Application of derivatives Questions and Answers

9 a If the curve y f x a x b is rotated about the horizontal line y c where f x c find a formula for the area of the resulting surface b Set up an integral to find the area of the surface generated by rotating the curve y x 0 x 4 about the line y 4 Then evaluate the integral numerically correct to four decimal places

Use a graphing calculator to graph the exponential decay p 100e 0 x 50 0 p 100 0 06x Choose the correct graph below OA OB AP 100

Find the indicated derivative dy dt dy dt for y 2 5t 5t 2t 1 2

Use a graphing calculator to graph the unlimited gro y 1 100e0 06t 0 t 10 0sy 2 500 the correct aranh holow

Show that y C 6x is a solution of the differen particular solution that passes through 2 5 3 How can it be shown that y C 6x is a solution

Find the particular soluti dy dx 8x7 e x y

Calculate the number of permutations in each problem below 9 How many possible ways can a group of 10 people line up to buy tickets to a movie 3 628 800 10 How many unique words can be made by arranging the letters of the word APPLE The words do not 81 have to be real words in any dictionary but each word must use every letter 1024

A function f x is given below Express the relationship b that f x satisfies f x e21x Express the relationship between f x and f x in words A The derivative of f x is 21 times f x roiced to the

A function f x is given below Express the re that f x satisfies 21x f x e Jac

3 Find the 11th term in an arithmetic sequence with a 10 and a common difference d of 3 20 40 80 3 3 24 6 The first 100 terms of an arithmetic sequence are 3 7 11 399 Find the sumy 4 Find the common ratio r in the geometric sequence 10 77 5 Find the sum of the whole numbers from 1 to 75 20 5 2 100

sin COS tan 1 0 2 3 ans 1 A truck with 30 in diameter wheels is traveling at 45 mi h Find the angular speed of the wheels in rad min hint convert miles to inches hours to minutes rad min How many revolutions per minute do the wheels make rpm

Without using a calculator compute the sine and cosine of What is the reference angle In what quadrant is this angle 57 3 sin COS 5 57 3 Type sqrt 2 for 2 and sqrt 3 51 5T 3 by using the reference angle radians answer 1 2 3 or 4

On a circle of radius 9 feet what angle would subtend an arc of length 4 feet degrees

3 0 ans Find the area of the sector of a circle with radius 7 yards formed by a central angle of 290 square yards Round your answer to two decimal places

Tim and Allison are married and have two children ages 12 and 14 Allison is a nonworking spouse who devotes all of her time to household activities Estimate how much life insurance Tim and Allison should carry on Allison Life insurance need

0 ans Find the distance along an arc on the surface of the earth that subtends a central angle of 4 minutes 1 minute 1 60 degree The radius of the earth is 3960 miles Round to the thousandths 3 decimal places

x y 0 ans Recall the equation for a circle with center h k and radius r At what point in the first quadrant does the line with equation y x 5 intersect the circle with radius 5 and center 0 5 1

R sin COS tan 1 0 5 2 6 3 ans X 1 1 t Please show all your work NO WORK NO CREDIT 1 x An object with initial temperature 190 F is submerged in large tank of water whose temperature 60 F Find a formula for F t the temperature of the object after t minutes if the cooling consta is k 0 4

Please show all your work NO WORK NO CREDIT Score on last try 0 of 10 pts See Details for more Next question At the beginning of an experiment a scientist has 132 grams of radioactive goo After 135 minute her sample has decayed to 4 125 grams What is the half life of the goo in minutes Round to one decimal place The half life of the goo is Get a similar question You can retry this question below Find a formula for G t the amount of goo remaining at time t G t 132 2 89 7 There will be 79 2 X How many grams of goo will remain after 65 minutes Round to one decimal places x grams of goo after 65 minutos

Score on last try 5 of 10 pts See Details for more Next question Solve the following equation 15 100 1 14 235 n Get a similar question You can retry this question below Write your answers exactly i e no decimals and simplified if possible separated by a comm 5 2 In 1 4 In x Hint Write your answers as decimals rounded to four docimal pl

Lowell Company makes and sells artistic frames for pictures The controller is responsible for preparing the master budget and has accumulated the following information for 2020 Estimated unit sales Sales price per unit Direct labor hours per unit Wage per direct labor hour a January plas 10 400 50 70 Desired Ending Direct Materials 20 7 February 11 800 48 40 2 0 7 March April 8 700 8 300 8 300 48 40 48 40 48 40 1 5 7 Jan 1 5 Lowell has a labor contract that calls for a wage increase to 8 per hour on April 1 New labor saving machinery has been installed and will be fully qperational by March 1 W Lowell expects to begin the year with 16 300 frames on hand and has a policy of carrying an end of month inventory of 100 of the following month s sales plus 50 of the second following month s sales May 8 Prepare a production budget for Lowell Company by month and for the first quarter of the year 14 157 1 5 8 LOWELL COMPANY Production Budget For the Year Ending March 31 2020 Feb Mar

Find the area of the surface obtained by rotating the circle x 2 y 2 36 about the line y 6 O 18 2 O 144 2 O None of the answer choices 100 12

The following pictures has graphs of f x and f x

1 point A rectangular tank that is 5 feet long 3 feet wide and 3 feet deep is filled with a heavy liquid that weighs 70 pounds per cubic foot In each part below assume that the tank is initially full Your answers mu clude the correct units You may enter lbf or lb ft for ft lb a How much work is done pumping all of the liquid out over the top of the tank 4725 b ft b How much work is done pumping all of the liquid out of a spout 2 feet above the top of the tank 11025 bf c How much work is done pumping two thirds of the liquid out over the top of the tank 4200lbf d How much work is done pumping two thirds of the liquid out of a spout 2 feet above the top of the tank 8400lbf

Let n be a positive integer Solve the initial value problem 27 a dy 2 dz y Answer 7 n sin na and determine the value of n so that y y 2T 0

29 33 Find the centroid of the region bounded by the given curves 29 y x x y 30 y 2x y x 31 y sin 2x y sin x 0 x T 3 C N

Evaluate dA where D is the shaded part inside the semicircle of radius 2 in the figure 5y y 4 1 Use symbolic notation and fractions where needed X 2 d dA 3 3 X

Use your conjecture to predict where the rational function f x 2 9 T 3 will have a vertical asymptote Graph the function and see whether or not your conjecture is true Create a rule for the discontinuity that occus at x 3 for this fur

Multiply and simplify sin x cotx csc x sin v P

Consider the functions f x x 9 and g x x 9 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other a What is f g x f g x Simplify your answer Give any values of x that need to be excluded from f g x Select the correct choice below and fill in any answer boxes within your choice OA x Use a comma to separate answers as needed OB No values should be excluded from the domain N b What is g f x g f x Simplify your answer Give any values of x that need to be excluded from g f x Select the correct choice below and fill in any answer boxes within your choice OA x Use a comma to separate answers as needed OB No values should be excluded from the domain c Are the functions f and g inverses of each other Choose the correct answer below No Yes

X 607 2 607 2 x bon for XE

C x The total cost in dollars of manufactur 50000 400x Find the average cost per unit if 400 un Hint Recall that a x 525 is the averag

1 Points DETAILS Evaluate the integral usin 6 f x x dx 31

2 Points DETAILS LARCALC12 4 3 017 Write a definite integral that yields the area of the reg f x 25 x 30 25 20 15 10 5

Solve for x log4 x log4 x 3 4 x Round your final answer to 6 decimal places Note Do not round until the final step

Please show all your work NO WORK NO CREDIT G R K If all the graphs above have equations with form y ab Which grap B has the largest value for b Select an answer Which graph has the smallest value for b Select an answer Which graph has the largest value for a Select an answer

Please show you Solve for w in the equation below using logarithms Round answer to 3 decimal places 2012 1 10 13 662

A flat circular plate has the shape of the region x y s1 The plate including the boundary where x y 1 is heated so that the temperature at the point x y is T x y x 2y 3x Find the temperatures at the hottest and coldest points on the plate

Here is a graph of the function g Use the graph to find the following If there is more than one answer separate them with commas a All local minimum values of g b All values at which g has a local minimum 0 DO

4 In AABC if BC 14 AC 8 and m2C 54 find AE B4 54 C

Ben and Carla Manchester plan to buy a condominium They will obtain a 210 000 20 year mortgage at 8 0 percent Their annual property taxes are expected to be 2 676 Property insurance is 1 296 a year and the condo association fee is 115 a month Based on these items determine the total monthly housing payment for the Manchesters Use Exhibit 9 9 Do not round intermediate calculations Round time value factor to 2 decimal places and final answer to the nearest whole dollar Total monthly housing payment

Estimate the affordable monthly mortgage payment the affordable mortgage amount and the affordable home purchase price for the following situation Refer to Exhibit 9 8 and Exhibit 9 9 Round time value factor to 2 decimal places intermediate and final answers to the nearest whole dollar Monthly gross income Down payment to be made percent of purchase price Other debt monthly payment Monthly estimate for property taxes and insurance 30 year loan Affordable monthly mortgage payment Affordable mortgage amount Affordable home purchase LA LA LA 5 150 300 400 20 percent 6 5 percent 000

Consider the function the following rational function 10 8 6 8 4 2 4 2 2 4 6 8 1 The equation of the horizontal asymptote for this function is 2 The equation of the vertical asymptote for this function is Which of the following would be the domain of the function Select an answer Question Help Post

asymptotes horizontal asymptotes and holes Show complete work on your worksheet f x Domain Select an answer v VA 5 2x 1 2 There is are vertical asymptote s at O There are no vertical asymptotes Hole s There is a hole at O There is no hole in this function T intercept s O There is are intercept s O There are no intercepts y intercept O There is a y intercept s O There is not a y intercept

Evaluate the following series a 3n 42n 1

Pectangular storage area is to be constructed along a side of a building A security fence is required along the remaining three sides of the area What is the maximum area that can be enclosed with 800 ft of fencing 800 ft of fence Length of the side parallel to the building is Length of the side perpendicular to the building is ho maxi Select an answer C Select an answer C

A trough is 8 ft long and its ends have the shape of isosceles triangles that are 2 ft across at the top and have a height of 1 ft If the trough is being filled with water at a rate of 15 ft3 min how fast is the water level rising when the water is 5 inches deep

Find the vertical asymptotes x 13x 42 f x 2 x 5x 14

A baseball team plays in a stadium that holds 66000 spectators With the ticket price at 10 the average attendance has been 30000 When the price dropped to 7 the average attendance rose to 33000 Assume that attendance is linearly related to ticket price What ticket price would maximize revenue

2 Polynomial Functions K For the polynomial function f x x x 3 x 5 an a Use the Leading Coefficient Test to determine the g OA The graph of f x rises to the left and rises to B The graph of f x falls to the left and falls to th OC The graph of f x rises to the left and falls to t OR The graph of f x falls to the left and rises to