f 0 5 help formulas f x

Zoom Meetings Rich LTI Question 6 of 10 1 point Attempt 1 of Unlimited View question in A large weather balloon is tethered by two ropes One rope me the ground The second rope attaches to the base of the ballo

Zoom Meetings Question 9 of 10 1 point Attempt 1 of Unlimited 1 333 U Find the bearing of the ship Round to the nearest

ge Homepage Zoom Meetings Question 1 of 10 1 point Attempt 1 of Unlimited 5 1 12 2 Find the exact values of the six trigonometric functions 3

Consider the following function f t 1 1 3 6 t Use Definition 7 1 1 to find f t Write your answer as a function of s

Solve each triangle ABC that exists B 34 42 a 38 7 b 31 2 Select the correct choice below and if necessary fill in the answer boxes within the choice O A There is only one possible solution for the triangle The measurements for the remaining angles A and C and side c are as follows A C c Simplify your answer Round to the nearest degree as needed Round to the nearest minute as needed Round to the nearest tenth as needed O B There are two possible solutions for the triangle The measurements for the solution with the longer side c are as follows A C C Simplify your answer Round to the nearest degree as needed Round to the nearest minute as needed The measurements for the solution with the shorter side c are as follows A Simplify your answer Round to the nearest degree as needed Round to the nearest minute as needed C There are no possible solutions for this triangle Round to the nearest tenth as needed Round to the nearest tenth as needed

Arrange the quantities in order from smallest 2 3 km 108 000 mm 39 5 hm Choose the correct answer below

cide whether the following equation is true or false sin e cos 0 tan 0 ose the correct answer below A True because B False because C False because sin 0 cos sin 0 cos e sin 0 cos A adjacent opposite and tan 0 hypotenuse adjacent adjacent hypotenuse adjacent opposite and tan 0 and tan 0 Ques Thus tan opposite adjacent opposite adiacent Thus Thus

open topped box is to be A rectangular constructed out of 14 inch square sheets of thin cardboard by cutting x inch squares out of each corner and bending the sides up What is the area of the cardboard after the corners have been removed

Fill in the equation for this function y 2 x 1

State the domain and range of logg 2 Domain Range Select the graph of logg z 1 2 3 4 5 5 5 4 3 2 4 3 2 1 1 3 4 5 2 3 4 5 6 7 8 9 10 4 5 6 7 8 9 10 O 3 2 may 5 I 1 2 3 4 5 3 27 773 T 3 1 2 3 4 5 6 7 8 9 10 1 m M 5 6 7 8 9 10

Part 1 of 2 e concentration C of phenylbutazone in micrograms per milliliter g mL in plasma of a calf injected with this anti inflammatory agent is given proximately by C t 42 06e 0 01045t where t is the number of hours after the ection and Osts 120 O Points 0 of 1 Given that the model is accurate for 0 st 120 what is the initial dosage What is the average amount of phenylbutazone in the calf s body for the time between 15 and 120 hours The initial dosage is g mL ype an integer or a decimal www AC 50 40 30 20 10 O a

3 Question 8 Instructor created question suming that b is positive solve the following equation for b 4x 9 dx 18 Round your final answer to 4 decimal place Give the positive answer only

3 4R 2 a Find dS in term of dr What is dS if dr 0 1cm when r 10 cm b Express the radius r in terms of the surface area S Find dr in terms of dS cm Find dS if dV 1 cm when V 36 Ans a ds 8tr dr dS 8x cm

a There are 2160 b There are 2 16 c The cost per liter Round to the neare

a How many milliliters are c b How many liters does the c At 2 05 for the carton of here are milliliters of so

painting including the fram a How many centimeters b How many millimeters cm were needed to fra Simplify your answer Type

el y 4 3 2 1 0 1 2 3 4 1 x 1 4 6 12 8x x 3 x 91 8 10 12X

Op plify each of the following and w 5 14i 1 12i

3 Find g 0 g 5 g 7 and g for g x 2 O A g 0 X 25 x Find g 0 Select the correct choice below and if necessary fill in the answer box to complete y choice OB g 0 does not exist OC g 0 is not a real number Simplify your answer Type an exact answer using radicals as needed

1 point An anagram of a word is just a rearrangement of its letters How many different anagrams of troublemakings are there

At the end of each year 5000 is invested in an IRA earning 2 interest compounded annually Answer parts A and B below A How much will be in the account at the end of 30 years Use the following annuity formula whe P periodic payment i rate per period n number of payments periods and F FV future valu 1 i n 1 F P i n P There will be in the account at the end of 30 years Simplify your answer Do not round until the final answer Then round to two decimal places as needed

If all other quantities remain the same how does the indicated change affect the width of a confidence interval a Increase in the level of confidence b Increase in the sample size c Increase in the population standard deviation a How does an increase in the level of confidence affect the width of a confidence interval Choose the correct answer below An increase in the level of confidence the confidence interval b How does an increase in the sample size affect the width of a confidence interval Choose the correct answer below An increase in the population standard deviation An increase in the sample size c How does an increase in the population standard deviation affect the width of a confidence interval Choose the correct answer below the confidence interval the confidence interval

The percentage of adults who retire at age 65 is greater than 62 Identify the type I error Choose the correct answer below OA Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62 when it is actually false OB Reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62 when it is actually true OC Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 when it is actually false OD Reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 when it is actually true Identify the type II error Choose the correct answer below OA Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62 when it is actually false B Reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62 when it is actually true OC Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 when it is actually false OD Reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 when it is actually true

Let f x y xy 4x 6y 63 Find all values of x such that f x x 0 X Use a comma to separate answers as needed

Find the indicated value of the function T P 4 6 for P r T x dx 2 P 4 6 Sir lif

Find the indicated value of the function V r h h V 4 5 VICA ww Type an exact answer in terms

1 a x 4 2x b f x 4 5 c w x 4 9 3 d n x 4 6 e m x x Which of the following are exponential functions Select all that apply X 5 5 6

Homework C2S5 Question 10 of 10 1 point Question Attempt 1 2 3 c x Graph the function Be sure to plot all necessary asymp 3x x x 2 8 6 5 c x