Select (W) take QUEEN'S FACE (X), 2/4 LIGHT BULBS (S).Select (U) place ROSE (V) speak to character.Place MOON, SUN and BLUE CANDLE use MATCHES (Q). Place BLUE EYE (N) select book for MINI-HOP (O) take 1/6 FIGURINE.Place LADDER (L) take SUN, BLUE EYE (M).Boards NAILS, HAMMER on BROKEN LADDER for LADDER.Use HAMMER 2x (J) take BLUE CANDLE (K).Take note, NAILS (G) move hand, take BOX (H) take 2/3 TRIANGLES (I).Take drawing place BRICK take 3/3 TOKENS (A).Play HOP (T) receive RED EYE PIECE take BROKEN LADDER (U).Use WRENCH (Q) remove cover, take VALVE KNOB (R).Use KNIFE take MOON (N) play HOP (O) receive HAMMER.Take note use KNIFE 3x (L) take 1/3 FLOWER TOKEN (M).Place TORCH use MATCHES (F) take SNOWFLAKE (G).Take RAG (A) use RAG 2x (B) take 2/2 BOARDS, GLOVE (C).Place MECHANISM PART take LIGHTNING SIGN (V).Place 2 GONDOLA KEY PIECE (R) TICKET FRAGMENT (S).Take GONDOLA KEY PIECE place STAINED GLASS PIECE (O) take MECHANISM PART (P), GONDOLA KEY PIECE (Q).Place COIN use TONGS for HEATED COIN (K).Place BLUE ROSE, RED ROSE (I) read journal take DOOR CODE (J).Speak to character remove cloth take KEY (F).Open cabinet place BOOK (B) select 1-4 take BLUE ROSE (C).Place BUNDLED HEART (A) speak to character receive ICY HEART.Place BAG CODE match symbols (T) take diagram, 4/5 GEMS (U).
0 Comments
Many users with newer Windows computers using the Intel Gen-12 processor report that MMD opens but the stage area is covered by a white screen. – The White Screen covering the Stage area? Still need help? Leave a comment or send Reggie an email. See that post to find the answers you need as you Our Parkeerwacht has written a single article describing the common errors and the latest solutions to those errors. Runtime packages are products specifically designed to be able for all versions to coexist on the same machine. ¹ The above does not mean you have to rollback higher versions of these libraries (that you most probably have) in favor of more obsolete ones. The majority of comments asking for help about MMD acting wrong will be countered with “Have you DirectX 9.0c and MS Visual C++ runtimes installed?” inquiry, and more likely than not, resolving these will resolve your problem as well. MMD will not run properly without them, and will not accept higher versions of the same as a proper replacement¹. It is critically important to have those packages installed in your system. ・ Microsoft Visual C++ 2010 Redistributable Package (圆4) ・ Microsoft Visual C++ 2008 Redistributable Package (圆4) ・ DirectX 9.0c End-User Runtime (a BIG one: 98MB) ・ Microsoft Visual C++ 2008 Redistributable Package ・ Microsoft Visual C++ 2005 Redistributable Package The VPVP page recommends that you download and install: MMD 9.32 runs great for most users of Windows XP, Windows Vista, Windows 7, 8 and Windows 10 … MikuMikuDance MMD requires a Windows PC computer with a mouse and a strong graphics card.ĭownload MMD 9.32 from LearnMMD, open it up and see what you have … and then hurry back to for MMD tutorials! See LearnMMD’s Step-by-Step MMD instructions page. MMD 9.32 from ! MMD 9.32 is the latest release of MikuMikuDance!Ĭheck out this video by not kakaiya which clearly explains the steps you will take in order to Download and set-up MikuMikuDance… MMDįollow Step-by-Step instructions to learn how to run MikuMikuDance! They created a masterful collection of models, accessories and techniques for which all users today are most grateful!ĭownload the Latest Version of MikuMikuDance: The Japanese MMD Community is very strong and very active. The MMD program was introduced in Japan about 2007, without an English translation until 2010. Featuring a high-style Japanese feel, MikuMikuDance has caught-on around the globe with tens of thousands of users and millions of MMD videos uploaded world-wide. MikuMikuDance is a free 3D animation software developed as a promotional element for fans of the Sony/Sega Vocaloid product. Try some of LearnMMD’s accessories and stages.Load other useful programs that will help you.Download the latest version of MikuMikuDance.Play is here to be The MikuMikuDance Free 3d Animation Software Instruction Sheet that you have been looking for.īunches of downloads are here … Scroll down and enjoy! So, don't give up, it takes time but you'll get it. Another 4 hours and my entire roofline, attic, and second story are complete to studs. Another 4 hours and my window was done (learning to curve things is a bitch). It took me about 4 hours to make my first 2x4 and understand components and groups and layers and how they interact. Now I'm building the entire house out, I see how valuable this is on a 100+ year old structure. Those plans are proving invaluable in getting my project approved by the historic association. I made plans to restore a missing double-hung wood window, and replace some old vents with arched sashes. If nothing else - download the Mac/PC version! It's much better, and the tutorials are almost exclusively for this version (I didn't understand why the menus were not matching up, turns out they're not there in the web version). There is a serious learning curve to the software (I can't speak to arizona-lad's recommendations, they may be right). I just taught myself Sketchup this month. Regarding sustainability, more than 70% separate different types of waste and throw it in the appropriate bin and 69.4% agree that it is necessary to work on sustainability competences in the curricula. In this respect, more than half say they suffer from stress. It is worth noting that 33% say they have some disability or limiting condition, including psychological ones. In terms of healthy habits, 40% do physical activity or sport two or three times a week. Moreover, 78.3% of the ones who participated in the survey are enrolled full-time. Of these, 47% notes that their jobs are not related to their studies. Of these, 47% indicate that work is not related to their studies.Īlso, 62.7% combine their studies and work, with an average of 22.76 hours per week (including weekdays and weekends). only a minority are enrolled part-time- which contrasts with the fact that 62.7% combine study and work, with an average of 22.76 hours per week (including working days and weekends). Again, 78.3% are enrolled full-time -i.e. Among those who receive grants, 24.4 % are totally dependent on this source to be able to study. Also, on the financial side, 38.3% say they are informed about grants and financial aid, while 44.7% say they have only some information and 17% have no information at all. The main source of income for 34.3% is their family or partner, and 26% have a paid job. The survey also shows that 56.6 % of the participants live with family members, 20 % share a flat and 14 % live with a partner. And it is worth noting that the survey was passed in the post-pandemic stage. The novelty is that it has incorporated innovative elements, such as an entire blog dedicated to health and healthy habits or questions on sustainability and digital, linguistic and gender competences, as well as functional diversity. It has also drawn on surveys on segmented topics (participation, nutrition, expectations, etc.) carried out by the Student Observatory itself. The survey “Studentsʼ living and study conditions” has been inspired by other surveys such as the Eurostudent, in Europe ECoVIPEU, in Spain, and VIU, published by the Vives Network. The aim was to analyse the living and study conditions of all students in order to facilitate decision-making and the design of university policies. The survey was open to all undergraduate, official university master's, master's and postgraduate students, and doctoral students, and it was completed by some 3,300 people. It is also relevant that, for example, 65% of students are convinced that the university education they are taking will help them find a job more than 90% prefer face-to-face or blended rather than virtual learning, and less than 5% are involved in student associations or unions. In this sense, it is also noteworthy that there are more students who identify as non-binary gender in the studies of arts and humanities. The results also show inequalities in gender distribution according to subject areas: women are more present in health sciences and men in sciences and technical disciplines, and in dual pathways. This is one of the conclusions of the first edition of the survey “The studentsʼ living and study conditions”, carried out by the Student Observatory of the UB's Vice-Rector's Office for Students and Participation. The results of the survey “The studentsʼ living and study conditions” have been published.Ī minority of students of the University of Barcelona (14.5%) have family members with a low level of employment, a figure that illustrates that equity in higher education is a challenge that has yet to be met. Demos are usually not time-limited (like Trial software) but the functionality is limited. In some cases, all the functionality is disabled until the license is purchased. Demoĭemo programs have a limited functionality for free, but charge for an advanced set of features or for the removal of advertisements from the program's interfaces. In some cases, ads may be show to the users. Basically, a product is offered Free to Play (Freemium) and the user can decide if he wants to pay the money (Premium) for additional features, services, virtual or physical goods that expand the functionality of the game. This license is commonly used for video games and it allows users to download and play the game for free. There are many different open source licenses but they all must comply with the Open Source Definition - in brief: the software can be freely used, modified and shared. Programs released under this license can be used at no cost for both personal and commercial purposes. Open Source software is software with source code that anyone can inspect, modify or enhance. Freeware products can be used free of charge for both personal and professional (commercial use). Usually commercial software or games are produced for sale or to serve a commercial purpose.Freeware programs can be downloaded used free of charge and without any time limitations. Even though, most trial software products are only time-limited some also have feature limitations. After that trial period (usually 15 to 90 days) the user can decide whether to buy the software or not. Trial software allows the user to evaluate the software for a limited amount of time. Also Available: MuLab (32-bit) and MuLab for Macįreeware programs can be downloaded used free of charge and without any time limitations. Note: Limited functionality in the demo version. Scalable GUI also suits high-resolution monitors.Many preferences so to tweak MuLab to your flavor. Streamlined user-friendly interface and workflow.Including support for extracting grids from audio. Top-quality support for audio & MIDI VST plug-ins.Deep modular editing lets you build your own synths and effects, including nice front panels.Modulate any VST parameter with any of the MUX modulators like LFO, ADSR, Multi-Point Envelope.Freely mix MUX modules and VST plug-ins without limits.Includes hundreds of inspiring instruments and effect presets.Versatile Step Sequencer and Arpeggiator.Includes the MuSampla, MuPad, and MultiSampla sample players.
Lamellar corpuscles, or Pacinian corpuscles or Vater-Pacini corpuscle, are deformation or pressure receptors located in the skin and also in various internal organs. Mechanoreceptors found in areas of the body with less tactile acuity tend to have larger receptive fields. These two types of mechanoreceptors have small discrete receptive fields and are thought to underlie most low-threshold use of the fingers in assessing texture, surface slip, and flutter. In the fingertips and lips, innervation density of slowly adapting type I and rapidly adapting type I mechanoreceptors are greatly increased. Rapidly adapting type II mechanoreceptors (usually called Pacinian) have single Pacinian corpuscle end-organs.Ĭutaneous mechanoreceptors with small, accurate receptive fields are found in areas needing accurate taction (e.g.Rapidly adapting type I mechanoreceptors have multiple Meissner corpuscle end-organs.Rapidly adapting: Rapidly adapting mechanoreceptors include Meissner corpuscle end-organs, Pacinian corpuscle end-organs, hair follicle receptors and some free nerve endings.Intermediate adapting: Some free nerve endings are intermediate adapting.Slowly adapting type II mechanoreceptors have single Ruffini corpuscle end-organs.Slowly adapting type I mechanoreceptors have multiple Merkel corpuscle end-organs.Slowly adapting: Slowly adapting mechanoreceptors include Merkel and Ruffini corpuscle end-organs, and some free nerve endings.Phasic mechanoreceptors are useful in sensing such things as texture or vibrations, whereas tonic receptors are useful for temperature and proprioception among others. Those receptors that are slow to return to their normal firing rate are called tonic. Receptors that adapt quickly (i.e., quickly return to a normal pulse rate) are referred to as "phasic". The cell, however, will soon "adapt" to a constant or static stimulus, and the pulses will subside to a normal rate. When a mechanoreceptor receives a stimulus, it begins to fire impulses or action potentials at an elevated frequency (the stronger the stimulus, the higher the frequency). Ĭutaneous mechanoreceptors can also be separated into categories based on their rates of adaptation. Indeed, the most sensitive mechanoreceptors in humans are the hair cells in the cochlea of the inner ear (no relation to the follicular receptors – they are named for the hair-like mechanosensory stereocilia they possess) these receptors transduce sound for the brain. Hair follicle receptors called hair root plexuses sense when a hair changes position.Itch sensations are caused by stimulation of free nerve ending from chemicals. Free nerve endings detect touch, pressure, stretching, as well as the tickle and itch sensations.They also produce transient responses, but have large receptive fields. The Pacinian corpuscle or Vater-Pacinian corpuscles or Lamellar corpuscles in the skin and fascia detect rapid vibrations of about 200–300 Hz.They have small receptive fields and produce transient responses to the onset and offset of stimulation. It adapts rapidly to changes in texture (vibrations around 50 Hz). The Rapidly Adapting (RA) or Meissner corpuscle end-organ mechanoreceptor (also known as the tactile corpuscles) underlies the perception of light touch such as flutter and slip on the skin. They also produce sustained responses to static stimulation, but have large receptive fields.
The current basic model of the Mini-14 is known as the Ranch Rifle, featuring either wood or synthetic furniture, a blued or stainless steel receiver, and an 18.5" barrel, along with a detachable scope mount. In 2003, the Mini-14 was upgraded with a number of functional and cost-saving features and thereafter, the Mini-14 name became used to describe a family of weapons rather than a sole rifle design. Despite this, it is more mechanically similar to the M1 Garand with its self-cleaning, fixed-piston gas system. Introduced in 1973, the Mini-14 is so named because of its resemblance to the M14 Battle Rifle. It is one of the primary competitors to the AR-15-style rifle on the civilian market. The Ruger Mini-14 is a semi-automatic rifle designed and manufactured by Ruger. I also have a Ruger Letter of Authenticity for it.Black Ruger Mini-14 with 20-round magazine - 5.56x45mm Includes factory 30 for sale by RickA on the best. It took me a while but I finally found mine - a 1985 factory produced stainless Mini 14 folder in excellent condition with the original serial numbered box, original paperwork and 5rd mag. Buy a For Sale: Ruger Mini 14 GB Stainless Steel Factory Folder in MINT99 condition. Note that there may be nothing mechanically or otherwise wrong with a non-factory configured folder, it simply won't have the provenance of a factory-produced folder. Receiver and 20 round magazine are marked for law enforcement and government use only. Synthetic pistol grip and vented upper handguard. They have been tremendously helpful in running S/N's for me and saved me from a few non factory folders. 223 has 20 inch barrel including cage style flash suppressor. If you have the serial number of one that you are considering purchasing you can call Ruger and they might be able to look it up and tell you the configuration that it left the factory. You need to be careful and do your homework. non-factory folders and pay the former's price for an example which is the latter. The problem with attempting to ascertain prices for Mini 14 folders is that many buyers fail to distinguish between factory vs. GB Folding stock models made piror to 1989. (Photo: Samson Mfg.) By now you’re probably. is almost exactly the same as the original dating back to the seventies and eighties. 15Some are referring to the new rifle as the. The Ruger Mini-14 Side Folding Stock by Samson Mfg. Factory configured stainless folders, GB models were $1,500-1,800. They have beensuperceded by the RugerNew Mini-14 Ranch Rifle. Factory configured stainless folders were selling for $1,200-1,500. Factory configured blue folders, GB models were selling for around $1,200. Factory configured blued folders were going for around $1,000-1,200. Non-factory configured stainless folders are next at $900-1,100. Non-factory configured blued folders are at the bottom for $800-1,000. I found prices to be the following as of early 2018 with the highest prices realized on gunbroker: I recently had similar questions as the OP and researched as many completed auctions and sales as I could find. The former commands a premium.how much is up to you. The former was produced as and left the factory in a folding stock, the former did not and was assembled as a folder aftermarket. First you need to distinguish between a factory configured folder and a non-factory configured folder. Lunch Sweet potato stuffed with shredded chicken, drizzled with low-sugar barbecue sauceĭinner Shrimp and veggie kabobs with cauliflower rice Lunch Mediterranean lentil salad with sun-dried tomatoes, kalamata olives, and chopped raw veggiesĭinner Veggie and bean soup with a grilled chicken breast DAY 7īreakfast Greek yogurt layered with apples, cinnamon, and walnuts Lunch Quinoa mixed with chopped veggies and cubed chicken breast, tossed with vinaigretteĭinner Salmon, steamed broccoli, sautéed mushrooms DAY 6īreakfast 2 hard-boiled eggs with blueberries Lunch Open-faced turkey, veggie, and avocado sandwich on whole-wheat toastĭinner Sliced steak stir-fry over cauliflower rice DAY 5īreakfast Omelet made with peppers and spinach, topped with avocado slices “These are the carbs that will keep you full,” says Catudal.īefore you adopt any new diet, you should check with a registered dietitian nutritionist to find the best nutrition plan for your individualized needs.ġ0 Great Sources of Plant-Based Protein DAY 4īreakfast Smoothie made with Greek yogurt, berries, and almond milk Maximize carbs and calories, and build volume by focusing on eating a lot of fiber-rich veggies. Catudal suggests a higher protein intake (40 percent of calories per day), a good amount of fat (40 percent of calories per day), and a lower-carbohydrate diet (20 percent of calories per day), aiming for 1,300 to 1,500 calories per day to start. With more body fat, the thinking goes, you’ll also burn fewer calories compared with a naturally muscular body, like a mesomorph, adds Catudal.Īll this means that you’ll have to keep a tighter watch on calories, the diet says. ( 4) Accordingly, proponents of the endomorph diet advise limiting these, especially highly processed, refined carbs, which contain fewer nutrients and less dietary fiber than whole grains, says Montenegro. ( 3) Insulin resistance affects the way your body processes carbohydrates. Insulin resistance is when your cells have trouble responding to the insulin that your pancreas pumps out, which ultimately affects your blood glucose levels. “This visceral body fat hangs out around your organs and is related to insulin resistance,” says Marta Montenegro, PhD, a specialist in fitness nutrition based in Miami. In addition, this excess fat often deposits around the waist. Even when eating a similar diet as another body type, an endomorph will tend to hold on to more excess fat, he says. ( 2) Catudal says that endomorphs tend to gain weight more easily compared with ectomorphs and mesomorphs. Endomorphs are primarily characterized by their propensity to store fat, as well as a wider waistline and bigger bone structure. Investment amounts vary but most Series A investments are for at least $1 million. This whole investment process in a company is called venture capital financing.Īs I have mentioned before, the typical sequence for financing a company is: bootstrapping by company founders, then friends & family financing, then angel financing (in the form of convertible notes or series seed rounds), then Series A round (venture capital financing), then Series B round (VC financing), then Series C round (VC financing) and so on until an initial public offering (IPO). This return expectation is 3 to 5+ times over a 10 year period. Venture capitalists are investors that make these types of investments through a pooling of money (via a venture capital firm/venture capital fund.) Venture capital is money that is invested in the early stage of a company's life where ownership shares of the company is purchased by investors and where that company is expected to grow quickly with an expectation of a high return. I'm going to go through a few basic points and then summarize those points in this section. THE TERM SHEET > Management/Founder TermsĪrticle I. Preferred stock can convert into common stockĭ. There are different types of stock in a company.į. Venture capital funds look for an exit event in order to get their return on investmentĮ. So here is a comprehensive overview of what a venture capital financing deal is about from a system level, big picture point of view.Ĭ. However, the fact of the matter is that most industries operate in very similar ways. These all come with their own quirks. For example, here is an article about the oil and gas industry and venture capital and includes observations from Dallas and Houston, Texas: Texas Startups and Venture CapitalĪ lot of startups in Texas are focused on life sciences, clean energy tech, oil & gas, etc. I also want you to keep in mind that different industries have slightly different ways of doing things and have their own subtleties. It is all about understanding what's going on from a big picture point of view. I can tell you that my clients who have achieved without a doubt the most success think this way. You would be surprised at how few people think this way. Don't focus on bits of random knowledge without context. All you need is a good working knowledge of the basics. Your job is to focus on and develop your business-be it investments or entrepreneurship and make key strategic decisions and maneuvers. Go for it. But it's not your bread and butter. That's fine if you are genuinely interested in it. This is a dangerous type of subtle goofing off because you can convince yourself that it is noble to learn as much as possible. but you don’t have an overarching system level understanding of a deal that you're involved in, then your priorities are off and you're just messing around. If you're trying to learn about something like Code Section 163(l) disallowing any deduction for interest paid or accrued including original issue discount amortization on a debt instrument under certain tests blah blah blah. VENTURE CAPITAL 101-WHAT IS VC FINANCING? This will allow you to build your nutrition “tool kit” and apply it to your life appropriately. In future blogs, we will be introducing more nutrition concepts, such as the science of macronutrients and fueling properly for different levels of activity & sports. Focus on making small changes that fit into your lifestyle and eating healthy whole-food meals. If you are starting off with your nutrition journey, do NOT get caught up with the details or dive into an approach that is hard to keep up with. For example, if you’re eating toast, make sure to add some eggs and/or cheese to squeeze some protein in your muscles will thank you. The plate method makes it easy to visualize how much of each food you should consume to make sure you’re getting the right amounts of each. This will provide you with the micronutrients you need, your body will thank you for it! Although whole foods are emphasized, it does not mean you can’t enjoy some cookies and ice cream every so often -)Įating the correct proportions of food: As mentioned above, many people do not get enough protein. Instead, replace them with healthier, whole food options. Removing processed foods: Processed foods should be kept to a minimum in healthy diets. Increasing protein intake is usually what most people need to do to enhance their nutrition. Protein is essential for muscle synthesis and is extremely satiating. The Plate Method will help you with taking the first steps to a healthy life by focusing on the following:Įmphasizing protein intake: I have noticed that many people do not get enough protein in their diets. This is the foundation of all nutrition practices. Having trouble finding foods for each category? Here’s a list of potential foods for each: As a result, feel free to use a bit of olive oil or light dressing, but use in moderation. However, if you have a pure protein source such as 99% lean ground turkey (which has very minimal fat) with steamed broccoli as the vegetable source, then there will be minimal fat. Instead of emphasizing fats on the plate, we want to make sure you know that you will probably get enough fats from the foods already on the plate. On the plate, the main focus is protein and carbohydrates, but where are the fats? Well, fats add up easily and usually are found from traces in meats, eggs, and oils that are used for cooking. Trust me, the food choices you make will influence your performance in the gym! The goal is to make sure you are making healthy choices while getting the foods you need to fuel your body properly. This method ensures you get enough protein and carbs, without having to weigh any food out or make any drastic, intricate changes. You’ll see that the Plate is ½ veggies, ¼ protein, and ¼ “smart carbohydrates”. So, what is the Plate Method? As shown in the picture above, it is a visual tool that shows the recommended servings of food on a plate. Most of the time, the Plate Method is all you need. Once the person is comfortable with the plate method and adheres to the basics of nutrition, then they are ready to dive in a little deeper such as manipulating their macronutrient ratios, calculating calories and tracking.but remember, that’s not always the best approach for everyone. If nutrition and healthy eating were illustrated as a pyramid, the plate method would be the foundational piece of the structure because it emphasizes the basics and guides people to a sustainable approach that can be tailored to their lifestyle and behavior. Instead of getting wrapped up in calorie counting, eliminating certain food groups, and other approaches preached in social media, the Plate Method is simple and easy to implement. In this blog, we will describe a foundational concept to healthy eating- The Plate Method. If you are new to the nutrition realm, or unfamiliar with what approach to take, then the first step should be one that is smart and sustainable. This can potentially lead to an overwhelming feeling, cause burn out, and be hard to maintain unless you have advanced experience with nutrition. Further, people often find themselves jumping into common diet trends like the Keto diet, carb-cutting, intermittent fasting, and macro counting (commonly referred to as IIFYM- “if it fits your macros”). The general population neglects their nutrition because it seems difficult to maintain, driving people to opt for fast food restaurants and processed food options. There is a common misconception in the health industry that nutrition and healthy eating are intricate. The moment of inertia of a particle of mass m m about an axis is m r 2, m r 2, where r r is the distance of the particle from the axis. Moments of Inertiaįor a clear understanding of how to calculate moments of inertia using double integrals, we need to go back to the general definition of moments and centers of mass in Section 6.6 of Volume 1. Ĭalculate the centroid of the region between the curves y = x y = x and y = x y = x with uniform density in the interval 0 ≤ x ≤ 1. x c = M y m = ∬ R x d A ∬ R d A and y c = M x m = ∬ R y d A ∬ R d A, x c = M y m = ∬ R x d A ∬ R d A = ∫ x = 1 x = 3 ∫ y = 0 y = e x x d y d x ∫ x = 1 x = 3 ∫ y = 0 y = e x d y d x = ∫ x = 1 x = 3 x e x d x ∫ x = 1 x = 3 e x d x = 2 e 3 e 3 − e = 2 e 2 e 2 − 1, y c = M x m = ∬ R y d A ∬ R d A = ∫ x = 1 x = 3 ∫ y = 0 y = e x y d y d x ∫ x = 1 x = 3 ∫ y = 0 y = e x d y d x = ∫ x = 1 x = 3 e 2 x 2 d x ∫ x = 1 x = 3 e x d x = 1 4 e 2 ( e 4 − 1 ) e ( e 2 − 1 ) = 1 4 e ( e 2 + 1 ). X c = M y m = ∬ R x d A ∬ R d A and y c = M x m = ∬ R y d A ∬ R d A, x c = M y m = ∬ R x d A ∬ R d A = ∫ x = 1 x = 3 ∫ y = 0 y = e x x d y d x ∫ x = 1 x = 3 ∫ y = 0 y = e x d y d x = ∫ x = 1 x = 3 x e x d x ∫ x = 1 x = 3 e x d x = 2 e 3 e 3 − e = 2 e 2 e 2 − 1, y c = M x m = ∬ R y d A ∬ R d A = ∫ x = 1 x = 3 ∫ y = 0 y = e x y d y d x ∫ x = 1 x = 3 ∫ y = 0 y = e x d y d x = ∫ x = 1 x = 3 e 2 x 2 d x ∫ x = 1 x = 3 e x d x = 1 4 e 2 ( e 4 − 1 ) e ( e 2 − 1 ) = 1 4 e ( e 2 + 1 ). The lamina is perfectly balanced about its center of mass. Figure 5.64 shows a point P P as the center of mass of a lamina. If the object has uniform density, the center of mass is the geometric center of the object, which is called the centroid. The center of mass is also known as the center of gravity if the object is in a uniform gravitational field. The density is usually considered to be a constant number when the lamina or the object is homogeneous that is, the object has uniform density. In this section we develop computational techniques for finding the center of mass and moments of inertia of several types of physical objects, using double integrals for a lamina (flat plate) and triple integrals for a three-dimensional object with variable density. We have already discussed a few applications of multiple integrals, such as finding areas, volumes, and the average value of a function over a bounded region. 5.6.3 Use triple integrals to locate the center of mass of a three-dimensional object.5.6.2 Use double integrals to find the moment of inertia of a two-dimensional object.5.6.1 Use double integrals to locate the center of mass of a two-dimensional object. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |