Simple addition or subtraction in 2 digit

Problem solving about simple addition or subtraction

Lide 1: Introduction to Bioreactor A bioreactor is a vessel used for growing microorganisms, plant or animal cells Provides controlled conditions for biological reactions Maintains optimum pH, temperature, oxygen, and nutrients Widely used in fermentation, enzyme, vaccine, and antibiotic production Ensures sterile and aseptic environment Scale ranges from laboratory to industrial production Slide 2: Basic Design Requirements of a Bioreactor Must be constructed with non-toxic, corrosion-resistant materials Should allow effective mixing and mass transfer Provision for sterilization (in situ sterilization) Must maintain uniform temperature and pH Easy sampling without contamination Should support scalability and automation Slide 3: Materials Used in Bioreactor Construction Stainless steel (SS-316) for industrial bioreactors Glass for laboratory-scale bioreactors Plastic (polycarbonate) for disposable bioreactors Materials must withstand heat and pressure Should be smooth to prevent microbial attachment Resistant to chemicals and cleaning agents Slide 4: Main Parts of a Bioreactor Vessel: holds the culture medium and microorganisms Agitator (impeller): provides mixing Sparger: supplies sterile air Baffles: prevent vortex formation Sensors: monitor pH, temperature, dissolved oxygen Ports: used for inoculation, sampling, and feeding Slide 5: Agitation System Ensures uniform mixing of nutrients and cells Improves oxygen transfer rate Common impellers: Rushton turbine, marine propeller Speed controlled by motor Prevents settling of cells Affects shear stress on cells Slide 6: Aeration System Supplies oxygen for aerobic fermentation Air introduced through sparger Types of spargers: ring, nozzle, sintered Maintains dissolved oxygen concentration Air is filtered for sterility Essential for high cell density cultures Slide 7: Temperature and pH Control Temperature controlled by heating/cooling jackets pH maintained using acid or alkali addition Sensors continuously monitor parameters Automated control systems used Ensures optimal microbial growth Prevents enzyme denaturation Slide 8: Foam Control System Foam formed due to protein and agitation Excess foam reduces oxygen transfer Mechanical foam breakers used Chemical antifoam agents added Foam sensor detects foam formation Maintains efficient fermentation Slide 9: Types of Bioreactors – Based on Mode of Operation Batch bioreactor Fed-batch bioreactor Continuous bioreactor Choice depends on product type Widely used in industrial fermentation Controls productivity and yield Slide 10: Batch Bioreactor All nutrients added at the beginning No addition or removal during process Simple and easy to operate Low risk of contamination Used for antibiotics and enzymes Limited control over nutrient depletion Slide 11: Fed-Batch Bioreactor Nutrients added during fermentation Prevents substrate inhibition High product yield Widely used in industrial fermentation Allows better control of growth rate Used in insulin and enzyme production Slide 12: Continuous Bioreactor Fresh medium continuously added Culture removed at same rate Maintains steady-state conditions High productivity Risk of contamination is high Used in wastewater treatment and SCP production Slide 13: Types of Bioreactors – Based on Design Stirred tank bioreactor Airlift bioreactor Bubble column bioreactor Packed bed bioreactor Fluidized bed bioreactor Photobioreactor Slide 14: Stirred Tank Bioreactor (STR) Most commonly used bioreactor Mechanical agitation using impellers Suitable for aerobic fermentation Excellent mixing and oxygen transfer Used for bacteria and fungi Easy scale-up Slide 15: Airlift Bioreactor Mixing achieved by air circulation No mechanical agitator Low shear stress Energy efficient Suitable for shear-sensitive cells Used in wastewater treatment Slide 16: Bubble Column Bioreactor Air bubbles provide mixing Simple design and low cost No moving parts Limited mixing efficiency Used for microbial fermentation Suitable for large-scale operations Slide 17: Packed Bed Bioreactor Contains immobilized cells or enzymes Substrate flows through packed matrix High cell density Used in continuous processes Limited oxygen transfer Used in enzyme and wastewater treatment Slide 18: Fluidized Bed Bioreactor Immobilized particles kept in suspension Better mass transfer than packed bed Reduced clogging Suitable for continuous operation Used in biotransformations Higher operational complexity Slide 19: Photobioreactor Designed for photosynthetic organisms Provides light source Used for algae and cyanobacteria Controls light, CO₂, and temperature Used in biofuel and pigment production Can be tubular or flat-plate design Slide 20: Applications of Bioreactors Production of antibiotics and vaccines Enzyme and organic acid production Single cell protein production Wastewater treatment Biofertilizer and biopesticide production Biopharmaceutical manufacturing

Addition of Simple Fractions and Mixed Numbers with or without Regrouping

Hi, I'm John Green, this is Crash Course U.S. History, and today, we're going to talk about slavery, which is not funny. 0:06 Yeah, so we put a lei on the eagle to try and cheer you up, but let's face it, this is going to be depressing. 0:10 With slavery, every time you think, like, "Aw, it couldn't have been that bad," it turns out to have been much worse. 0:14 Mr. Green, Mr. Green! But what about – 0:15 Yeah, Me from the Past, I'm going to stop you right there, because you're going to embarrass yourself. Slavery was hugely important to America. 0:20 I mean, it led to a civil war and it also lasted what, at least in U.S. history, counts as a long-ass time, from 1619 to 1865. 0:29 And yes, I know there's a 1200-year-old church in your neighborhood in Denmark, but we're not talking about Denmark! 0:35 But slavery is most important because we still struggle with its legacy. 0:38 So, yes, today's episode will probably not be funny, but it will be important. 0:42 [Theme Music] North & South economic ties 0:51 So the slave-based economy in the South is sometimes characterized as having been separate from the Market Revolution, but that's not really the case. 0:57 Without southern cotton, the North wouldn't have been able to industrialize, at least not as quickly, because cotton textiles were one of the first industrially products. 1:04 And the most important commodity in world trade by the nineteenth century, and 3/4 of the world's cotton came from the American South. 1:11 And speaking of cotton, why has no one mentioned to me that my collar has been half popped this entire episode, like I'm trying to recreate the Flying Nun's hat. 1:18 And although there were increasingly fewer slaves in the North as northern states outlawed slavery, cotton shipments overseas made northern merchants rich. 1:26 Northern bankers financed the purchase of land for plantations. 1:29 Northern insurance companies insured slaves who were, after all, considered property, and very valuable property. 1:35 And in addition to turning cotton into cloth for sale overseas, northern manufacturers sold cloth back to the South, where it was used to clothe the very slaves who had cultivated it. 1:45 But certainly the most prominent effects of the slave-based economy were seen in the South. Slave-based agriculture in the South 1:49 The profitability of slaved-based agriculture, especially King Cotton, meant that the South would remain largely agricultural and rural. 1:56 Slave states were home to a few cities, like St. Louis and Baltimore, but with the exception of New Orleans, 2:00 almost all southern urbanization took place in the upper South, further away from the large cotton plantations. 2:06 And slave-based agriculture was so profitable that it siphoned money away from other economic endeavors. 2:11 Like, there was very little industry in the South. 2:13 It produced only 10% of the nation's manufactured goods. 2:16 And, as most of the capital was being plowed into the purchase of slaves, there was very little room for technological innovation, like, for instance, railroads. 2:23 This lack of industry and railroads would eventually make the South suck at the Civil War, thankfully. 2:27 In short, slavery dominated the South, shaping it both economically and culturally, and slavery wasn't a minor aspect of American society. Popular attitudes concerning slavery 2:35 By 1860, there were four million slaves in the U.S., and in the South, they made up one third of the total population. 2:42 Although in the popular imagination, most plantations were these sprawling affairs with hundreds of slaves, 2:47 in reality, the majority of slaveholders owned five or fewer slaves. 2:51 And, of course, most white people in the South owned no slaves at all, though, if they could afford to, they would sometimes rent slaves to help with their work. 2:57 These were the so-called yeoman farmers who lived self-sufficiently, raised their own food, and purchased very little in the Market Economy. 3:04 They worked the poorest land and, as a result, were mostly pretty poor themselves. 3:08 But even they largely supported slavery, partly, perhaps, for aspirational reasons, and partly because the racism inherent to the system gave even the poorest whites legal and social status. 3:18 And southern intellectuals worked hard to encourage these ideas of white solidarity and to make the case for slavery. 3:23 Many of the founders, a bunch of whom you'll remember, held slaves, saw slavery as a necessary evil. 3:29 Jefferson once wrote, quote, "As it is, we have the wolf by the ear, and we can neither hold him, nor safely let him go. 3:37 Justice is on one scale, and self-preservation in the other." 3:41 The belief that justice and self-preservation couldn't sit on the same side of the scale was really opposed to the American idea, 3:47 and, in the end, it would make the Civil War inevitable. 3:50 But as slavery became more entrenched in these ideas of liberty and political equality were embraced by more people, 3:55 some southerners began to make the case that slavery wasn't just a necessary evil. 3:59 They argued, for instance, that slaves benefited from slavery. 4:03 Because, you know, because their masters fed them and clothed them and took care of them in their old age. 4:07 You still hear this argument today, astonishingly. 4:09 In fact, you'll probably see asshats in the comments saying that in the comments. 4:12 I will remind you, it's not cursing if you are referring to an actual ass. 4:15 This paternalism allowed masters to see themselves as benevolent and to contrast their family-oriented slavery with the cold, mercenary Capitalism of the free-labor North. 4:26 So yeah, in the face of rising criticism of slavery, some southerners began to argue that the institution was actually good for the social order. 4:33 One of the best-known proponents of this view was John C. Calhoun, who, in 1837, said this in a speech on the Senate floor: 4:40 "I hold that, in the present state of civilization, 4:43 where two races of different origin and distinguished by color and other physical differences as well as intellectual, are brought together, 4:51 the relation now existing in the slave-holding states between the two is, instead of an evil, a good. A positive good." 4:59 Now, of course, John C. Calhoun was a fringe politician, and nobody took his views particularly seriously. 5:04 Stan: Well, he was Secretary of State from 1844 to 1845. 5:07 John: Well, I mean, who really cares about the Secretary of State, Stan? 5:10 Danica: Eh, he was also Secretary of War from 1817 to 1825. 5:13 John: All right, but we don't even have a Secretary of War anymore, so... 5:16 Meredith: And he was Vice President from 1825 to 1832. 5:19 John: Oh my god, were we insane?! 5:21 We were, of course, but we justified the insanity with Biblical passages and with the examples of the Greeks and Romans, 5:28 and with outright racism, arguing that black people were inherently inferior to whites. 5:33 And that not to keep them in slavery would upset the natural order of things. 5:37 A worldview popularized millennia ago by my nemesis, Aristotle. God, I hate Aristotle. 5:42 You know what defenders of Aristotle always say? 5:44 "He was the first person to identify dolphins." 5:47 Well, ok, dolphin identifier. 5:50 Yes, that is what he should be remembered for, but he's a terrible philosopher! Lives & experiences of enslaved people 5:53 Here's the truth about slavery: 5:55 It was coerced labor that relied upon intimidation and brutality and dehumanization. 6:00 And this wasn't just a cultural system, it was a legal one. 6:03 I mean, Louisiana law proclaimed that a slave "owes his master... a respect without bounds, and an absolute obedience." 6:09 The signal feature of slaves' lives was work. 6:12 I mean, conditions and tasks varied, but all slaves labored, usually from sunup to sundown, and almost always without any pay. 6:20 Most slaves worked in agriculture on plantations, and conditions were different, depending on which crops are grown. 6:25 Like, slaves on the rice plantations of South Carolina had terrible working conditions, 6:29 but they labored under the task system, which meant that once they had completed their allotted daily work, they would have time to do other things. 6:36 But lest you imagine this is like how we have work and leisure time, bear in mind that they were owned and treated as property. 6:42 On cotton plantations, most slaves worked in gangs, usually under the control of an overseer, or another slave who was called a "driver." 6:49 This was back-breaking work done in the southern sun and humidity, and so it's not surprising that whippings – or the threat of them – were often necessary to get slaves to work. 6:58 It's easy enough to talk about the brutality of slave discipline, but it can be difficult to internalize it. 7:03 Like, you look at these pictures, but because you've seen them over and over again, they don't have the power they once might have. 7:09 The pictures can tell a story about cruelty, but they don't necessarily communicate how arbitrary it all was. 7:14 As, for example, in this story, told by a woman who was a slave as a young girl: 7:18 "[The] overseer... went to my father one morning and said, "Bob, I'm gonna whip you this morning." 7:22 Daddy said, "I ain't done nothing," and he said, "I know it, I'm going to whip you to keep you from doing nothing," 7:28 and he hit him with that cowhide – you know it would cut the blood out of you with every lick if they hit you hard." 7:33 That brutality – the whippings, the brandings, the rape – was real, and it was intentional, because, in order for slavery to function, slaves had to be dehumanized. 7:43 This enabled slaveholders to rationalize what they were doing, and it was hoped to reduce slaves to the animal property that is implied by the term "chattel slavery." 7:51 So the idea was that slaveholders wouldn't think of their slaves as human, and slaves wouldn't think of themselves as human. 7:57 But it didn't work. Let's go to the Thought Bubble. 7:59 Slaves' resistance to their dehumanization took many forms, but the primary way was by forming families. Family, love, & religion of enslaved people 8:05 Family was a refuge for slaves and a source of dignity that masters recognized and sought to stifle. 8:10 A paternalistic slave owner named Bennet H. Barrow wrote in his rules for the Highland Plantation: 8:15 "No rule that I have stated is of more importance than that relating to Negroes marrying outside of the plantation... It creates a feeling of independence." 8:23 Most slaves did marry, usually for life, and, when possible, slaves grew up in two-parent households. 8:28 Single-parent households were common, though, as a result of one parent being sold. 8:32 In the upper South, where the economy was shifting from tobacco to different, less labor-intensive cash crops, the sale of slaves was common. 8:40 Perhaps one-third of slave marriages in states like Virginia were broken up by sale. 8:45 Religion was also an important part of life in slavery. 8:47 While masters wanted their slaves to learn the parts of the Bible that talked about being happy in bondage, 8:52 slave worship tended to focus on the stories of Exodus, where Moses brought the slaves out of bondage, 8:57 or Biblical heroes, who overcame great odds, like Daniel and David. 9:01 And, although most slaves were forbidden to learn to read and write, many did anyway. And some became preachers. 9:07 Slave preachers were often very charismatic leaders, and they roused the suspicion of slave owners, and not without reason. 9:13 Two of the most important slave uprisings in the South were led by preachers. 9:16 Thanks, Thought Bubble. 9:17 Oh, it's time for the Mystery Document? Mystery Document 9:19 We're doing two set pieces in a row? All right. [buzzing noise] [music] 9:24 The rules here are simple. 9:26 I wanted to re-shoot that, but Stan said no. 9:29 I guess the author of the Mystery Document. 9:30 If I am wrong, I get shocked with the shock pen. 9:33 "Since I have been in the Queen's dominions I have been well contented, yes well contented for sure, man is as God intended he should be. 9:40 That is, all are born free and equal. 9:43 This is a wholesome law, not like the southern laws which puts man made in the image of God on level with brutes. 9:49 O, what will become of the people, and where will they stand in the day of judgment. 9:53 Would that the 5th verse of the 3rd chapter of Malachi were written as with a bar of iron, 9:59 and the point of a diamond upon every oppressor's heart that they might repent of this evil, and let the oppressed go free..." 10:06 All right, it's definitely a preacher, because only preachers have read Malachi. 10:10 Probably African American, probably not someone from the South. 10:13 I'm going to guess that it is Richard Allen, the founder of the African Methodist Episcopal Church? 10:18 [buzzing noise] DAAAH, DANG IT! 10:19 It's Joseph Taper, and Stan just pointed out to me that I should have known it was Joseph Taper because it starts out, 10:24 "Since I have been in the Queen's dominions..." 10:27 He was in Canada. He escaped slavery to Canada. The Queen's dominions! 10:31 All right, Canadians, I blame you for this, although, thank you for abolishing slavery decades before we did. 10:36 [electric sounds] AHHH! How people resisted & escaped slavery 10:37 So, the Mystery Document shows one of the primary ways that slaves resisted their oppression: by running away. 10:42 Although some slaves like Joseph Taper escaped for good by running away to northern free states, 10:47 or even to Canada, where they wouldn't have to worry about fugitive slave laws, even more slaves ran away temporarily, hiding out in the woods or the swamps, and eventually returning. 10:55 No one knows exactly how many slaves escaped to freedom, but the best estimate is that a thousand or so a year made the journey northward. 11:01 Most fugitive slaves were young men, but the most famous runaway has been hanging out behind me all day long: Harriet Tubman. 11:07 Harriet Tubman escaped to Philadelphia at the age of 29, and over the course of her life, she made about 20 trips back to Maryland to help friends and relatives make the journey north on the Underground Railroad. 11:17 But a more dramatic form of resistance to slavery was actual, armed rebellion, which was attempted. 11:22 Now, individuals sometimes took matters into their own hands and beat or even killed their white overseers or masters. 11:27 Like Bob, the guy who received the arbitrary beating, responded to it by killing his overseer with a hoe. 11:33 But that said, large-scale slave uprisings were relatively rare. 11:36 The four most famous ones all took place in a 35-year period at the beginning of the 19th century. Slave rebellions 11:41 Gabriel's Rebellion in 1800 – which we've talked about before – was discovered before he was able to carry out his plot. 11:45 Then, in 1811, a group of slaves upriver from New Orleans seized cane, knives, and guns, and marched on the city before militia stopped them. 11:52 And in 1822, Denmark Vesey, a former slave who had purchased his freedom, may have organized a plot to destroy Charleston, South Carolina. 11:59 I say "may have" because the evidence against him is disputed and comes from a trial that was not fair. 12:05 But regardless, the end result of that trial was that he was executed, as were 34 slaves. Nat Turner's Rebellion 12:09 But the most successful slave rebellion, at least in the sense that they actually killed some people, was Nat Turner's in August 1831. 12:15 Turner was a preacher, and with a group of about 80 slaves, he marched from farm to farm in South Hampton County, Virginia, 12:21 killing the inhabitants, most of whom were women and children, because the men were attending a religious revival meeting in North Carolina. 12:27 Turner and 17 other rebels were captured and executed, but not before they struck terror into the hearts of whites all across the American South. 12:34 Virginia's response was to make slavery worse, passing even harsher laws that forbade slaves from preaching, and prohibited teaching them to read. 12:42 Other slave states followed Virginia's lead and, by the 1830s, slavery had grown, if anything, more harsh. 12:47 So, this shows that large-scaled armed resistance was – Django Unchained aside – not just suicidal, but also a threat to loved ones and, really, to all slaves. How enslaved people resisted their oppression & why it matters 12:55 But, it is hugely important to emphasize that slaves did resist their oppression. 12:59 Sometimes this meant taking up arms, but usually it meant more subtle forms of resistance, 13:03 like intentional work slowdowns or sabotaging equipment, or pretending not to understand instructions. 13:08 And, most importantly, in the face of systematic legal and cultural degradation, they re-affirmed their humanity through family and through faith. 13:16 Why is this so important? 13:17 Because too often in America, we still talk about slaves as if they failed to rise up, 13:21 when, in fact, rising up would not have made life better for them or for their families. 13:26 The truth is, sometimes carving out an identity as a human being in a social order that is constantly seeking to dehumanize you, is the most powerful form of resistance. 13:34 Refusing to become the chattel that their masters believed them to be is what made slavery untenable and the Civil War inevitable, so make no mistake, slaves fought back. 13:45 And in the end, they won. I'll see you next week. Credits 13:48 Crash Course is produced and directed by Stan Muller. 13:50 The script supervisor is Meredith Danko. 13:52 Our associate producer is Danica Johnson. 13:54 The show is written by my high school history teacher Raoul Meyer and myself. 13:57 And our graphics team is Thought Cafe. 13:58 Every week, there's a new caption to the Libertage, but today's episode was so sad that we couldn't fit a Libertage in... 14:04 UNTIL NOW! [Libertage Rock Music] 14:08 Suggest Libertage caption in comments, where you can also ask questions about today's video that will be answered by our team of historians. 14:13 Thanks for watching Crash Course, and as we say in my home town, don't forget to be abolitionist.

LARGE CARBON MOLECULES Many carbon compounds are built up from smaller, simpler molecules known as monomers (MAH-ne-mers), such as the ones shown in Figure 3-3. As you can also see in Figure 3-3, monomers can bond to one another to form polymers (PAWL-eh-mer). A polymer is a molecule that consists of repeated, linked units. The units may be identical or structurally related to each other. Large polymers are called macromolecules. There are many types of macromolecules, such as carbohydrates, lipids, proteins and nucleic acids. Monomers link to form polymers through a chemical reaction called a condensation reaction. Each time a monomer is added to a polymer, a water molecule is released. In the condensation reac- tion shown in Figure 3-4, two sugar molecules, glucose and fruc- tose, combine to form the sugar sucrose, which is common table sugar. The two sugar monomers become linked by a C—O—C bridge. In the formation of that bridge, the glucose molecule releases a hydrogen ion, H, and the fructose molecule releases a hydroxide ion, OH. The OH and H ions that are released then combine to produce a water molecule, H2O. In addition to building polymers through condensation reac- tions, living organisms also have to break them down. The break- down of some complex molecules, such as polymers, occurs through a process known as hydrolysis (hie-DRAHL-i-sis). In a hydrolysis reaction, water is used to break down a polymer. The water molecule breaks the bond linking each monomer. Hydrolysis is the reverse of a condensation reaction. The addition of water to some complex molecules, including polymers, under certain con- ditions can break the bonds that hold them together. For example, in Figure 3-4 reversing the reaction will result in sucrose breaking down into fructose and glucose. 2H2O Monomers Polymer C C O H OH C OH H CH2OH C H CH2OH C HO H C O H C OH H C CH2OH H C H OH O Sucrose C C O H OH C OH H CH2OH C H CH2OH C HO H C OH OH H C OH H C CH2OH H C H OH O Glucose Fructose H2O The condensation reaction below shows how glucose links with fructose to form sucrose. One water molecule is produced each time two monomers form a covalent bond. FIGURE 3-4 monomer from the Greek mono, meaning “single or alone,” and meros, meaning “a part” Word Roots and Origins A polymer is the result of bonding between monomers. In this example, each monomer is a six-sided carbon ring. The starch in potatoes is an example of a molecule that is a polymer. FIGURE 3-3 Copyright © by Holt, Rinehart and Winston. All rights reserved. 54 CHAPTER 3 ENERGY CURRENCY Life processes require a constant supply of energy. This energy is available to cells in the form of certain compounds that store a large amount of energy in their overall structure. One of these com- pounds is adenosine (uh-DEN-uh-SEEN) triphosphate, more commonly referred to by its abbreviation, ATP. The left side of Figure 3-5 shows a simplified ATP molecule struc- ture. The 5-carbon sugar, ribose, is represented by the blue carbon ring. The nitrogen-containing compound, adenine, is represented by the 2 orange rings. The three linked phosphate groups, —PO4 , are represented by the blue circles with a “P.” The phospate groups are attached to each other by covalent bonds. The covalent bonds between the phosphate groups are more unstable than the other bonds in the ATP molecule because the phosphate groups are close together and have negative charges. Thus, the negative charges make the bonds easier to break. When a bond between the phosphate groups is broken, energy is released. This hydrolysis of ATP is used by the cell to provide the energy needed to drive the chemical reactions that enable an organism to function.

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