Functions Questions and Answers

K Solve the equation for the stated variable S 2 wf 2 w solve for f f Simplify your answer

K Solve for m F m p 2

Solve the following trignometric equation analytically using identities if necessary for exact values if possible for values of x for 0 x 2 10 tan x 8 9 1 tan x C XE Type an exact answer using it as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression Simplify your ans

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells external hard drives The solid line represents the revenue function R x 45x the dashed line represents the cost function C x 10 000 25x a Use the formulas to write the company s profit function P from producing and selling x hard drives b Find the company s profit if 18 000 hard drives are produced and sold a The company s profit function is P x Simplify your answer b The company s profit from producing and selling 18 000 hard drives is S AY 40 000 30 000 20 000 10 000 0 0 Rix 45x Simplify your answer F Cx 10 000 25x X 200 400 600 800 Hard Drives Produced and Sold o Q Ty

Sketch the region enclosed by the given curves x 2y x 4 y 3 y 3 7 2 1 y 2 6 8 Find the area of the region 1 2 3 6 8 X X 60 3 8 6 2 1 8 N 2 1 2 3 N 1 2 J 3 X X

point s possible According to a census there were 65 people per square mile this is called the population density in a certain country in 1980 By 2000 the number of people per square mile had grown to 80 Use this information to develop a linear equation in slope intercept form In developing the equation think of 1980 as year zero ELE Let x be the time in years and let y be the population density Write a linear equation in slope intercept form to model the given information The equation is Simplify your answer Use integers or fractions for any numbers in the equation

10 10 IRR calculations Given the following free cash flows determine the the three independent projects A B and C Initial outlay Cash inflows Year 1 Year 2 Year 3 Year 4 Year 5 PROJECT A 50 000 10 000 15 000 20 000 25 000 30 000 PROJECT B 100 000 125 000 25 000 25 000 25 000 25 000 PROJECT C 450 000 200 000 200 000 200 000

10 6 Payback period NPV PI and IRR calculations You are considering a proj ect with an initial cash outlay of 80 000 and expected free cash flows of 20 000 at the end of each year for 6 years The required rate of return for this project is 10 percent a What is the project s payback period b What is the project s NPV c What is the project s PI d What is the project s IRR

10 6 Payback period NPV PI and IRR calculations You are considering a proj ect with an initial cash outlay of 80 000 and expected free cash flows of 20 000 at the end of each year for 6 years The required rate of return for this project is 10 percent a What is the project s payback period b What is the project s NPV c What is the project s PI d What is the project s IRR

Use Lagrange multipliers to find the maximum and minimum values of f x y x 3y subject to the constraint if such values exist Enter the exact answers If there is no global maximum or global minimum enter NA in the appropriate answer area Maximum x y 3 Minimum

Write 1 242 102 in standard notation

oblem 2 A model rocket is shot upward from a height of 10 feet Its height H in feet above the ground after t seconds is given by H t 10 159 16t a Determine the time at which the rocket strikes the ground b Sketch the graph of the height function labels all axes and include units dH c Sketch the graph of the upward velocity dt of the rocket labels all axes and include units

5 Determine if each logarithm is defined If not explain why not If it is defined determine if the value is whole number or not a log312 b log3 9 c log255 5 x 109 x y 109 x y

14 14 Use the Divergence Theorem to evaluate the surface integral SS F F ds where F x y z x siny i cos y j z sin y k and S is the boundary of the region bounded by th planes x 1 y 0 y z 0 and z x with outward normal vector You must use this method to receive full credit

6 10 Find the directional derivative of the function f x y 13exy at the point 1 0 in the direction of the vector v 3 4

7 Find the area of the triangle with sides u 0 6 0 v 4 4 4 and u v

Find the area of the region bounded by the graphs of the given equations y 4x y x x 0 x 2 B C 2 S 4x x dx S dx S dx The area is

Find the area of the region bounded by the graphs of the given equations y x y x OA OB Set up the integral s that will give the area of the region Select the correct choice below and fill in any answer box e to complete the choice S S dx 0 25 dx 0 25 Q

3 y In x 3 3 Ay 8 4 2 6 2 2 2 6

Find all solutions in the interval 0 2 2 sin 2x cos x sinx 0 X Type an exact answer using as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the

question 2 point s possible Solve the following trignometric equation analytically using identities if necessary for exact values if possible for values of x for 0 x 2 11 tanx 9 10 1 tan x x Type an exact answer using zas needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression Simplify your answ

A store orders 800 units of a product every 4 months If the product is steadily depleted to 0 by the end of each 4 months the inventory on hand I at any time t during the year is shown in the figure to the right What is the average number of units on hand for a 4 month period Inventory units on hand 800 MM 4 8 12 16 t Time months Write an inventory function assume that it is continuous for the first 4 months The graph is a straight line joining 0 800 and 4 0 The inventory function for the first 4 months is 1 0

Construct a sinusoidal function with the provided information and then solve the equation for the requested values Outside temperatures over the course of a day can be modeled as a sinusoidal function Suppose the high temperature of 108 F occurs at 5 p m and the average temperature for the day is 86 F Find the temperature to the nearest degree at 9 a m

A radioactive material decays according to the function A t Age 0 02451 where Ao is the initial amount present and A is the amount present at time t in years Assume that a scientist has a sample of 400 grams of the radioactive material a What is the decay rate of the radioactive material b Graph the function using a graphing utility c How much radioactive material is left after 40 years d When will only 300 grams of the ladioactive material be left e What is the half life of the radioactive material b Graph the function Choose the correct graph below The graphing window is 0 800 100 by 0 1 0 25 O A OD Q B c There will be about 150 1 gram s of the radioactive material left after 40 years Do not round until the final answer Then round to the nearest tenth as needed d In about 11 7 year s only 300 grams of the radioactive material will be left Do not round until the final answer Then round to the nearest tenth as needed e The half life of the radioactive material is about year s Do not round until the final answer Then round to the nearest tenth as needed Q

Triangles ABC and DEF are similar B 10 m C 8 m A E 12 m F Find the perimeter of triangle DEF in m 16 m D

tion 6 of 6 Macmillan Learning When you start working you are offered two retirement options When you retire you will be given the balance of a retirement account Retirement option A The initial balance is zero The growth rate of your retirement fund A in dollars is given by dA dt Retirement option B The initial balance is 9400 The growth rate of your retirement fund B in dollars is given by dB Incorrect 20000 0 1 B dt Attempt 2 In each case time t is measured in years Find a formula that gives balances A and B for each retirement fund after 1 years Express numbers in exact form Use symbolic notation and fractions where needed Give the equations in terms of the dependent variable A or B and the independent variable t balance A equation

0 Name one way in which the parabolas shown here are DIFFERENT VE Share With Class

Question 2 of 6 A change equation together with an initial value are given Find the solution dy dt y y 0 5 Express numbers in exact form Use symbolic notation and fractions where needed Give the equation in terms of y an solution

3 80 5 47 Cengage Learning 2013 Cengage Learning 2013 The grille has the the dimensions shown with a gap of 3 8 between each opening Find the dimensions a and b of each opening

Give the first 5 values found using Newton s Method with the given function and initial value f x x 3x x 3 xo 1 1 32 03 4 35 Why does Newton s Method fail in finding the root The function has no roots The derivative becomes 0 The approximations will not converge

In this question we will use Newton s Method to approximate the x value of the intersection between f x and g x 1 F x f x closest to 2 Start your approximation with a 2 and apply two iterations of Newton s Method to the function g x Give your answers correct to at least 4 decimal places Remember that WeBWork can understand calculator ready numbers and make liberal use of copy paste 31

8 Yeast is often used in biological experiments A research technician estimates that a sample of yeast suspension contains 2 million organisms per cubic centimeter Two hours later she estimates the population density to be 6 million organisms per cubic centimeter Let t be the time elapsed since the first observation measured in hours Assume that the yeast growth follows the Law of Uninhibited Growth that is the number of organisms N at time t is given by the formula N t Noekt where N 0 No is the initial number of organisms and k 0 is a constant a Find the growth constant k Round your answer to four decimal places b Find a function that gives the number of yeast in millions per cubic centimeter N t after t hours c What is the doubling time for this strain of yeast

d Solve 3t 3 2t 6 2t 7 Ther

K Prove the given identity sec x csc x sin x sec x cos x CSC X Choose the correct proof below OA sec x csc x sin x sec x 1 1 cos X sin x sin x cos x 1 sin x 2 sin x cos X COS X cos X CSC X cos X sin x 2 1 sin x OC sec xcsc x sin x sec x 1 1 sin x sin x cos x 2 cos X sin x sin x cos x cos x CSC X 1 cos X 1 cos X OB sec x csc x sin 1 1 cos x sin X sin x cos X 1 sin X sin x cos x 2 COS X COS X CSC X 1 OD sec x csc x sin 1 COS X sin x 2 1 sin X sin x cos x 2 COS X sin x cos X COS X CSC X

Use differentials to estimate the amount of paint needed to apply a coat of paint 0 04 cm thick to a hemispherical dome with diameter 43 m Round your answer to two decimal places m 3 Enter an integer or decimal number more Question Help Message instructor

Draw a tree diagram for spinning Spinner A one time and then Spinner B two times Use the diagram to find the number of possible outcomes A P B V V V V V V OB Spinner A R R D V V V V V V V Spinner B 3 4 O OU O C Viller 26 86 Villere P N Yeller Gen Villen Val M Vallen Rad Vollere 2 Kw Vilhey Y Villow Kal P Ma Vellow kad O D 2 VVV

A 0 700 m rigid tank contains refrigerant 134a initially at 200 kPa and 40 percent quality Heat is transferred now to the refrigerant from a source at 35 C until the pressure rises to 400 kPa Problem 07 047 a Entropy change of R134a heated in a rigid tank Determine the entropy change of the refrigerant Use the tables for R 134a The entropy change of the refrigerant is kJ K

4 1 relation r 4 relation N 3 2 3 4 1 4 relation r relation r 2 2 3 4 attempts remaining The link below gives the digraphs for four different relations r 72 73 74 on the set A 1 2 3 4 Click this link to view the digraphs Which of these relations are reflexive Select all that apply Be able to explain your answ nswers A Ti B 73 OC T2 OD T4 Submit answer

n 1 of 13 Macmillan Learning Solve the triangle which is a case of ASA B 40 a 11 70 C Use decimal notation Give your answers to two decimal places if needed Include the degree symbol in your answer where needed B

While in a foreign country Ben rented a car whose speedometer is calibrated in both miles and kilometers per hour The marking on the speedometer shows that 30 miles per hour corresponds to 48 kilometers per hour While driving from the airport to the coast he sees a road sign that says Ocean 40 kilometers How many miles does he still have to drive He still has to drive miles www

The braking distance of a car varies directly as the square of the speed of that car Assume that a car traveling 40 miles per hour can stop 44 feet after the brakes are applied How long is the braking distance for that same car traveling at 55 www feet Round the final answer to the nearest integer as needed Round all intermediate values to four decimal places as needed

If the speed limit is 50 miles per hour and a person s trip takes 2 5 hours at that speed how much time does the person save by traveling 60 miles per hour www The person saves minutes Round the final answer to two decimal places as needed Round all intermediate values to four decimal places as needed

Points 0 of 1 GALLE Tamyra has invested 15 900 in the stock market Some of the stock is in Hunt Houses that costs 37 a share and the rest is in Simply Software that costs 69 a share Write an equation that models this situation Save Let h represent the number of shares purchased of Hunt Houses stock and let s represent the number of shares purchased of Simply Software stock What is the equation Do not include the symbol in your answer

ts 0 5 OT A health club charges a yearly membership fee of 115 and members must pay 3 00 per hour to use its facilities How many hours did Michael use the club last year if his bill was 673 First writ an equation that describes the situation Use meaningful names for the variables Let B be the amount of the bill at the end of the year and let t be the amount of time in hours Michael used the club Use the variables to write an equation that describes the situation A B 3 00t 115 OB t 115 3 00 B OC t B 115 3 00 OD B 115t 3 00 Using the equation describing the situation calculate the number of hours Michael used the club facilities last year hours Simplify your answer Type an integer or a decimal Save

Question 31 Suppose we roll a die once What is the probability that we roll a 4 or an even number

Assignment 9 Problem 1 point Find a vector orthogonal to both 1 3 0 and to 0 3 3 of the form 00

lodine 123 is a radioactive isotope used in medicine to test the function of the thyroid gland Its half life is 13 1 hours A 575 microcurie uci dose of iodine 123 is administered to t 13 1 patient The quantity Q left in the body after t hours is given by the equation Q 575 1 2 a Determine the time it takes for the level of iodine 123 to drop to 25 Ci It takes 59 26 hr for the level of iodine 123 to drop to 25 Ci Type an integer or decimal rounded to two decimal places as needed b Determine the rate of change of the quantity of iodine 123 at 10 hr The rate of change of iodine 123 at 10 hr is 17 92 Ci hr Type an integer or decimal rounded to two decimal places as needed c Determine the rate of change of the quantity of iodine 123 at 1 day The rate of change of iodine 123 at 1 day is Ci hr Type an integer or decimal rounded to two decimal places as needed Answer parts a through d

Suppose an Egyptian mummy is discovered in which the amount of carbon 14 present is only about three fourths the amount found in living human beings The amount of carbon 14 0 0001216t where yo is the amount of carbon 14 present in living human beings About how long ago did the Egyptian die present in animal bones after t years is given by y Yoe About yr ago the Egyptian had died Round to the nearest integer as needed

REVIEW 1 For the following quadratic functions state the transformations then graph them on the grid provided a y x 2 4 b y x 1 3 c y 2 x 2 101 ID X 10 X

What is wrong with either one or the other of the two definitions of holiness referred to here I humbly conceive there has been too little attention to the nature of holiness among divines in general and that a proper and intelligible definition of it is not easily to be found in bodies of divinity or elsewhere And most of those who think it a very easy matter to tell what holiness is and that we are all agreed in this have been contented with a set of words which express no distinct ideas but leave the thing wholly in the dark They will perhaps say God s holiness is his purity If it is asked In what does this purity consist the common answer is In that which is opposite to all sin the greatest impurity We have now got what I think is the most common definition of holiness But who is the wiser Samuel Hopkins Inquiry into the Nature of True Holiness O Vagueness O Circularity O All the above O None of the above