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17.7E: Exercises


Practice Makes Perfect

Exercise SET A: Solve Radical Equations

In the following exercises, solve.

1. (sqrt{5 x-6}=8)

2. (sqrt{4 x-3}=7)

3. (sqrt{5 x+1}=-3)

4. (sqrt{3 y-4}=-2)

5. (sqrt[3]{2 x}=-2)

6. (sqrt[3]{4 x-1}=3)

7. (sqrt{2 m-3}-5=0)

8. (sqrt{2 n-1}-3=0)

9. (sqrt{6 v-2}-10=0)

10. (sqrt{12 u+1}-11=0)

11. (sqrt{4 m+2}+2=6)

12. (sqrt{6 n+1}+4=8)

13. (sqrt{2 u-3}+2=0)

14. (sqrt{5 v-2}+5=0)

15. (sqrt{u-3}+3=u)

16. (sqrt{v-10}+10=v)

17. (sqrt{r-1}=r-1)

18. (sqrt{s-8}=s-8)

19. (sqrt[3]{6 x+4}=4)

20. (sqrt[3]{11 x+4}=5)

21. (sqrt[3]{4 x+5}-2=-5)

22. (sqrt[3]{9 x-1}-1=-5)

23. ((6 x+1)^{frac{1}{2}}-3=4)

24. ((3 x-2)^{frac{1}{2}}+1=6)

25. ((8 x+5)^{frac{1}{3}}+2=-1)

26. ((12 x-5)^{frac{1}{3}}+8=3)

27. ((12 x-3)^{frac{1}{4}}-5=-2)

28. ((5 x-4)^{frac{1}{4}}+7=9)

29. (sqrt{x+1}-x+1=0)

30. (sqrt{y+4}-y+2=0)

31. (sqrt{z+100}-z=-10)

32. (sqrt{w+25}-w=-5)

33. (3 sqrt{2 x-3}-20=7)

34. (2 sqrt{5 x+1}-8=0)

35. (2 sqrt{8 r+1}-8=2)

36. (3 sqrt{7 y+1}-10=8)

Answer

1. (m=14)

3. no solution

5. (x=-4)

7. (m=14)

9. (v=17)

11. (m=frac{7}{2})

13. no solution

15. (u=3, u=4)

17. (r=1, r=2)

19. (x=10)

21. (x=-8)

23. (x=8)

25. (x=-4)

27. (x=7)

29. (x=3)

31. (z=21)

33. (x=42)

35. (r=3)

Exercise SET B: Solve Radical Equations with Two Radicals

In the following exercises, solve.

37. (sqrt{3 u+7}=sqrt{5 u+1})

38. (sqrt{4 v+1}=sqrt{3 v+3})

39. (sqrt{8+2 r}=sqrt{3 r+10})

40. (sqrt{10+2 c}=sqrt{4 c+16})

41. (sqrt[3]{5 x-1}=sqrt[3]{x+3})

42. (sqrt[3]{8 x-5}=sqrt[3]{3 x+5})

43. (sqrt[3]{2 x^{2}+9 x-18}=sqrt[3]{x^{2}+3 x-2})

44. (sqrt[3]{x^{2}-x+18}=sqrt[3]{2 x^{2}-3 x-6})

45. (sqrt{a}+2=sqrt{a+4})

46. (sqrt{r}+6=sqrt{r+8})

47. (sqrt{u}+1=sqrt{u+4})

48. (sqrt{x}+1=sqrt{x+2})

49. (sqrt{a+5}-sqrt{a}=1)

50. (-2=sqrt{d-20}-sqrt{d})

51. (sqrt{2 x+1}=1+sqrt{x})

52. (sqrt{3 x+1}=1+sqrt{2 x-1})

53. (sqrt{2 x-1}-sqrt{x-1}=1)

54. (sqrt{x+1}-sqrt{x-2}=1)

55. (sqrt{x+7}-sqrt{x-5}=2)

56. (sqrt{x+5}-sqrt{x-3}=2)

Answer

37. (u=3)

39. (r=-2)

41. (x=1)

43. (x=-8, x=2)

45. (a=0)

47. (u=frac{9}{4})

49. (a=4)

51. (x=0: x=4)

53. (x=1: x=5)

55. (x=9)

Exercise SET C: Use Radicals in Applications

In the following exercises, solve. Round approximations to one decimal place.

  1. Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of (75) square feet. Use the formula (s=sqrt{A}) to find the length of each side of his garden. Round your answer to the nearest tenth of a foot.
  2. Landscaping Vince wants to make a square patio in his yard. He has enough concrete to pave an area of (130) square feet. Use the formula (s=sqrt{A}) to find the length of each side of his patio. Round your answer to the nearest tenth of a foot.
  3. Gravity A hang glider dropped his cell phone from a height of (350) feet. Use the formula (t=frac{sqrt{h}}{4}) to find how many seconds it took for the cell phone to reach the ground.
  4. Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, (4000) feet above the Colorado River. Use the formula (t=frac{sqrt{h}}{4}) to find how many seconds it took for the hammer to reach the river.
  5. Accident investigation The skid marks for a car involved in an accident measured (216) feet. Use the formula (s=sqrt{24d}) to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.
  6. Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was (175) feet. Use the formula (s=sqrt{24d}) to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.
Answer

57. (8.7) feet

59. (4.7) seconds

61. (72) feet

Exercise SET D: Writing Exercises

  1. Explain why an equation of the form (sqrt{x}+1=0) has no solution.
    1. Solve the equations (sqrt{r+4}-r+2=0).
    2. Explain why one of the "solutions" that was found was not actually a solution to the equation.
Answer

63. Answers will vary.

Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

b. After reviewing this checklist, what will you do to become confident for all objectives?


Course 7E (solution)

An observant solver who has played StarCraft II may notice some camouflaged references to the Zerg race within the fake subject descriptions. Once this aha is reached, closer inspection should eventually lead to the realization that the clues within each description can be mapped to one of the Zerg structures (buildings). Note that the hidden clues may reference units or upgrades that the structure enables. The fact that there are 16 fake subjects and 16 Zerg structures further confirms that this mapping is correct and intentional.

Here are the mappings in the original alphabetical order:

Subject titleSubject descriptionClues hidden withinAssociated
Zerg structure
Animal Flight IStudies two species of flying animals for contrast. Students will be expected to compare their height, weight, flight-enabling appendages, air speed, color, likelihood of each liking the other&rsquos color better than their own, and likelihood of being corrupt and cheating at games.&rdquoflying animals&rdquo &ldquotwo species&rdquo (Mutalisk and Corruptor) &ldquocorrupt&rdquo (Corruptor)Spire
Animal Flight IIA follow-up to the previous course of learning. Greater emphasis on specialization in flying creatures. Students attempting to emulate these mechanisms themselves do so at their own risk.&rdquofollow-up to the previous&rdquo (follow-up to an existing Spire) &ldquogreater&rdquo (word is in structure name) &ldquospecialization in flying creatures&rdquo (Brood Lord only attacks ground)Greater Spire
Basic Lifeforms ISome claim life began in pools of primordial ooze. Others say life began after the universe was bored and wanted someone to talk to. Regardless, what we do know is that even the most basic species were eventually able to develop evolutionary advantages such as increased metabolism and epinephrine production.&rdquopools&rdquo (&ldquopool&rdquo is in structure name) &ldquomost basic species&rdquo (enables Zergling) &ldquoincreased metabolism and epinephrine production&rdquo (Metabolic Boost and Adrenal Glands upgrades)Spawning Pool
Basic Lifeforms IIA continuation of Basic Lifeforms I. This subject covers new research into the most basic species, showing that chemical imbalances in some individuals&rsquo cells can cause their bodies to bloat and eventually burst. This has also been known to happen to students taking this subject, so caution is advised.&rdquonew research into the most basic species&rdquo (newer properties of Zergling that were not present in StarCraft I) &ldquochemical imbalances in some individuals&rsquo cells, causing their bodies to bloat and eventually burst&rdquo (describes Baneling)Baneling Nest
Colony Behavior ISurveys bees as the representative example of colony behavior. Studies how colonies expand their reach by having some members leave and establish a new colony, resource gathering by worker bees, and structures for developing the young in their pre-metamorphosis stage. English-to-bee translator available. Students should bring their own bee-to-English translator if desired.&rdquoexpand&rdquo (Hatchery is often first structure built when expanding) &ldquoresource gathering by worker bees&rdquo &ldquostructures for developing the young in their pre-metamorphosis stage&rdquoHatchery
Colony Behavior IISurveys bees as the representative example of colony behavior. Examines highly developed hives and their effects in enabling further evolutionary differentiation. This has led to behaviors including the creation of the Bee-52&rsquos rock group, the show Bee-witched, and monologues such as To Bee or Not to Bee.&rdquohighly developed&rdquo (high in the Zerg tech tree) &ldquohives&rdquo (structure name) &ldquoeffects in enabling further evolutionary differentiation&rdquo (enables further structures and upgrades)Hive
Life Underground IExamines the advantages of digging underground for land species, either to hide from enemies and safely rest, or to lie in wait for unsuspecting prey. Also, I&rsquove heard that some sophisticated animal shelters enable their inhabitants to go underground. Don&rsquot ask me how that works. I&rsquom only a first-year professor. Ask the professor of Life Underground II.&rdquosome sophisticated animal shelters enable their inhabitants to go underground&rdquo (Burrow upgrade is enabled by Lair)Lair
Life Underground IIUnlike Life Underground I, this course looks at creatures who spend their whole lifetime underground within sophisticated underground networks that are further extended by each individual.&rdquonetworks&rdquo (&ldquonetwork&rdquo is in structure name) &ldquocreatures who spend their whole lifetime underground within sophisticated underground networks that are further extended by each individual&rdquo (describes Nydus Worm)Nydus Network
Nest Protection IWould you like to know how animals protect their nests? I bet you would. Nests are cool. Get hands-on by prototyping some structures in lab for protection of nests from aerial predators. Students are requested to bring their own predators for testing.&rdquostructures . for protection . from aerial predators&rdquoSpore Crawler
Nest Protection IIGet ready to be dazzled. You can now learn to build new structures for protection from terrestrial predators. Students are not required to bring predators, as they will be expected to attack each other&rsquos nests for testing.&rdquostructures for protection from terrestrial predators&rdquoSpine Crawler
Non-Oxygen-Based LifeformsDiscusses evolution and lifeforms aided by gases other than oxygen. Lab supplies include gas masks, clean suits, volcano suits, and very long tongs.&rdquoevolution and lifeforms aided by gases other than oxygen&rdquo (Vespene gas)Extractor
ParasitesEwwwwww, parasites. Parasites are gross. Students will learn to classify parasites (temporary vs. permanent, affecting neurological circuits of the host, etc.) and determine the best way to squish, smash, slap, or otherwise get rid of them. Gross.&rdquoparasites&rdquo &ldquotemporary vs. permanent&rdquo (Neural Parasite vs. Infested Terran) &ldquoaffecting neurological circuits of the host&rdquo (Neural Parasite)Infestation Pit
Predator Mutations IA variety of subjects require students to provide their own predators. Students wishing help in breeding such predators would benefit from this course. For a small lab fee, ineffective predators can be exposed to radiation to garner useful mutations like stronger claws, sharper spines, and tougher shells. Then, a series of specialized exercises will help them make good use of their new modifications.&rdquostronger claws, sharper spines, and tougher shells&rdquo (Melee Attacks, Missile Attacks, and Ground Carapace upgrades, respectively)Evolution Chamber
Predator Mutations IIThis subject studies a species of land predators that has adapted to prey in an unusual way: developing the ability to kill prey from a distance by launching spines. There will be mandatory field visits to the species&rsquos den for research. Students who get themselves maimed or killed will not receive a passing grade.&rdquoability to kill prey from a distance by launching spines&rdquo (describes Hydralisk) &ldquoden&rdquo (word is in structure name)Hydralisk Den
Predator Mutations IIIStudies the evolution of massive land predators at the top of the food chain. The professor and TAs will absolutely not be accompanying students on mandatory research trips to the caverns where these beasts reside. Best of luck.&rdquomassive land predators&rdquo (Ultralisks are the largest Zerg units) &ldquocaverns&rdquo (&ldquocavern&rdquo is in structure name)Ultralisk Cavern
Wound HealingSuitable for students who are too cowardly to take Predator Mutations II and III but require the extra units. Most animals have evolved the ability to heal wounds by regenerating tissue over time. This subject examines the development of species that have the highest tissue recuperation rates (as measured in the laboratory under ideal conditions).&rdquospecies that have the highest tissue recuperation rates (as measured in the laboratory under ideal conditions)&rdquo (Roach has the fastest regeneration rate when burrowed)Roach Warren

The next step is to rearrange the subject titles/descriptions back under the correct subject numbers. Notice that the Zerg tech tree is a dependency graph with the structures (subject descriptions) as the nodes, just as the prereqs for the subject numbers create a dependency graph. The two dependency graphs match up exactly, so that it&rsquos possible to determine which subject goes with which number, with only a few exceptions.

  • The Baneling Nest, Roach Warren, and Spine Crawler all depend on the Spawning Pool but nothing depends on these structures. So it&rsquos initially unclear how to assign these three subjects.
  • Similarly, the Hydralisk Den and Nydus Network both depend on the Lair but nothing depends on these structures, so it&rsquos initially unclear how to assign these two subjects.

However, notice that the subject numbers that should match up with these five structures all come with an extra bit of info called the &ldquolab time.&rdquo In fact, the listed &ldquolab times&rdquo are simply the amounts of time it takes to build these five structures. They enable you to disambiguate the mappings for these five structures.

The extraction method is to use the digits after the decimal point in each subject number to index into the letters of the subject description.

Here are the subject associations and extracted letters:

Subject
number
Subject
prereqs
Subject
&ldquolab time&rdquo
Matching
Zerg structure
Zerg prereqsZerg
build time
Subject description (initial portion)Index
(subject number)
Letter
7E.01none Extractornone Discusses. 01D
7E.02none Hatcherynone Surveys. 02U
7E.037E.02 Evolution ChamberHatchery A variety. 03A
7E.047E.03 Spore CrawlerEvolution Chamber Would. 04L
7E.097E.02 Spawning PoolHatchery Some claim. 09M
7E.127E.0960Baneling NestSpawning Pool60A continuation. 12O
7E.137E.02, 7E.09 LairHatchery, Spawning Pool Examines the advantages. 13D
7E.157E.13 Infestation PitLair Ewwwwww, parasites. 15E
7E.177E.0955Roach WarrenSpawning Pool55Suitable for students. 17N
7E.187E.1350Nydus NetworkLair50Unlike Life Underground. 18O
7E.207E.13, 7E.15 HiveLair, Infestation Pit Surveys bees as the representative. 20R
7E.267E.1340Hydralisk DenLair40This subject studies a species. 26S
7E.287E.20 Ultralisk CavernHive Studies the evolution of massive. 28E
7E.297E.13 SpireLair Studies two species of flying animals. 29M
7E.317E.0950Spine CrawlerSpawning Pool50Get ready to be dazzled. You can now learn. 31A
7E.357E.20, 7E.29 Greater SpireHive, Spire A follow-up to the previous course of learning. 35N

The final message is DUAL-MODE NORSEMAN, which clues the answer VIKING (a StarCraft II unit that has two modes).


Stewart Calculus 7e Solutions Chapter 14 Partial Derivatives Exercise 14.3

Stewart Calculus 7e Solutions Chapter 14 Partial Derivatives Exercise 14.3

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< Answer 63E.
img src=”https://c1.staticflickr.com/1/325/32279267215_0da1c5b142_o.jpg” width=�″ height=�″ alt=”Stewart-Calculus-7e-Solutions-Chapter-14.3-Partial-Derivatives-63E”>

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Q: Elampei et an object moves r(4)= tit12tj+ 3.64 k [email protected]=2 k) Velocity @ tz/ ) speed d) Accelera.

A: Click to see the answer

Q: Solve for the Taylor series of the following

Q: Consider the function seen in the attached image: A) Find all points x where the function g(x) is di.

A: Click to see the answer

Q: 1. Find The Fourier series for the function defined by 0 < x < 4 1 -4 < x<0) Sx - 2 f(x) = <*

A: “Since you have asked multiple question, we will solve the first question for you. If you want any s.

Q: 113. Write an example that illustrates why log,(x + y) + log2 x + log2 y.

A: To write an example that illustrates log2x+y≠log2x+log2y. Example: Let x=1 and y=3. LHS=log2x+y=log2.

Q: Curve Sketching of Rational function

A: y=4x2-4x4-16⇒y=4x2-1x22-42⇒y=4x-1x+1x2-4x2+4⇒y=4x-1x+1x-2x+2x2+4 Since the value of denominator is z.

Q: In Exercises 78–81, find all the complex roots. Write roots in rectangular form. 78. The complex fou.

A: Given: 78. 16cos2π3+i sin2π3 79. 8i 80.-1

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x 2s + 2, y = s + 3, z.

A: find out point of intersection of lines x=t,y=-t+2,z=t+1 and x=2s+2, y=s+3,z=5s+6


SSLStream Exception RemoteCertificateNameMismatch #26583

I have SSL exception when call RemoteCertificateValidationCallback from a tcp client.

Follow the test case (.NET Core 2.1 on Ubuntu 18.04) :

The server and the client are on the same local computer. I created a self-signed certificate with openssl with example.net as the server name (CN = example.net).

I modified my /etc/hosts file in order to have the example.net resolution on 127.0.0.1:

I then copied the certificate to /usr/share/ca-certificates
dpkg-reconfigure ca-certificates

The server is running well with dotnet run server.crt . On the other hand it generates a TCP connection on the address 52.216.133.3:443, I think it is due to the use of:
new TcpListener (IPAddress.Any, 8080)

On the other hand I can not make the client work.
I get an exception at launch:

dotnet run 52.169.64.244 example.net

Do you have any information to help me?

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Karelz commented Jun 23, 2018

@bartonjs @GrabYourPitchforks would you be the right people to answer it?

Bartonjs commented Jun 23, 2018

In order to say I'd need to see the certificate, or the output of openssl x509 -in server.crt -text (optionally with -noout to avoid re-printing the certificate).

Quick guess is that while the CN says "example.net" there's a Subject Alternative Name extension and it doesn't contain a dNSName entry for "example.net". (SAN isn't additive to CN, it replaces it for TLS host matching)

Aborderon commented Jun 23, 2018

@bartonjs thank you for your comeback,
here is the output of the certificate with the command:

openssl x509 -in server.crt -text -noout

To create the certificate, I followed the official documentation of ubuntu :

Aborderon commented Jun 25, 2018

I just created a new self signed certificate with openssl using SAN.

I followed this procedure: https://fabianlee.org/2018/02/17/ubuntu-creating-a-self-signed-san-certificate-using-openssl/
I added the certificate to /usr/share/ca-certificates and I modified my /etc/hosts file in order to have the example example.net resolution on 127.0.0.1

Here is the new certificate output:

However, I always get the same message with the client at launch whether with:
dotnet run 52.169.64.244 example.net
or :
dotnet run 52.169.64.244 example

Bartonjs commented Jun 25, 2018

Both of those certificates do seem like they should work for example.net .

I'd recommend one or both of

  1. openssl s_client -connect 52.169.64.244:443 , copy the certificate out of the output and see if it is the same as the one you generated.
  2. Register a certificate validation callback and inspect the certificate presented in the callback to see if it is the one you generated.

The simplest explanation at this point feels like the server certificate isn't actually the one you generated.

Aborderon commented Jun 25, 2018

I am in the middle of testing, a pity that there is no example on the document for the use of SslStream.

I would like to understand some points to solve my problem.

Do I need to use the server.crt file with dotnet cli or a .pfx file containing the private key?

The TCP listener is created with:
new TcpListener (IPAddress.Any, 8080)

Why I have with an IP address 52.169.64.244:443, what is 52.169.64.244?

Here is the output of the command: openssl s_client -connect 52.169.64.244:443

The certificate does not match the generated certificate .

Here is the output of the command netstat -anopt when the server is started:
tcp 0 0 0.0.0.0:8080 0.0.0.0:* LISTEN 8977/dotnet off (0.00/0/0)
tcp 0 0 192.168.0.18:43867 52.169.64.244:443 ESTABLISHED 8929/dotnet off (0.00/0/0)

Bartonjs commented Jun 25, 2018

Do I need to use the server.crt file with dotnet cli or a .pfx file containing the private key?

If you're being the TLS server or doing client auth you probably need the PFX. But if you use the public-only certificate there's some logic to try to find the private key using the CurrentUserMy and/or LocalMachineMy certificate stores (if I recall correctly).

Why I have with an IP address 52.169.64.244:443, what is 52.169.64.244?

52.169.64.244:443 is an endpoint, specifying the host (an IPv4 address) of 52.169.64.244 and a port number of 443.

Here is the output of the command: openssl s_client -connect 52.169.64.244:443 .

Looks like that IP address / endpoint belong to a visualstudio.com. Presumably that's not where your server application is running, which is why you get a hostname mismatch (because that property's certificate doesn't claim to be good for example.net).

If you've followed the linked sample code exactly then the server you're trying to host is listening on port 8080 (which is shown in your netstat command as the first line, any incoming IP, port 8080).


5 Benefits of Back Strengthening Exercises for Seniors

  1. Balance: Back strength supports balance, and reduces the risk of falls and fractures.
  1. Pain Relief: Weak back muscles tend to be associated with low back pain. However, pain may be relieved by strengthening the back muscles.
  1. Prevention: Back strengthening can prevent or postpone adverse effects of diseases that reduce muscle and bone mass, and further injury.
  1. Posture Improvement: Back-focused exercises can strengthen the spine and muscles. This can prevent the spine from curving.
  1. Quality of life: Older adults can continue performing everyday tasks independently. A strong back will reduce the demand for long-term care.

19.3N, 17.7E - Mount Alphus Menhir Ring

Four Empyrean Standing Stones at 19.3N, 17.7E on the top of Mount Alphus.
Standing in between the stones restores Mana:

You feel a great swell of power rise from the ground beneath you, restoring 10 points of your mana.


17.7E: Exercises

Short-Answer Questions ➢ Name and describe four cost behavior patterns. ➢ Describe two methods of determining the fixed and variable components of mixed costs. ➢ What is meant by the term break-even point? ➢ What are two ways in which the break-even point can be expressed? ➢ What is the relevant range? ➢ What is the formula for calculating the break-even point in sales revenue? ➢ What formula is used to solve for the break-even point in units? ➢ How can the break-even formula be altered to calculate the number of units that must be sold to achieve a desired level of income? ➢ Why might a business wish to lower its break-even point? How would it go about lowering the break-even point? ➢ What effect would you expect the mechanization and automation of production processes to have on the break-even point? ➢ Real world question Assume your college is considering hiring a lecturer to teach a special class in communication skills. Identify at least two costs that college administrators might consider in deciding whether to hire the lecturer and add the class. ➢ Real world question Two enterprising students are considering renting space and opening a class video recording service. They would hire camera operators to record large introductory classes. The students taking the classes would be charged a fee to rent and view the video on their laptops or smart phones. Identify as many costs of this business as you can and indicate which would be variable and which would be fixed. Exercises Exercise A Name and match the types of cost behavior with the appropriate diagram below: Exercise B Research Inc., performs laboratory tests. Use the high-low method to determine the fixed and variable components of a mixed cost, given the following observations:

Volume (number of tests) Total cost
4,800 $6,000
19,200 9,600

Exercise C Compute the break-even point in sales dollars if fixed costs are $200,000 and the total contribution margin is 20% of revenue.

Exercise D Barney Company makes and sells stuffed animals. One product, Michael Bears, sells for $28 per bear. Michael Bears have fixed costs of $100,000 per month and a variable cost of $12 per bear. How many Michael Bears must be produced and sold each month to break even?

Exercise E Peter Garcia Meza is considering buying a company if it will break even or earn net income on revenues of $80,000 per month. The company that Peter is considering sells each unit it produces for $5. Use the following cost data to compute the variable cost per unit and the fixed cost for the period. Calculate the break-even point in sales dollars. Should Peter buy this company?

Volume (units) Cost
8,000 $70,000
68,000 190,000

Exercise F Never Late Delivery currently delivers packages for $9 each. The variable cost is $3 per package, and fixed costs are $60,000 per month. Compute the break-even point in both sales dollars and units under each of the following independent assumptions. Comment on why the break-even points are different.

  1. The costs and selling price are as just given.
  2. Fixed costs are increased to $75,000.
  3. Selling price is increased by 10%. (Fixed costs are $60,000.)
  4. Variable cost is increased to $4.50 per unit. (Fixed costs are $60,000 and selling price is $9.)

Exercise G Best Eastern Motel is a regional motel chain. Its rooms rent for $100 per night, on average. The variable cost is $40 a room per night. Fixed costs are $5,000,000 per year. The company currently rents 200,000 units per year, with each unit defined as one room for one night. Should this company undertake an advertising campaign resulting in a $500,000 increase in fixed costs per year, no change in variable cost per unit, and a 10% increase in revenue (resulting from an increase in the number of rooms rented)? What is the margin of safety before and after the campaign?

Exercise H Fall-For-Fun Company sells three products. Last year’s sales were $600,000 for parachutes, $800,000 for hang gliders, and $200,000 for bungee jumping harnesses. Variable costs were: parachutes, $400,000 hang gliders, $700,000 and bungee jumping harnesses, $100,000. Fixed costs were $240,000. Find (a) the break-even point in sales dollars and (b) the margin of safety.

Exercise I Early Horizons Day Care Center has fixed costs of $300,000 per year and variable costs of $10 per child per day. If it charges $25 a child per day, what will be its break-even point expressed in dollars of revenue? How much revenue would be required for Early Horizons Day Care to earn $100,000 net income per year?

Problem A Assume the local franchise of Togorio Sandwich Company assigns you the task of estimating total maintenance cost on its delivery vehicles. This cost is a mixed cost. You receive the following data from past months:

  1. Using the high-low method, determine the total amount of fixed costs and the amount of variable cost per unit. Draw the cost line.
  2. Prepare a scatter diagram, plot the actual costs, and visually fit a linear cost line to the points. Estimate the amount of total fixed costs and the amount of variable cost per unit.
  1. Using the preceding graph, label the relevant range, total costs, fixed costs, break-even point, and profit and loss areas.
  2. At 8,000 units, what are the variable costs, fixed costs, sales, and contribution margin amounts in dollars?
  3. At 8,000 units, is there net income or loss? How much?

Problem C The management of Bootleg Company wants to know the break-even point for its new line hiking boots under each of the following independent assumptions. The selling price is $50 pair of boots unless otherwise stated. (Each pair of boots is one unit.)

  1. Fixed costs are $300,000 variable cost is $30 per unit.
  2. Fixed costs are $300,000 variable cost is $20 per unit.
  3. Fixed costs are $250,000 variable cost is $20 per unit.
  4. Fixed costs are $250,000 selling price is $40 and variable cost is $30 per unit.

Compute the break-even point in units and sales dollars for each of the four independent case.

Problem D Refer to the previous problem. Bootleg Company’s sales are $1,100,000. Determine the margin (safety in dollars for cases (a) through (d).

Problem E Using the data in the Bootleg Company problem (a through d), determine the level of sales dollars required achieve a net income of $125,000.

Problem F Bikes Unlimited, Inc., sells three types of bicycles. It has fixed costs of $258,000 per month. The sales and variable costs of these products for April follow:

Bikes
Racing Mountain Touring
Sales $1,00,000 $1,500,000 $2,500,000
Variable costs 700,000 900,000 1,250,000

Compute the break-even point in sales dollars.

Problem G a. Assume that fixed costs of Celtics Company are $180,000 per year, variable cost is $12 per unit, and selling price is $30 per unit. Determine the break-even point in sales dollars.

  1. Hawks Corporation breaks even when its sales amount to $89,600,000. In 2010, its sales were $14,400,000, and its variable costs amounted to $5,760,000. Determine the amount of its fixed costs.
  2. The sales of Niners Corporation last year amounted to $20,000,000, its variable costs were $6,000,000, and its fixed costs were $4,000,000. At what level of sales dollars would the Niners Corporation break even?
  3. What would have been the net income of the Niners Corporation in part (c), if sales volume had been 10% higher but selling prices had remained unchanged?
  4. What would have been the net income of the Niners Corporation in part (c), if variable costs had been 10% lower?
  5. What would have been the net income of the Niners Corporation in part (c), if fixed costs had been 10% lower?
  6. Determine the break-even point in sales dollars for the Niners Corporation on the basis of the data given in (e) and then in (f).

Answer each of the preceding questions.

Problem H After graduating from college, M. J. Orth started a company that produced cookbooks. After three years, Orth decided to analyze how well the company was doing. He discovered the company has fixed costs of $1,200,000 per year, variable cost of $14.40 per cookbook (on average), and a selling price of $26.90 per cookbook (on average).

How many units (that is, cookbooks) must be sold to break even? How many units will the company have to sell to earn $48,000?

Problem I The operating results for two companies follow:

  1. Prepare a cost-volume-profit chart for Sierra Company, indicating the break-even point, the contribution margin, and the areas of income and losses.
  2. Compute the break-even point of both companies in sales dollars and units.
  3. Assume that without changes in selling price, the sales of each company decline by 10%. Prepare income statements similar to the preceding statements for both companies.

Problem J Soundoff, Inc., a leading manufacturer of electronic equipment, decided to analyze the profitability of its new portable compact disc (CD) players. On the CD player line, the company incurred $2,520,000 of fixed costs per month while selling 20,000 units at $600 each. Variable cost was $240 per unit.

Recently, a new machine used in the production of CD players has become available it is more efficient than the machine currently being used. The new machine would reduce the company’s variable costs by 20%, and leasing it would increase fixed costs by $96,000 per year.

  1. Compute the break-even point in units assuming use of the old machine.
  2. Compute the break-even point in units assuming use of the new machine.
  3. Assuming that total sales remain at $12,000,000 and that the new machine is leased, compute the expected net income.
  4. Should the new machine be leased? Why?

Problem K Surething CD Company reports sales of $720,000, variable costs of $432,000, and fixed costs of $108,000. If the company spends $72,000 on a sales promotion campaign, it estimates that sales will be increased by $270,000.

Determine whether the sales promotion campaign should be undertaken. Provide calculations.

Alternate problems

Alternate problem A Hear Right Company has identified certain variable and fixed costs in its production of hearing aids. Management wants you to divide one of its mixed costs into its fixed and variable portions. Here are the data for this cost:

  1. Using the high-low method, determine the total amount of fixed costs and the amount of variable cost per unit. Draw the cost line.
  2. Prepare a scatter diagram, plot the actual costs, and visually fit a linear cost line to the points. Estimate the amount of total fixed costs and the variable cost per unit.

Alternate problem B

  1. Using the preceding graph, label the relevant range, total costs, fixed costs, break-even point, and profit and loss areas.
  2. At 18,000 units, what would sales revenue, total costs, fixed and variable costs be?
  3. At 18,000 units, would there be a profit or loss? How much?

Alternate problem C Jefferson Company has a plant capacity of 100,000 units, at which level variable costs are $720,000. Fixed costs are expected to be $432,000. Each unit of product sells for $12.

  1. Determine the company’s break-even point in sales dollars and units.
  2. At what level of sales dollars would the company earn net income of $144,000?
  3. If the selling price were raised to $14.40 per unit, at what level of sales dollars would the company earn $144,000?

Alternate problem D a. Determine the break-even point in sales dollars and units for Cowboys Company that has fixed costs of $63,000, variable cost of $24.50 per unit, and a selling price of $35.00 per unit.

  1. Wildcats Company breaks even when sales are $280,000. In March, sales were $670,000, and variable costs were $536,000. Compute the amount of fixed costs.
  2. Hoosiers Company had sales in June of $84,000 variable costs of $46,200 and fixed costs of $50,400. At what level of sales, in dollars, would the company break even?
  3. What would the break-even point in sales dollars have been in (c) if variable costs had been 10% higher?
  4. What would the break-even point in sales dollars have been in (c) if fixed costs had been 10% higher?
  5. Compute the break-even point in sales dollars for Hoosiers Company in (c) under the assumptions of (d) and (e) together.

Answer each of the preceding questions.

Alternate problem E See Right Company makes contact lenses. The company has a plant capacity of 200,000 units. Variable costs are $4,000,000 at 100% capacity. Fixed costs are $2,000,000 per year, but this is true only between 50,000 and 200,000 units.

  1. Prepare a cost-volume-profit chart for See Right Company assuming it sells its product for $40 each. Indicate on the chart the relevant range, break-even point, and the areas of net income and losses.
  2. Compute the break-even point in units.
  3. How many units would have to be sold to earn $200,000 per year?

Alternate problem F Mr Feelds Cookies has fixed costs of $360,000 per year. It sells three types of cookies. The cost and revenue data for these products follow:

Cookies
Cream cake Goo fill Sweet tooth
Sales $64,000 $95,0000 $131,000
Variable costs 38,400 55,100 66,000

Compute the break-even point in sales dollars.

Beyond the numbers—Critical thinking

Business decision case A Quality Furniture Company is operating at almost 100% of capacity. The company expects sales to increase by 25% in 2011. To satisfy the demand for its product, the company is considering two alternatives: The first alternative would increase fixed costs by 15% but not affect variable costs. The second alternative would not affect fixed costs but increase variable costs to 60% of the selling price of the company’s product.

This is Quality Furniture Company’s condensed income statement for 2010:

  1. Determine the break-even point in sales dollars for 2011 under each of the alternatives.
  2. Determine projected income for 2011 under each of the alternatives.
  3. Which alternative would you recommend? Why?

Business decision case B When the Weidkamp Company’s plant is completely idle, fixed costs amount to $720,000. When the plant operates at levels of 50% of capacity or less, its fixed costs are $840,000 at levels more than 50% of capacity, its fixed costs are $1,200,000. The company’s variable costs at full capacity (100,000 units) amount to $1,800,000.

  1. Assuming that the company’s product sells for $60 per unit, what is the company’s break-even point in sales dollars?
  2. Using only the data given, at what level of sales would it be more economical to close the factory than to operate it? In other words, at what level would operating losses approximate the losses incurred if the factory closed down completely?
  3. Assume that Weidkamp Company is operating at 50% of its capacity and decides to reduce the selling price from $60 per unit to $36 per unit to increase sales. At what percentage of capacity must the company operate to break even at the reduced sales price?

Business decision case C Monroe Company has recently been awarded a contract to sell 25,000 units of its product to the federal government. Monroe manufactures the components of the product rather than purchasing them. When the news of the contract was released to the public, President Mary Monroe, received a call from the president of the McLean Corporation, Carl Cahn. Cahn offered to sell Monroe 25,000 units of a needed component, Part J, for $15.00 each. After receiving the offer, Monroe calls you into her office and asks you to recommend whether to accept or reject Cahn’s offer.

You go to the company’s records and obtain the following information concerning the production of Part J.

You calculate the unit cost of Part J to be $12.12 or ($2,424,000/200,000). But you suspect that this unit cost may not hold true at all production levels. To find out, you consult the production manager. She tells you that to meet the increased production needs, equipment would have to be rented and the production workers would work some overtime. She estimates the machine rental to be $60,000 and the total overtime premiums to be $108,000. She provides you with the following information:

The production manager advises you to reject Cahn’s offer, since the unit cost of Part J would be only $12.80 or ($2,880,000/225,000 units) with the additional costs of equipment rental and overtime premiums. This amount still is less than the $15.00 that Cahn would charge. Undecided, you return to your office to consider the matter further.

  1. Using the high-low method, compute the variable cost portion of manufacturing overhead. (Remember that the costs of equipment rental and overtime premiums are included in manufacturing overhead. Subtract these amounts before performing the calculation).
  2. Compute the total costs to manufacture the additional units of Part J. (Note: include overtime premiums as a part of direct labor.)
  3. Compute the unit cost to manufacture the additional units of Part J.
  4. Write a report recommending that Monroe accept or reject Cahn’s offer.

Business decision case D Refer to the “A broader perspective: Major television networks are finding it harder to break even” discussion of cost-volume-profit analysis for television networks. Write a memo to your instructor describing how the networks can reduce their break-even points.

Group project E In teams of two or three students, develop a cost-volume-profit equation for a new business that you might start. Examples of such businesses are a portable espresso bar, a pizza stand, a campus movie theater, a package delivery service, a campus-to-airport limousine service, and a T-shirt printing business.

Your equation should be in the form: Profits = (Price per unit X Volume) – (Variable cost per unit X Volume) – Fixed costs per period. Pick a period of time, say one month, and project the unit price, volume, unit variable cost, and fixed costs for the period. From this information, you will be able to estimate the profits—or losses—for the period. Select one spokesperson for your team to tell the class about your proposed business and its profits or losses. Good luck, and have fun.

Group project F Refer to “A broader perspective: Even colleges use CVP” discussion of how cost-volume-profit analysis is used by colleges. In teams of two or three students, write a memo to your instructor defining step costs and explain why the step costs identified in the case are classified as such. Also include in your memo how the school might lower its break-even point.

Group project G In teams of two or three students, address the following questions:

  • Why would a company consider increasing automation and decreasing the use of labor if the result would be an increase in the break-even point?
  • Would an increase in automation increase fixed costs over the short-run, long-run, or both?

Write a memo to your instructor that addresses both questions. Be sure to explain your answers.

Using the Internet—A view of the real world

Visit the website for Intel Corporation, a high technology manufacturing company.

Go to the company’s most recent financial statements and review the consolidated statement of income. What additional information, if any, would you need to perform cost-volume-profit analysis? Why is this information excluded from Intel’s income statement?

Visit the website for Wal-Mart Corporation, a retail company.

Go to the company’s most recent financial statements and review the statement of income. What additional information, if any, would you need to perform cost-volume-profit analysis? Why is this information excluded from Wal-Mart Corporation’s income statement?

level (225,000 units)Direct labor$1,404,000Direct materials648,000

(including equipmental rental and overtime premiums)

The production manager advises you to reject Cahn’s offer, since the unit cost of Part J would be only $12.80 or ($2,880,000/225,000 units) with the additional costs of equipment rental and overtime premiums. This amount still is less than the $15.00 that Cahn would charge. Undecided, you return to your office to consider the matter further.


17.7E: Exercises

The exercises are numbered according to the numbers of the relevant sections of the manual.

Exercise 2.1 Mean value and variance

In this exercise we use part of the length-frequency data of the coral trout ( Plectropomus leopardus ) presented in Fig. 3.4.0.2, namely those in the length interval 23-29 cm. These fish are assumed to belong to one cohort. The length-frequencies are presented in Fig. 17.2.1.

Fig. 17.2.1 Length-frequency sample

Exercise 2.2 The normal distribution

This exercise consists of fitting a normal distribution to the length-frequency sample of Exercise 2.1, by using the expression:

for a sufficient number of x-values allowing you to draw the bell-shaped curve.

For your convenience introduce the auxiliary symbols:

so that the formula above can be written

Since A and B do not depend on L and as they are going to be used many times, it is convenient to calculate them separately before-hand.

2) Calculate Fc(x) for the following values of x:

3) Draw the bell-shaped curve on Fig. 17.2.1

Exercise 2.3 Confidence limits

Exercise 2.4 Ordinary linear regression analysis

It is often observed that the more boats participate in a fishery the lower the catch per boat will be. This is not surprising when one considers the fish stock as a limited resource which all boats have to share. In Chapter 9 we shall deal with the fisheries theory behind this model.

The data shown below in the worksheet are from the Pakistan shrimp fishery (Van Zalinge and Sparre, 1986).

Student's distribution: t n-2 =
confidence limits of b and a:
b - sb * t n-2 , b + sb * t n-2 = [________________,________________]
a - sa * t n-2 , a + sa * t n-2 = [________________,________________]

Exercise 2.5 The correlation coefficient

Refer to Exercise 2.4. Does the correlation coefficient make sense in the example of catch per boat regressed on number of boats? Consider which of the variables is the natural candidate as independent variable. Can we (in principle) decide in advance on the values of one of them?

Exercise 2.6 Linear transformations of normal distributions, used as a tool to separate two overlapping normal distributions (the Bhattacharya method)

Fig. 17.2.6A shows a frequency distribution which is the result of two overlapping normal distributions "a" and "b". We assume that the length-frequencies presented in Fig. 17.2.6B are also a combination of two normal distributions. The aim of the exercise is to separate these two components. The total sample size is 398. Assume that each component has 50% of the total or 199. Further assume that the frequencies at the left somewhat below the top are fully representative for component "a", while those at the bottom of the right side are fully representative for component "b".

Fig. 17.2.6A Combined distribution of two overlapping normal distributions

Fig. 17.2.6B Length-frequency sample (assumed to consist of two normal distributions

1) Complete Worksheet 2.6a.

2) Plot D ln F(z) = y' against x + dL/2 = z and decide which points lie on straight lines with negative slopes (see Fig. 2.6.5).

3) On the basis of the plot select the points to be used for the linear regressions. (Avoid the area of overlap and points based on very few observations). Do the two linear regressions and determine a and b.

4) Calculate , s 2 = -1/b and s = Ö s 2 for each component.

5) Draw the two plots which represent each distribution in linear form.

6) We now want to convert the straight lines into the corresponding theoretical (calculated) normal distributions. Using Eq. 2.2.1 calculate Fc(x) for both normal distributions for a sufficient number of x-values to allow you to draw the two bell-shaped curves superimposed on Fig. 17.2.6B. Assume n = 199 for both components. (Use the same method as presented in Exercise 2.2). Complete Worksheet 2.6b.


17.7E: Exercises

Liveness and readiness probes

kubernetes.io > Documentation > Tasks > Configure Pods and Containers > Configure Liveness and Readiness Probes

Create an nginx pod with a liveness probe that just runs the command 'ls'. Save its YAML in pod.yaml. Run it, check its probe status, delete it.

Modify the pod.yaml file so that liveness probe starts kicking in after 5 seconds whereas the interval between probes would be 5 seconds. Run it, check the probe, delete it.

Create an nginx pod (that includes port 80) with an HTTP readinessProbe on path '/' on port 80. Again, run it, check the readinessProbe, delete it.

Lots of pods are running in qa , alan , test , production namespaces. All of these pods are configured with liveness probe. Please list all pods whose liveness probe are failed in the format of <namespace>/<pod name> per line.

A typical liveness probe failure event

collect failed pods namespace by namespace

Create a busybox pod that runs 'i=0 while true do echo "$i: $(date)" i=$((i+1)) sleep 1 done'. Check its logs

Create a busybox pod that runs 'ls /notexist'. Determine if there's an error (of course there is), see it. In the end, delete the pod

Create a busybox pod that runs 'notexist'. Determine if there's an error (of course there is), see it. In the end, delete the pod forcefully with a 0 grace period

Get CPU/memory utilization for nodes (metrics-server must be running)

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