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properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | check your understanding now that you are familiar with matrix multiplication and its properties , let 's see if you can use them to determine equivalent matrix expressions . for the problems below , let $ a $ , $ b $ , and $ c $ be $ 2\times 2 $ matrices and let $ o $ be the $ 2\times 2 $ zero matrix . | in the second challenge question , which is given as follows : 2 ) which of the following expressions are equivalent to a ( b+c ) ? |
properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | distributive properties we can distribute matrices in much the same way we distribute real numbers . $ a ( b+c ) =ab+ac $ $ ( b+c ) a=ba+ca $ if a matrix $ a $ is distributed from the left side , be sure that each product in the resulting sum has $ a $ on the left ! similarly , if a matrix $ a $ is distributed from the... | selecting i ) : ab+ac , & ii ) : a ( c+b ) will mark the answers right , but selecting `` ( b+c ) a `` is wrong ? |
properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | similarly , if a matrix $ a $ is distributed from the right side , be sure that each product in the resulting sum has $ a $ on the right ! multiplicative identity property the $ n\times n $ identity matrix , denoted $ i_n $ , is a matrix with $ n $ rows and $ n $ columns . the entries on the diagonal from the upper lef... | just a minor detail , why is the identity matrix notation i2 instead of just i ? |
properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | a zero matrix is indicated by $ o $ , and a subscript can be added to indicate the dimensions of the matrix if necessary . the multiplicative property of zero states that the product of any $ n\times n $ matrix and the $ n\times n $ zero matrix is the $ n\times n $ zero matrix . in other words , $ a\cdot o=o\cdot a=o $... | is there any m times n zero matrix or m times n identity matrix ? |
properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | in other words , $ a\cdot i=i\cdot a=a $ . the role that the $ n\times n $ identity matrix plays in matrix multiplication is similar to the role that the number $ 1 $ plays in the real number system . if $ a $ is a real number , then we know that $ a\cdot 1=a $ and $ 1\cdot a=a $ . | i remember when a real number times its inverse , will get 1.how to find inverse of a matrix ? |
properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | if this is new to you , we recommend that you check out our matrix multiplication article . here are other relevant articles : matrix multiplication dimensions intro to identity matrices properties of matrix addition matrix multiplication is not commutative one of the biggest differences between real number multiplicat... | if matrix addition is commutative does that mean that matrix addition and subtraction are two different functions ? |
properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | $ ab $ will be a $ \blued3\times \goldd4 $ matrix . check your understanding now that you are familiar with matrix multiplication and its properties , let 's see if you can use them to determine equivalent matrix expressions . for the problems below , let $ a $ , $ b $ , and $ c $ be $ 2\times 2 $ matrices and let $ o ... | in q2 of `` check your understanding it says : which of the following expressions are equivalent to a ( b+c ) ? |
properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | distributive properties we can distribute matrices in much the same way we distribute real numbers . $ a ( b+c ) =ab+ac $ $ ( b+c ) a=ba+ca $ if a matrix $ a $ is distributed from the left side , be sure that each product in the resulting sum has $ a $ on the left ! similarly , if a matrix $ a $ is distributed from the... | why is ( b+c ) a wrong ? |
properties of matrix multiplication in this table , $ a $ , $ b $ , and $ c $ are $ n\times n $ matrices , $ i $ is the $ n\times n $ identity matrix , and $ o $ is the $ n\times n $ zero matrix property | example - | - the commutative property of multiplication $ \small { \red { \text { does not hold ! } } } $ | $ ab\... | if $ a $ is a real number , then we know that $ a\cdot 1=a $ and $ 1\cdot a=a $ . multiplicative property of zero a zero matrix is a matrix in which all of the entries are $ 0 $ . for example , the $ 3\times 3 $ zero matrix is $ o_ { 3\times 3 } =\left [ \begin { array } { rrr } 0 & amp ; 0 & amp ; 0 \ 0 & amp ; 0 & am... | should n't the best and easiest way to multiply a matrix to get 0 , be to just use the scalar quantity 0 rather than a matrix full of zeros ? |
eighteenth-century venice was dominated by the tiepolo family of artists . venice had lost influence as an artistic center since the sixteenth-century , the era of titian and veronese . exciting new artists such as caravaggio and the carracci brothers were working primarily in central italy , rome in particular . by ad... | eighteenth-century venice was dominated by the tiepolo family of artists . venice had lost influence as an artistic center since the sixteenth-century , the era of titian and veronese . | did the tiepolo family even paint portraits ? |
overview in the spring of 1774 , the british parliament passed the coercive acts , which quickly became known in the north american colonies as the intolerable acts . the intolerable acts were aimed at isolating boston , the seat of the most radical anti-british sentiment , from the other colonies . colonists responded... | why couldn ’ t the legislation be tolerated ? what do you think was most significant about the first continental congress ? | why did n't georgia join the first continental congress ? |
overview in the spring of 1774 , the british parliament passed the coercive acts , which quickly became known in the north american colonies as the intolerable acts . the intolerable acts were aimed at isolating boston , the seat of the most radical anti-british sentiment , from the other colonies . colonists responded... | the administration of justice act authorized the governor to send indicted government officials to other colonies or to london for trial . the quartering act , which applied to all of the north american colonies , was designed to provide shelter for the british troops , allowing them to be housed in private buildings. ... | close our harbor and expect us to pay back lord north $ 270 million ? |
overview in the spring of 1774 , the british parliament passed the coercive acts , which quickly became known in the north american colonies as the intolerable acts . the intolerable acts were aimed at isolating boston , the seat of the most radical anti-british sentiment , from the other colonies . colonists responded... | this would give the southern colonies some time to prepare for the economic impact of the export ban. $ ^4 $ on october 17 , 1774 , the first continental congress issued the declaration of colonial rights and grievances . the declaration denied parliament ’ s right to tax the colonies and lambasted the british for stat... | who were the pro-british allies ? |
overview in the spring of 1774 , the british parliament passed the coercive acts , which quickly became known in the north american colonies as the intolerable acts . the intolerable acts were aimed at isolating boston , the seat of the most radical anti-british sentiment , from the other colonies . colonists responded... | the purpose of the congress was to show support for boston and to work out a unified approach to the british . nevertheless , divisions plagued the colonies . though the congress agreed to implement a boycott of british imported goods , the northern and southern colonies argued fiercely over a measure to ban all export... | also were the colonies forced to buy and sell the tea ? |
overview in the spring of 1774 , the british parliament passed the coercive acts , which quickly became known in the north american colonies as the intolerable acts . the intolerable acts were aimed at isolating boston , the seat of the most radical anti-british sentiment , from the other colonies . colonists responded... | why was boston singled out for punishment ? why did boston ’ s radicals refer to the coercive acts as the intolerable acts ? why couldn ’ t the legislation be tolerated ? | what did the colonists not like about the quartering acts ( sheltering the red coats ) ? |
overview in the spring of 1774 , the british parliament passed the coercive acts , which quickly became known in the north american colonies as the intolerable acts . the intolerable acts were aimed at isolating boston , the seat of the most radical anti-british sentiment , from the other colonies . colonists responded... | the delegates ultimately reached a compromise , agreeing that all exports to britain , ireland , and the british west indies would be banned after a year , starting in september 1775 . this would give the southern colonies some time to prepare for the economic impact of the export ban. $ ^4 $ on october 17 , 1774 , the... | what was britain 's first move against the declaration of colonial rights and grievance ? |
overview in the spring of 1774 , the british parliament passed the coercive acts , which quickly became known in the north american colonies as the intolerable acts . the intolerable acts were aimed at isolating boston , the seat of the most radical anti-british sentiment , from the other colonies . colonists responded... | was britain ’ s divide-and-conquer strategy effective ? why was boston singled out for punishment ? why did boston ’ s radicals refer to the coercive acts as the intolerable acts ? | why was boston singled out for punishment ? |
enzymes : what they are and what they do right now , as you read this , there are billions of chemical reactions happening inside your body . although they happen at lightning speed inside cells , when these reactions are run inside test-tubes -- - in a lab instead of a body -- - they happen at a snail ’ s pace . what ... | this device is a container with a series of small screens coated in precious metals -- - platinum , rhodium , etc . these metals are catalysts for the conversion of nitric oxide -- - a nitrogen atom bonded to an oxygen atom -- - into nitrogen and oxygen . the metals in a catalytic converter speed up the creation of nit... | in the example with the `` o 's '' ( oxygens ) and `` n 's '' ( nitrogens ) , why does each atom want to be with an atom identical to itself more than it wants to be with an opposite atom ? |
enzymes : what they are and what they do right now , as you read this , there are billions of chemical reactions happening inside your body . although they happen at lightning speed inside cells , when these reactions are run inside test-tubes -- - in a lab instead of a body -- - they happen at a snail ’ s pace . what ... | they are the “ gnomes ” inside each one of us that take molecules like nucleotides and align them together to create dna , or amino acids to make proteins , to name two of thousands of such functions . they are so important for life that scientists weren ’ t satisfied with calling them catalysts , and had to invent the... | how does structure lead to specific function of an enzyme ? |
enzymes : what they are and what they do right now , as you read this , there are billions of chemical reactions happening inside your body . although they happen at lightning speed inside cells , when these reactions are run inside test-tubes -- - in a lab instead of a body -- - they happen at a snail ’ s pace . what ... | this magnet thought experiment is a good approximation of what happens with real-life molecules like nitric oxide . if one n-o collides with another n-o , and they are in the exact right orientation , with n ’ s aligned with n ’ s and o ’ s aligned with o ’ s , the two n-o ’ s will go away and a new n-n and new o-o wil... | if vitamins are considered coenzymes because they are organic and fad is a vitamin-derivative , should n't fad be considered a coenzyme as well ? |
enzymes : what they are and what they do right now , as you read this , there are billions of chemical reactions happening inside your body . although they happen at lightning speed inside cells , when these reactions are run inside test-tubes -- - in a lab instead of a body -- - they happen at a snail ’ s pace . what ... | they are the “ gnomes ” inside each one of us that take molecules like nucleotides and align them together to create dna , or amino acids to make proteins , to name two of thousands of such functions . they are so important for life that scientists weren ’ t satisfied with calling them catalysts , and had to invent the... | where is the enzyme in our body ? |
enzymes : what they are and what they do right now , as you read this , there are billions of chemical reactions happening inside your body . although they happen at lightning speed inside cells , when these reactions are run inside test-tubes -- - in a lab instead of a body -- - they happen at a snail ’ s pace . what ... | what explains this difference in speed ? what do our cells have , that a test-tube lacks ? the answer is : enzymes ! enzymes are life ’ s great facilitators . they create the conditions needed for biochemical reactions to happen fast . | how do enzymes function in living cells ? |
enzymes : what they are and what they do right now , as you read this , there are billions of chemical reactions happening inside your body . although they happen at lightning speed inside cells , when these reactions are run inside test-tubes -- - in a lab instead of a body -- - they happen at a snail ’ s pace . what ... | and second , it can ’ t be used up or altered in any permanent way by the reaction -- - it still has to be there after the reaction is over . a catalyst speeds up a reaction , but isn ’ t consumed by it . this second part of the catalyst definition is very important . | so is it fine to call a protein an enzyme if it just speeds up the reaction without being consumed ? |
enzymes : what they are and what they do right now , as you read this , there are billions of chemical reactions happening inside your body . although they happen at lightning speed inside cells , when these reactions are run inside test-tubes -- - in a lab instead of a body -- - they happen at a snail ’ s pace . what ... | the general name that chemists use for a chemical entity that increases the speed of a reaction is a “ catalyst. ” enzymes are biological catalysts -- they catalyze the chemical reactions that happen inside living things . the definition of catalysis consider a chemical reaction where a molecule a bonds with a molecule... | what part of the molecule does the enzyme react on ? |
background flux in three dimensions unit normal vector surface integral the steps in the last article , i talked about how the flux of a flowing fluid through a surface is a measure of how much fluid passes through that surface per unit of time . if that fluid flow is represented with a vector field $ \bluee { f ( x , ... | to do this , draw yourself a picture of $ d_2 $ , and imagine cutting it into vertical stripes : the value $ t $ ranges from $ -2 $ to $ 2 $ . the range for $ s $ depends on the value of $ t $ , which you can find using the pythagorean theorem . from the diagram , you can see that $ s $ ranges from $ -\sqrt { 4-t^2 } $... | why did we have to parameterize this using s & t ? |
background flux in three dimensions unit normal vector surface integral the steps in the last article , i talked about how the flux of a flowing fluid through a surface is a measure of how much fluid passes through that surface per unit of time . if that fluid flow is represented with a vector field $ \bluee { f ( x , ... | in practice , there is quite a lot that goes into solving this integral . step 1 : rewrite the integral in terms of a parameterization of $ \rede { s } $ , as you would for any surface integral . step 2 : insert the expression for the unit normal vector $ \greene { \hat { \textbf { n } } ( x , y , z ) } $ . | would you be able to use cylindrical coordinates in order to make it a nicer integral ? |
background flux in three dimensions unit normal vector surface integral the steps in the last article , i talked about how the flux of a flowing fluid through a surface is a measure of how much fluid passes through that surface per unit of time . if that fluid flow is represented with a vector field $ \bluee { f ( x , ... | \bluee { \textbf { f } } ( \textbf { v } ( t , s ) ) \cdot \greene { \hat { \textbf { n } } } ( \textbf { v } ( t , s ) ) \ ; \underbrace { \left| \dfrac { \partial \textbf { v } } { \partial t } \times \dfrac { \partial \textbf { v } } { \partial s } \right| \ , da } { \rede { d\sigma } } \end { align } $ if this tran... | is there some better way to find out where the normal vector points ? |
what you need to know for this lesson factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . for more on this , check out our previous article on taking common factors . what you will learn in this lesson in this lesson , you will lear... | this is because their product needs to be negative $ ( -6 ) $ . in general , when factoring $ x^2+bx+c $ , if $ c $ is negative , then one factor will be positive and one factor will be negative . summary in general , to factor a trinomial of the form $ x^2+\goldd bx+\purplec c $ , we need to find factors of $ \purplec... | what if i can not find a common factor in b and c ? |
what you need to know for this lesson factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . for more on this , check out our previous article on taking common factors . what you will learn in this lesson in this lesson , you will lear... | these two numbers are $ \blued { 2 } $ and $ \greend { -3 } $ since $ ( \blued { 2 } ) \cdot ( \greend { -3 } ) =-6 $ and $ \blued { 2 } + ( \greend { -3 } ) =-1 $ . we can then add each of these numbers to $ x $ to form the two binomial factors : $ ( x+\blued2 ) $ and $ ( x+ ( \greend { -3 } ) ) $ . the factorization ... | for question 5 , why ca n't ( x-10 ) ( x+3 ) work ? |
what you need to know for this lesson factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . for more on this , check out our previous article on taking common factors . what you will learn in this lesson in this lesson , you will lear... | however , not all trinomials with $ x^2 $ as a leading term can be factored . for example , $ x^2+2x+2 $ can not be factored because there are no two integers whose sum is $ 2 $ and whose product is $ 2 $ . in future lessons we will learn more ways of factoring more types of polynomials . | how to factorize ( 12m^2-27 ) ? |
what you need to know for this lesson factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . for more on this , check out our previous article on taking common factors . what you will learn in this lesson in this lesson , you will lear... | in general , when factoring $ x^2+bx+c $ , if $ c $ is positive and $ b $ is negative , then both factors will be negative ! example 3 : factoring $ x^2-x-6 $ we can write $ x^2-x-6 $ as $ x^2-1x-6 $ . to factor $ x^2\goldd { -1 } x\purplec { -6 } $ , let 's first find two numbers that multiply to $ \purplec { -6 } $ a... | my solution : ( x+1 ) ( 2x+1 ) is it right ? |
what you need to know for this lesson factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . for more on this , check out our previous article on taking common factors . what you will learn in this lesson in this lesson , you will lear... | in general , when factoring $ x^2+bx+c $ , if $ c $ is positive and $ b $ is negative , then both factors will be negative ! example 3 : factoring $ x^2-x-6 $ we can write $ x^2-x-6 $ as $ x^2-1x-6 $ . to factor $ x^2\goldd { -1 } x\purplec { -6 } $ , let 's first find two numbers that multiply to $ \purplec { -6 } $ a... | my solution : ( x+1 ) ( 2x+1 ) is it right ? |
what you need to know for this lesson factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . for more on this , check out our previous article on taking common factors . what you will learn in this lesson in this lesson , you will lear... | this is because their product needs to be positive $ ( 6 ) $ and their sum negative $ ( -5 ) $ . in general , when factoring $ x^2+bx+c $ , if $ c $ is positive and $ b $ is negative , then both factors will be negative ! example 3 : factoring $ x^2-x-6 $ we can write $ x^2-x-6 $ as $ x^2-1x-6 $ . | how would i be able to solve this when there is no factors of c that add up to b ? |
overview calvin coolidge became the 30th president of the united states in 1923 , after the death of warren g. harding . he was elected president in 1924 and served until 1929 . although coolidge was a fiscally conservative republican who believed that the size and scope of the federal government should be limited , he... | his major foreign policy initiative was the kellogg-briand pact , which was an agreement between the united states , the united kingdom , japan , france , italy , and germany to renounce war as an instrument of national policy . though the pact did not stave off a second world war , it did constitute one of the endurin... | what were some of the reasons that calvin coolidge chose not to run for office for re-election in the 1928 presidential campaign ? |
overview calvin coolidge became the 30th president of the united states in 1923 , after the death of warren g. harding . he was elected president in 1924 and served until 1929 . although coolidge was a fiscally conservative republican who believed that the size and scope of the federal government should be limited , he... | coolidge took the oath of office and ascended to the presidency on august 3 . the presidency of calvin coolidge as president , coolidge immediately set to work on cutting taxes and reducing federal spending . in 1924 , he signed the immigration act , which imposed limits on immigration from parts of eastern and souther... | this article makes coolidge seem like a really great president but i want to know , what are some of the bad things about his presidency ? |
overview calvin coolidge became the 30th president of the united states in 1923 , after the death of warren g. harding . he was elected president in 1924 and served until 1929 . although coolidge was a fiscally conservative republican who believed that the size and scope of the federal government should be limited , he... | coolidge took the oath of office and ascended to the presidency on august 3 . the presidency of calvin coolidge as president , coolidge immediately set to work on cutting taxes and reducing federal spending . in 1924 , he signed the immigration act , which imposed limits on immigration from parts of eastern and souther... | is calvin coolidge the only president that was in office for 1 and 1/2 terms ? |
overview calvin coolidge became the 30th president of the united states in 1923 , after the death of warren g. harding . he was elected president in 1924 and served until 1929 . although coolidge was a fiscally conservative republican who believed that the size and scope of the federal government should be limited , he... | during his second term in office , the country experienced a period of economic growth and low unemployment . coolidge subscribed to the laissez-faire ideology of free-market capitalism , and his administration lowered income tax rates , cut spending , and limited federal regulation of the economy . the federal debt an... | was n't a bank , and the stock market , at fault for the great depression ? |
the heavens often rain down the richest gifts on human beings , but sometimes they bestow with lavish abundance upon a single individual beauty , grace and ability , so that whatever he does , every action is so divine that he distances all other men , and clearly displays how his greatness is a gift of god and not an ... | the heavens often rain down the richest gifts on human beings , but sometimes they bestow with lavish abundance upon a single individual beauty , grace and ability , so that whatever he does , every action is so divine that he distances all other men , and clearly displays how his greatness is a gift of god and not an ... | what was leonardo like in every day life ? |
the heavens often rain down the richest gifts on human beings , but sometimes they bestow with lavish abundance upon a single individual beauty , grace and ability , so that whatever he does , every action is so divine that he distances all other men , and clearly displays how his greatness is a gift of god and not an ... | isn ’ t it clear that leonardo thought of himself as a thinker , a philosopher , an intellectual ? leonardo 's naturalism ancient greek physicians dissected cadavers . the early church ’ s rejection of the science of the classical world , along with the possibility of bodily resurrection led to prohibitions against dis... | 1 - `` a reference to an ancient greek painter revered for his great naturalism `` , do any of the greek paintings survived ? |
the heavens often rain down the richest gifts on human beings , but sometimes they bestow with lavish abundance upon a single individual beauty , grace and ability , so that whatever he does , every action is so divine that he distances all other men , and clearly displays how his greatness is a gift of god and not an ... | the heavens often rain down the richest gifts on human beings , but sometimes they bestow with lavish abundance upon a single individual beauty , grace and ability , so that whatever he does , every action is so divine that he distances all other men , and clearly displays how his greatness is a gift of god and not an ... | or you mean vase paintings ? |
the heavens often rain down the richest gifts on human beings , but sometimes they bestow with lavish abundance upon a single individual beauty , grace and ability , so that whatever he does , every action is so divine that he distances all other men , and clearly displays how his greatness is a gift of god and not an ... | ( vasari , lives of the most excellent painters , sculptors , and architects ) leonardo : from florence to milan leonardo was born illegitimate to a prominent tuscan family of potters and notaries . he may have traveled from vinci to florence where his father worked for several powerful families including the medici . ... | is the da vinci code credible ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | slavery and the civil war washington d.c. , summer 1862 . the civil war had been going on for over a year , and it was not going well for abraham lincoln . 11 of the 15 southern states where slavery was legal had formed the confederate states of america ( csa ) and were waging a war to break free from the united states... | how did a statue of abraham lincoln ended up in the capital of scotland ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | it was becoming more and more apparent that the civil war was going to be a long and bloody conflict . ironically , when lincoln became president , he had had no intention of abolishing slavery . though he personally despised slavery , and had won the presidency on an anti-slavery platform , he would gladly have given ... | why is their still slavery in parts of the world today ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | the civil war had been going on for over a year , and it was not going well for abraham lincoln . 11 of the 15 southern states where slavery was legal had formed the confederate states of america ( csa ) and were waging a war to break free from the united states . lincoln was determined that the nation was not going to... | are there any moral , legal or academic reasons why the concept of `` states rights '' had validity for the south seceding , or is it just a convenient meme used by southerners to justify their ancestor 's practice of slavery ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | second , why is the emancipation proclamation considered lincoln 's most important legacy if it did n't actually free anyone ? slavery and the civil war washington d.c. , summer 1862 . the civil war had been going on for over a year , and it was not going well for abraham lincoln . | what would have happened if the south won the civil war ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | in the summer of 1862 , he began to hash out the details of the emancipation proclamation . the emancipation proclamation lincoln wrote the first draft of the emancipation proclamation while staying with his family at the soldier 's home , a cottage on the outskirts of washington d.c. where they could get away from the... | why were parts of louisiana ( namely except the parishes of st. bernard , plaquemines , jefferson , st. john , st. charles , st. james ascension , assumption , terrebonne , lafourche , st. mary , st. martin , and orleans , including the city of new orleans ) and virginia ( berkley , accomac , northampton , elizabeth ci... |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | significance of the proclamation because the emancipation proclamation applied only the rebellious states , it did n't directly free any slaves when it went into effect . nevertheless , it had a huge impact : it made emancipation an official part of the north 's military strategy . as the u.s. army made its way across ... | where can i find my answer to this question , how was the north able to replenish its military in the face of staggering loses on the battlefield ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | at first , the army had no idea what to do with this massive influx of former slaves , referring to them as `` contrabands '' since they were still technically considered pieces of property . some commanders found them irritating , since it was difficult to feed and move so many extra civilians , and treated them abomi... | how did the northern military anticipate the amount of food needed to feed the slaves that joined them ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | the states of the csa were not going to backtrack on their bid for independence . lincoln 's dilemma with no hope of bringing the south back into the united states by protecting slavery , lincoln had a new dilemma . his own political party , the republicans , had formed around their opposition to slavery . many of the ... | what where the political parties in the us before the institution of the republican party and lincoln ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | lincoln feared that if he advocated emancipation he would provoke those states into joining the confederacy , making the war even more difficult to win . of the border states , maryland was particularly worrisome , because the us capital at washington d.c. sat on its border with virginia . if maryland decided to join t... | why are thay called the border states ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | the civil war had been going on for over a year , and it was not going well for abraham lincoln . 11 of the 15 southern states where slavery was legal had formed the confederate states of america ( csa ) and were waging a war to break free from the united states . lincoln was determined that the nation was not going to... | what about states ' rights ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . | why do so many people think that it ended slavery ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | as the us war dead piled up , more and more northerners began to push lincoln to punish the states that had seceded by making abolition a major goal of the war . the problem with abolishing slavery , however , was that there were still four slave states that had not seceded from the united states : missouri , kentucky ... | why was lincoln worried about the 4 slave states that were still in the union ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | it was becoming more and more apparent that the civil war was going to be a long and bloody conflict . ironically , when lincoln became president , he had had no intention of abolishing slavery . though he personally despised slavery , and had won the presidency on an anti-slavery platform , he would gladly have given ... | what is the difference between anti-slavery and abolition ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | the civil war had been going on for over a year , and it was not going well for abraham lincoln . 11 of the 15 southern states where slavery was legal had formed the confederate states of america ( csa ) and were waging a war to break free from the united states . lincoln was determined that the nation was not going to... | how can the confederate states bend those words to include slavery ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | second , why is the emancipation proclamation considered lincoln 's most important legacy if it did n't actually free anyone ? slavery and the civil war washington d.c. , summer 1862 . the civil war had been going on for over a year , and it was not going well for abraham lincoln . | could n't the northern states just show the confederates the declaration of independence and avoid the civil war ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | congress officially outlawed slavery when it passed the thirteenth amendment in january , 1865 . significance of the proclamation because the emancipation proclamation applied only the rebellious states , it did n't directly free any slaves when it went into effect . nevertheless , it had a huge impact : it made emanci... | could n't the emancipation proclamation be interpreted as a ( tacit ) commitment that slavery could continue in the border states ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | the civil war had been going on for over a year , and it was not going well for abraham lincoln . 11 of the 15 southern states where slavery was legal had formed the confederate states of america ( csa ) and were waging a war to break free from the united states . lincoln was determined that the nation was not going to... | did n't those states feel betrayed ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | black men were accepted into the army to play their own part in ending slavery . what 's more , the emancipation proclamation made a promise : it promised that the united states was committed to ending slavery once and for all . it promised african americans in the south that under no circumstances would they be return... | where did the emancipation proclamation end slavery ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | he even gave those states the opportunity to rejoin the union before january 1 , 1863 to prevent the proclamation from going into effect ( they declined ) . the emancipation proclamation did not apply to enslaved people in the border states of missouri , kentucky , delaware , and maryland , which had not joined the con... | why was tennessee and kentucky not apart of the union and confederacy ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | were these compromises held for the stretch of angry libertarians to figure what justice and freedom for all meant ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | how about zero ? although there were more than four million slaves living in the u.s. at this time , the emancipation proclamation did not formally free a single one of them . so that presents us with a couple of very interesting questions : first , why did lincoln issue the proclamation if it had no practical effect ? | were the slaves actually emancipated or were they still tied to the landowners in order to make a living ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | so that presents us with a couple of very interesting questions : first , why did lincoln issue the proclamation if it had no practical effect ? second , why is the emancipation proclamation considered lincoln 's most important legacy if it did n't actually free anyone ? slavery and the civil war washington d.c. , summ... | were the slaves actually free or were they still dependent upon land owners after president lincoln issued the emancipation proclamation ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | lincoln feared that if he advocated emancipation he would provoke those states into joining the confederacy , making the war even more difficult to win . of the border states , maryland was particularly worrisome , because the us capital at washington d.c. sat on its border with virginia . if maryland decided to join t... | why did the border states stay in the union ? |
when most people think of abraham lincoln , they think of his greatest achievement : ending the institution of slavery in the united states during the american civil war ( 1861-1865 ) . in fact , most statues of lincoln show him holding a piece of paper meant to represent the text of the emancipation proclamation . wha... | ironically , when lincoln became president , he had had no intention of abolishing slavery . though he personally despised slavery , and had won the presidency on an anti-slavery platform , he would gladly have given up any chance of ending slavery in the south if it meant that the confederate states would rejoin the u... | what do you think would happen if slavery still existed ? |
overview the civil rights movement is an umbrella term for the many varieties of activism that sought to secure full political , social , and economic rights for african americans in the period from 1946 to 1968 . civil rights activism involved a diversity of approaches , from bringing lawsuits in court , to lobbying t... | spearheaded by the national association for the advancement of colored people ( naacp ) , this strategy initiated lawsuits to undermine the legal foundation of jim crow segregation in the south . the landmark brown v. board of education of topeka ruling held that separate facilities were inherently unequal and thereby ... | why did the government not take action against the south 's resistance to desegregation ? |
overview the civil rights movement is an umbrella term for the many varieties of activism that sought to secure full political , social , and economic rights for african americans in the period from 1946 to 1968 . civil rights activism involved a diversity of approaches , from bringing lawsuits in court , to lobbying t... | mass direct action was highly effective , particularly due to widespread news media coverage of nonviolent protestors being harassed and physically beaten by law enforcement officers . black power although comprehensive civil rights legislation represented a major victory for the civil rights movement , the obstinacy o... | on the part of black power , how does is that help civil rights ? |
overview the civil rights movement is an umbrella term for the many varieties of activism that sought to secure full political , social , and economic rights for african americans in the period from 1946 to 1968 . civil rights activism involved a diversity of approaches , from bringing lawsuits in court , to lobbying t... | what do you think ? why did the twentieth-century civil rights movement emerge ? which of the strategies employed by civil rights activists do you think was most effective ? | what are some of the catalysts of the civil rights movement ? |
overview the civil rights movement is an umbrella term for the many varieties of activism that sought to secure full political , social , and economic rights for african americans in the period from 1946 to 1968 . civil rights activism involved a diversity of approaches , from bringing lawsuits in court , to lobbying t... | what do you think ? why did the twentieth-century civil rights movement emerge ? which of the strategies employed by civil rights activists do you think was most effective ? | how did the grassroots civil rights movement begin and how was it different from legal , legislative , and presidential efforts to achieve equality ? |
overview the civil rights movement is an umbrella term for the many varieties of activism that sought to secure full political , social , and economic rights for african americans in the period from 1946 to 1968 . civil rights activism involved a diversity of approaches , from bringing lawsuits in court , to lobbying t... | civil rights and the supreme court one of the earliest approaches was centered in the courts . spearheaded by the national association for the advancement of colored people ( naacp ) , this strategy initiated lawsuits to undermine the legal foundation of jim crow segregation in the south . the landmark brown v. board o... | why people call black people negro ? |
what is gastroenteritis ? gastro , infectious diarrhea , traveler 's diarrhea , stomach bug , “ stomach flu ” . whatever you like to call it , in medical terms , it all boils down to one thing - gastroenteritis - which literally means an inflammation ( itis ) of your stomach ( gastro ) and intestines ( entero ) that ty... | what is gastroenteritis ? gastro , infectious diarrhea , traveler 's diarrhea , stomach bug , “ stomach flu ” . | what is the domain classification for gastroenteritis ? |
what is gastroenteritis ? gastro , infectious diarrhea , traveler 's diarrhea , stomach bug , “ stomach flu ” . whatever you like to call it , in medical terms , it all boils down to one thing - gastroenteritis - which literally means an inflammation ( itis ) of your stomach ( gastro ) and intestines ( entero ) that ty... | what is gastroenteritis ? gastro , infectious diarrhea , traveler 's diarrhea , stomach bug , “ stomach flu ” . whatever you like to call it , in medical terms , it all boils down to one thing - gastroenteritis - which literally means an inflammation ( itis ) of your stomach ( gastro ) and intestines ( entero ) that ty... | can gastroenteritis be called as diarrhea ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | how does the chain continue to grow ? once the peptide bond is formed , the mrna is pulled onward through the ribosome by exactly one codon . this shift allows the first , empty trna to drift out via the e ( `` exit '' ) site . | the part about mrna shifting one codon , is n't it the ribosome that shifts one codon ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | if antibiotics interrupt bacterial ribosomes , how can bacteria become resistant to antibiotics ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | a shine-dalgarno sequence marks the start of each coding sequence , letting the ribosome find the right start codon for each gene . elongation i like to remember what happens in this `` middle '' stage of translation by its handy name : elongation is when the polypeptide chain gets longer . but how does the chain actua... | what happens to mrna after the polypeptide chain is formed ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | how does the chain continue to grow ? once the peptide bond is formed , the mrna is pulled onward through the ribosome by exactly one codon . this shift allows the first , empty trna to drift out via the e ( `` exit '' ) site . | after peptide bond formation , what pulls mrna to a new position ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | once the peptide bond is formed , the mrna is pulled onward through the ribosome by exactly one codon . this shift allows the first , empty trna to drift out via the e ( `` exit '' ) site . it also exposes a new codon in the a site , so the whole cycle can repeat . | do t-rna 's occupy the position at e site ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | initiation ( `` beginning '' ) : in this stage , the ribosome gets together with the mrna and the first trna so translation can begin . elongation ( `` middle '' ) : in this stage , amino acids are brought to the ribosome by trnas and linked together to form a chain . termination ( `` end '' ) : in the last stage , the... | section of stage 2 : elongation , why has one of the hydrogen atoms ( on the amino acid molecule ) that 's originally in the carboxyl group moved to the amino group ( and thus creating charges ) ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | these shine-dalgarno sequences come just before start codons and `` point them out '' to the ribosome . why use shine-dalgarno sequences ? bacterial genes are often transcribed in groups ( called operons ) , so one bacterial mrna can contain the coding sequences for several genes . | does this protein have any influence on the rate of water loss/use by plants ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | these shine-dalgarno sequences come just before start codons and `` point them out '' to the ribosome . why use shine-dalgarno sequences ? bacterial genes are often transcribed in groups ( called operons ) , so one bacterial mrna can contain the coding sequences for several genes . | for instance , can this protein grant drought tolerance to a plant by reducing its rate of water use ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | termination happens when a stop codon in the mrna ( uaa , uag , or uga ) enters the a site . stop codons are recognized by proteins called release factors , which fit neatly into the p site ( though they are n't trnas ) . release factors mess with the enzyme that normally forms peptide bonds : they make it add a water ... | does n't the carboxyl group have a hydrogen attached to the oxygen with the single bond ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | stop codons are recognized by proteins called release factors , which fit neatly into the p site ( though they are n't trnas ) . release factors mess with the enzyme that normally forms peptide bonds : they make it add a water molecule to the last amino acid of the chain . this reaction separates the chain from the trn... | does the water molecule that the release factors added on the polypeptide chain get deattached once termination is done ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics block translation . in the process of translation , a cell reads information from a molecule called a mes... | which events during translation involve molecular recognition between base sequences within different rnas ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | which events involve recognition between different protein molecules ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | inside your cells ( and the cells of other eukaryotes ) , translation initiation goes like this : first , the trna carrying methionine attaches to the small ribosomal subunit . together , they bind to the 5 ' end of the mrna by recognizing the 5 ' gtp cap ( added during processing in the nucleus ) . then , they `` walk... | i do n't think its a gtp cap on the 5 ' end of the mrna that the 40s unit attaches to is it ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | trnas bind to mrnas inside of a protein-and-rna structure called the ribosome . as trnas enter slots in the ribosome and bind to codons , their amino acids are linked to the growing polypeptide chain in a chemical reaction . the end result is a polypeptide whose amino acid sequence mirrors the sequence of codons in the... | what chemical translates the dna ? |
introduction ever wonder how antibiotics kill bacteria—for instance , when you have a sinus infection ? different antibiotics work in different ways , but some attack a very basic process in bacterial cells : they knock out the ability to make new proteins . to use a little molecular biology vocab , these antibiotics b... | how does the chain continue to grow ? once the peptide bond is formed , the mrna is pulled onward through the ribosome by exactly one codon . this shift allows the first , empty trna to drift out via the e ( `` exit '' ) site . | what happened to the information regarding codon recognition , peptide bond formation and translocation during the elongation process ? |
background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | how do i find the second partial derivatives for a function with 3 variables and how does this test work for that ? |
background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | using the values for the second derivatives you were asked to compute above , here 's what we get : $ \bluee { f_ { xx } ( 0 , 0 ) } \rede { f_ { yy } ( 0 , 0 ) } - \greene { f_ { xy } ( 0 , 0 ) } ^2 = ( \bluee { 2 } ) ( \rede { 2 } ) - \greene { p } ^2 $ when $ p & gt ; 2 $ , this is negative , so $ f $ has a saddle p... | how do you know if fxx or fyy is positive or negative ? |
background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | is the formula for the second partial derivative test ( fxx*fyy - ( fxy ) ^2 ) just the determinant of the hessian matrix learned earlier in this section ? |
background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | you can think of the quantity $ \greene { f_ { xy } ( x_0 , y_0 ) } $ as measuring how much the function $ f $ looks like the graph of $ g ( x , y ) = xy $ near the point $ ( x_0 , y_0 ) $ . considering how many directions have to agree with each other , it is actually quite surprising that we only need to consider thr... | i guess if h > 0 i could also check if the funcion has a max/min at the generic point by substituting ( x sub 0 , y sub 0 ) in fyy , right ? |
background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | considering how many directions have to agree with each other , it is actually quite surprising that we only need to consider three values , $ \bluee { f_ { xx } ( 0 , 0 ) } $ , $ \rede { f_ { yy } ( 0 , 0 ) } $ and $ \greene { f_ { xy } ( 0 , 0 ) } $ . the next article gives more detailed reasoning behind the second p... | is there a way to program ( in prgm ) the second partial derivative test into my ti 84 plus silver for faster working ? |
background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | i only ask because i have way too many formulas for the test ... : / if not can anyone tell me how to make my ti 84 calculate the partial derivatives for me at least ? |
background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | you can think of the quantity $ \greene { f_ { xy } ( x_0 , y_0 ) } $ as measuring how much the function $ f $ looks like the graph of $ g ( x , y ) = xy $ near the point $ ( x_0 , y_0 ) $ . considering how many directions have to agree with each other , it is actually quite surprising that we only need to consider thr... | what options are available if h=0 ? |
background maximums , minimums , and saddle points second partial derivatives not strictly necessary , but used in one section : the hessian matrix also , if you are a little rusty on the second derivative test from single-variable calculus , you might want to quickly review it here since it 's a good comparison for th... | loose intuition focus first on this term : $ \bluee { f_ { xx } ( x_0 , y_0 ) } \rede { f_ { yy } ( x_0 , y_0 ) } $ you can think of it as cleverly encoding whether or not the concavity of $ f $ 's graph is the same in both the $ x $ and $ y $ directions . for example , look at the function $ f ( x , y ) = x^2 - y^2 $ ... | in the equation for h , what is fxx ( x , y ) and fyy ( x , y ) and fxy ( x , y ) ^2 ? |
the euphrates river in 2005 the cradle of civilization mesopotamia , the area between the tigris and euphrates rivers ( in modern day iraq ) , is often referred to as the cradle of civilization because it is the first place where complex urban centers grew . the history of mesopotamia , however , is inextricably tied ... | the euphrates river in 2005 the cradle of civilization mesopotamia , the area between the tigris and euphrates rivers ( in modern day iraq ) , is often referred to as the cradle of civilization because it is the first place where complex urban centers grew . the history of mesopotamia , however , is inextricably tied ... | this is sort of an off beat question and probably a little hard to know but when you say mesopotamia was one of the first complex urban centers , about how many people actually lived there ? |
the euphrates river in 2005 the cradle of civilization mesopotamia , the area between the tigris and euphrates rivers ( in modern day iraq ) , is often referred to as the cradle of civilization because it is the first place where complex urban centers grew . the history of mesopotamia , however , is inextricably tied ... | it is largely because of the west 's interests in the biblical `` holy land '' that ancient near eastern materials have been regarded as part of the western canon of the history of art . the land of the bible an interest in finding the locations of cities mentioned in the bible ( such as nineveh and babylon ) inspired ... | what was excavated by the english and french in 19th century archaeological expeditions to the near east ? |
the euphrates river in 2005 the cradle of civilization mesopotamia , the area between the tigris and euphrates rivers ( in modern day iraq ) , is often referred to as the cradle of civilization because it is the first place where complex urban centers grew . the history of mesopotamia , however , is inextricably tied ... | the history of mesopotamia , however , is inextricably tied to the greater region , which is comprised of the modern nations of egypt , iran , syria , jordan , israel , lebanon , the gulf states and turkey . we often refer to this region as the near or middle east . what 's in a name ? | what were the conventions of art in the ancient middle east ? |
the euphrates river in 2005 the cradle of civilization mesopotamia , the area between the tigris and euphrates rivers ( in modern day iraq ) , is often referred to as the cradle of civilization because it is the first place where complex urban centers grew . the history of mesopotamia , however , is inextricably tied ... | the euphrates river in 2005 the cradle of civilization mesopotamia , the area between the tigris and euphrates rivers ( in modern day iraq ) , is often referred to as the cradle of civilization because it is the first place where complex urban centers grew . the history of mesopotamia , however , is inextricably tied ... | how is the euphrates river so big ? |
the euphrates river in 2005 the cradle of civilization mesopotamia , the area between the tigris and euphrates rivers ( in modern day iraq ) , is often referred to as the cradle of civilization because it is the first place where complex urban centers grew . the history of mesopotamia , however , is inextricably tied ... | it is the proximity of these countries to the west ( to europe ) that led this area to be termed `` the near east . '' ancient near eastern art has long been part of the history of western art , but history did n't have to be written this way . it is largely because of the west 's interests in the biblical `` holy land... | do you think the wars in iraq ( desert storm , freedom operation ) destroyed much of the ancient art there ? |
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