# on 18-Aug-2018 (Sat)

#### Flashcard 149625149

Tags
#calculus #elasticity #has-images #mathematics
Question

In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output)[1] at point a is defined as[2] using functions and their derivatives

meaning in words: [...]

It is thus the ratio of the relative (percentage) change in the function's output $$f(a)$$ with respect to the relative change in its input $$a$$, for infinitesimal changes from a point .

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the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output)[1] at point a is defined as[2] using functions and their derivatives meaning in words: <span>It is thus the ratio of the relative (percentage) change in the function's output $$f(a)$$ with respect to the relative change in its input $$a$$, for infinitesimal changes from a point . <span><body><html>

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Elasticity of a function - Wikipedia, the free encyclopedia
er:filter:minify-css:7:3904d24a08aa08f6a68dc338f9be277e */ Elasticity of a function From Wikipedia, the free encyclopedia Jump to: navigation, search <span>In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output)[1] at point a is defined as[2] or equivalently It is thus the ratio of the relative (percentage) change in the function's output with respect to the relative change in its input , for infinitesimal changes from a point . Equivalently, it is the ratio of the infinitesimal change of the logarithm of a function with respect to the infinitesimal change of the logarithm of the argument. The elasticity of a function is a constant if and only if the function has the form for a constant . The elasticity at a point is the limit of the arc elasticity between two points as

#### Annotation 3146206809356

 #mathematics #polynomials #precalculus Rewrite $$5^2-2^2$$ as a product. We have $5^2-2^2 = (5-2) \times (5+2) = 3\times 7.$

Difference Of Squares | Brilliant Math &amp; Science Wiki
ction contains examples and problems to boost understanding in the usage of the difference of squares identity: $$a^2-b^2=(a+b)(a-b)$$. Here are the examples to learn the usage of the identity. <span>Rewrite $$5^2-2^2$$ as a product. We have $5^2-2^2 = (5-2) \times (5+2) = 3\times 7. \ _\square$ Calculate $$299\times 301$$. You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At fir

#### Flashcard 3199204461836

Tags
#Gastroenterology #small_bowel_pathologies
Question
Which bacreria causes Whipple’s disease?
Whipple’s disease is a rare infectious bacterial disease caused by Tropheryma whipplei

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#### Annotation 3199208393996

 #Gastroenterology #small_bowel_pathologies In Whipple’s disease, 87% are males, usually white and middle- aged.It presents with arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss.Peripheral lymphadenopathy and involvement of the heart, lung, joints and brain occur, simulating many neurological conditions

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#### Flashcard 3199210753292

Tags
#Gastroenterology #small_bowel_pathologies
Question
• In Whipple’s disease, 87% are [...].
• It presents with arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss.
• Peripheral lymphadenopathy and involvement of the heart, lung, joints and brain occur, simulating many neurological conditions
males, usually white and middle- aged

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In Whipple’s disease, 87% are males, usually white and middle- aged. It presents with arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss. Peripheral lymphadenopat

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#### Flashcard 3199212326156

Tags
#Gastroenterology #small_bowel_pathologies
Question
• In Whipple’s disease, 87% are males, usually white and middle- aged.
• It presents with [...], progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss.
• Peripheral lymphadenopathy and involvement of the heart, lung, joints and brain occur, simulating many neurological conditions
arthritis and arthralgia

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In Whipple’s disease, 87% are males, usually white and middle- aged. It presents with arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss. Peripheral lymphadenopathy and involvement of the heart, lung, join

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#### Flashcard 3199213899020

Tags
#Gastroenterology #small_bowel_pathologies
Question
• In Whipple’s disease, 87% are males, usually white and middle- aged.
• It presents with arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss.
• Peripheral lymphadenopathy and involvement of the [...] occur, simulating many neurological conditions
heart, lung, joints and brain

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arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss. Peripheral lymphadenopathy and involvement of the <span>heart, lung, joints and brain occur, simulating many neurological conditions <span>

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#### Flashcard 3199217044748

Tags
#Gastroenterology #small_bowel_pathologies
Question
How diagnosis of Whipple’s disease is made?
• Diagnosis is made by small bowel biopsy.
• Periodic acid–Schiff (PAS)-positive macrophages are present but are nonspecific.
• On electron microscopy, the characteristic trilaminar cell wall of T. whipplei can be seen within macrophages.
• T. whipplei antibodies can be identified by immunohistochemistry.
• A confirmatory PCR-based assay is available

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#### Flashcard 3199219404044

Tags
#Gastroenterology #small_bowel_pathologies
Question
What is the treatment of Whipple’s disease?
• Treatment is with antibiotics which cross the blood-brain barrier,
• such as 160 mg Trimethoprim and 800 mg sulpha- methoxazole (co-trimoxazole) daily for 1 year.
• This is preceded by a 2-week course of streptomycin and penicillin or ceftriaxone.
• Treatment periods of less than a year are associated with relapse in about 40%

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#### Annotation 3199221763340

 #Gastroenterology #IBD in 10% of cases of IBD causing colitis a definitive diagnosis of either UC or CD is not possible and the diagnosis is termed colitis of undetermined type and etiology (CUTE).

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#### Flashcard 3199224909068

Tags
#Gastroenterology #IBD
Question
in 10% of cases of IBD causing colitis a definitive diagnosis of either UC or CD is not possible and the diagnosis is termed [...]
colitis of undetermined type and etiology (CUTE).

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in 10% of cases of IBD causing colitis a definitive diagnosis of either UC or CD is not possible and the diagnosis is termed colitis of undetermined type and etiology (CUTE).

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#### Annotation 3199226481932

 #Gastroenterology #IBD Jewish people are more prone to inflammatory bowel disease than any other ethnic group.

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#### Flashcard 3199228841228

Tags
#Gastroenterology #IBD
Question
[...] people are more prone to inflammatory bowel disease than any other ethnic group.
Jewish

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Jewish people are more prone to inflammatory bowel disease than any other ethnic group.

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#### Flashcard 3199230414092

Tags
#Gastroenterology #IBD
Question
Although the aetiology of IBD is unknown, it is increasingly clear that IBD represents the interaction between several co-factors, what are they?
• Genetic susceptibility
• The environment
• The intestinal microbiota
• Host immune response

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#### Annotation 3199232773388

 #Gastroenterology #IBD Crohn's Disease and Ulcerative colitis are complex polygenic diseases and having a positive family history is the largest independent risk factor.

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#### Flashcard 3199235132684

Tags
#Gastroenterology #IBD
Question
Crohn's Disease and Ulcerative colitis are [...] and having a positive family history is the largest independent risk factor.
complex polygenic diseases

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Crohn's Disease and Ulcerative colitis are complex polygenic diseases and having a positive family history is the largest independent risk factor.

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#### Annotation 3199236705548

 ORIE_LIGNE=( #next lines reorient all the line element on ’topbeam’ #along a vector lying along y global axis #with origin at node ’masseN

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#### Annotation 3199240113420

 An identity equation is an equation that is always true for any value substituted into the variable. $$_\square$$

Solving Identity Equations | Brilliant Math &amp; Science Wiki
ave an account? Log in here. Quiz Solving Identity Equations Relevant For... Algebra > Polynomial Arithmetic Ram Mohith , Beakal Tiliksew , Mahindra Jain , and 1 other Jimin Khim contributed <span>An identity equation is an equation that is always true for any value substituted into the variable. $$_\square$$ For example, $$2(x+1)=2x+2$$ is an identity equation. One way of checking is by simplifying the equation. \begin{align} 2(x+1)&=2x+2\\ 2x+2&=2x+2\\ 2&=2. \end{align} $$2 #### Flashcard 3199243783436 Tags #mathematics #polynomials #precalculus Question Since the two factors are different by , the factors will always have the same parity. That is, if is even then must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. Answer [default - edit me] status measured difficulty not learned 37% [default] 0 Difference Of Squares | Brilliant Math &amp; Science Wiki ue View solutions What is Note: Try it without using a calculator. Correct! The answer is 1. 74% of people got this right. Continue View solutions Don't use a calculator! Further Extension Edit <span>Since the two factors are different by , the factors will always have the same parity. That is, if is even then must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: Problem Solving Edit The examples and problems in this sections are a bit hard #### Flashcard 3199247453452 Question ou do not understand may seem like an utmost nonsense. Still, an amazing proportion of students commit the offence of learning without comprehension. Very often they have no Answer [default - edit me] status measured difficulty not learned 37% [default] 0 Effective learning: Twenty rules of formulating knowledge | SuperMemo.com not just learn once but you will repeat the material optimally (as in SuperMemo). The 20 rules of formulating knowledge in learning Do not learn if you do not understand Trying to learn things y<span>ou do not understand may seem like an utmost nonsense. Still, an amazing proportion of students commit the offence of learning without comprehension. Very often they have no other choice! The quality of many textbooks or lecture scripts is deplorable while examination deadlines are unmovable. If you are not a speaker of German, it is still possible to learn #### Flashcard 3199249812748 Question not a speaker of German, it is still possible to learn a history textbook in German. The book can be crammed word for word. However, the time needed for such "blind le Answer com here status measured difficulty not learned 37% [default] 0 Effective learning: Twenty rules of formulating knowledge | SuperMemo.com nce of learning without comprehension. Very often they have no other choice! The quality of many textbooks or lecture scripts is deplorable while examination deadlines are unmovable. If you are <span>not a speaker of German, it is still possible to learn a history textbook in German. The book can be crammed word for word. However, the time needed for such "blind learning" is astronomical. Even more important: The value of such knowledge is negligible. If you cram a German book on history, you will still know nothing of history. The German history #### Annotation 3199693884684  example is an extreme. However, the materials you learn may often seem well structured and you may tend to blame yourself for lack of comprehension. Soon you may pollute your learning process with a great deal of useless material that treacherously makes you believe "it will be useful some day". status not read Effective learning: Twenty rules of formulating knowledge | SuperMemo.com learning" is astronomical. Even more important: The value of such knowledge is negligible. If you cram a German book on history, you will still know nothing of history. The German history book <span>example is an extreme. However, the materials you learn may often seem well structured and you may tend to blame yourself for lack of comprehension. Soon you may pollute your learning process with a great deal of useless material that treacherously makes you believe "it will be useful some day". Learn before you memorize Before you proceed with memorizing individual facts and rules, you need to build an overall picture of the learned knowledge. Only when individual pieces fit t #### Flashcard 3199695457548 Question [default - edit me] Answer your learning process status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it example is an extreme. However, the materials you learn may often seem well structured and you may tend to blame yourself for lack of comprehension. Soon you may pollute your learning process with a great deal of useless material that treacherously makes you believe "it will be useful some day". #### Original toplevel document Effective learning: Twenty rules of formulating knowledge | SuperMemo.com learning" is astronomical. Even more important: The value of such knowledge is negligible. If you cram a German book on history, you will still know nothing of history. The German history book <span>example is an extreme. However, the materials you learn may often seem well structured and you may tend to blame yourself for lack of comprehension. Soon you may pollute your learning process with a great deal of useless material that treacherously makes you believe "it will be useful some day". Learn before you memorize Before you proceed with memorizing individual facts and rules, you need to build an overall picture of the learned knowledge. Only when individual pieces fit t #### Flashcard 3199899929868 Question e endings. “And th Answer surprise endings. “And then, status measured difficulty not learned 37% [default] 0 4 Steps to Reading a Textbook Quickly and Effectively e lame. If you know Bruce Willis is dead, don’t watch the 6th Sense. But textbooks are rarely building to a suspenseful twist at the end. I promise. I’ve read a lot. They don’t come with surpris<span>e endings. “And then, Abraham Lincoln dodged the bullet!” Yep, that’s never going to be in a textbook. Want to try this strategy? Try reading your textbook chapter in this order: Go to the questions at th #### Annotation 3200507579660  Hausdorff's Set theory. status not read #### pdf cannot see any pdfs #### Flashcard 3203067940108 Tags #mathematics #polynomials #precalculus Question \(5^2-2^2$$ = [...] $$\times (5+2) = 3\times 7$$
$$(5−2)$$

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Rewrite 52−22 as a product. We have 52−22=(5−2)×(5+2)=3×7. □

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Difference Of Squares | Brilliant Math &amp; Science Wiki
ction contains examples and problems to boost understanding in the usage of the difference of squares identity: $$a^2-b^2=(a+b)(a-b)$$. Here are the examples to learn the usage of the identity. <span>Rewrite $$5^2-2^2$$ as a product. We have $5^2-2^2 = (5-2) \times (5+2) = 3\times 7. \ _\square$ Calculate $$299\times 301$$. You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At fir

#### Annotation 3203247246604

 nstead of using a K_TR_D_L for the ’hinge’ group we may use a beam element with a null, or near null, value for the moment of inertia on the right axis.

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#### Annotation 3204471721228

 As we use a null or near null for one value of moment of inertia 1 it is of course meaningless to try to calculate the related bending stress in these elements, but the forces and moments are meaningful! Last but not least using short beam elements or discrete elements is not strictly equivalent, chapter 3.1 provides a deeper insight into discrete stiffness elements

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#### Annotation 3209506983180

 Axiomatic set theory by Suppes

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#### Annotation 3209508556044

 In set theory "naive" and "axiomatic" are contrasting words. The present treatment might best be described as axiomatic set theory from the naive point of view. It is axiomatic in that some axioms for set theory are stated and used as the basis of all subsequent proofs. It is naive in that the language and notation are those of ordinary informal (but for- malizable) mathematics.

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#### Annotation 3209514323212

 #mathematics #polynomials #precalculus Since the two factors are different by \2b\, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares.

Difference Of Squares | Brilliant Math &amp; Science Wiki
lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: $\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac) #### Flashcard 3209515896076 Tags #mathematics #polynomials #precalculus Question Since the two factors are different by [...], the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. Answer 2b status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it Since the two factors are different by 2b , the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is #### Original toplevel document Difference Of Squares | Brilliant Math &amp; Science Wiki lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ?$ Don't use a calculator! Further Extension <span>Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: $\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac) #### Flashcard 3209517468940 Tags #mathematics #polynomials #precalculus Question Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is [...] then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. Answer even status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot #### Original toplevel document Difference Of Squares | Brilliant Math &amp; Science Wiki lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ?$ Don't use a calculator! Further Extension <span>Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: $\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac) #### Flashcard 3209519303948 Tags #mathematics #polynomials #precalculus Question Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the [...] is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. Answer product status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 square #### Original toplevel document Difference Of Squares | Brilliant Math &amp; Science Wiki lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ?$ Don't use a calculator! Further Extension <span>Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: $\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac) #### Flashcard 3209521138956 Tags #mathematics #polynomials #precalculus Question Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be [...], so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. Answer even status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the differ #### Original toplevel document Difference Of Squares | Brilliant Math &amp; Science Wiki lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ?$ Don't use a calculator! Further Extension <span>Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: $\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac) #### Flashcard 3209522187532 Tags #mathematics #polynomials #precalculus Question Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by [...]. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. Answer four status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. #### Original toplevel document Difference Of Squares | Brilliant Math &amp; Science Wiki lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ?$ Don't use a calculator! Further Extension <span>Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: $\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac) #### Flashcard 3209524022540 Tags #mathematics #polynomials #precalculus Question Rewrite $$5^2-2^2$$ as a product. We have \[5^2-2^2 = (5-2) \times (5+2) = 3\times 7.$

5222

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Rewrite 52−22 as a product. We have 52−22=(5−2)×(5+2)=3×7.

#### Original toplevel document

Difference Of Squares | Brilliant Math &amp; Science Wiki
ction contains examples and problems to boost understanding in the usage of the difference of squares identity: $$a^2-b^2=(a+b)(a-b)$$. Here are the examples to learn the usage of the identity. <span>Rewrite $$5^2-2^2$$ as a product. We have $5^2-2^2 = (5-2) \times (5+2) = 3\times 7. \ _\square$ Calculate $$299\times 301$$. You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At fir

#### Flashcard 3209525071116

Tags
#mathematics #polynomials #precalculus
Question
Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if [...] is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares.
ab

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Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not

#### Original toplevel document

Difference Of Squares | Brilliant Math &amp; Science Wiki
lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)

#### 如何长时间高效学习[转一优秀答复]

①时间

②案例

③可实施性

“在学习一门新的知识时，短时间集中注意力不难” + “（刻意练习）高手的练习每次最多1到1.5小时，每天最多4到5小时。没人受得了更多”→→→→结合我们20小时学一门教材的目标，可以得出一个结论：我们进行的不是严格意义刻意练习，我们的强度也没有那个国外小子那么高，而且一轮下来只要20小时，即便是用刻意练习的方式进行，也是可以接受的。学完一科，我们可以进行休整放松，不用严打紧逼。而且就我个人而言，一天高效学习时间安排在八个小时左右，是可以执行的。

④如果保证利用好自己的高效时间？ 学习仪式感：

⑤为什么不首先直接去阅读文字呢？

（在重新排版的时候，我请额外圈出一句话：推荐者万万众，实践者几几人！——这句话太好了，且做我的名言2号。） 这个建议是这样：