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key points to predict if a population will grow or shrink , ecologists need to know birth and death rates for organisms at different ages as well as the current age and sex makeup of the population . life tables summarize birth and death rates for organisms at different stages of their lives . survivorship curves are g... | the second population is likely to shrink because it has many bears that are close to death and can no longer reproduce . so , who 's currently in a population makes a big difference when we are thinking about future population growth ! information about the age-sex structure of a population is often shown as a populat... | why is japan 's population shrinking ? |
key points to predict if a population will grow or shrink , ecologists need to know birth and death rates for organisms at different ages as well as the current age and sex makeup of the population . life tables summarize birth and death rates for organisms at different stages of their lives . survivorship curves are g... | species with type i curves usually have small numbers of offspring and provide lots of parental care to make sure those offspring survive . type ii . many bird species have a type ii survivorship curve . in a type ii curve , organisms die more or less equally at each age interval . | insects will have which type of survivorship curve ? |
key points to predict if a population will grow or shrink , ecologists need to know birth and death rates for organisms at different ages as well as the current age and sex makeup of the population . life tables summarize birth and death rates for organisms at different stages of their lives . survivorship curves are g... | this is particularly important in the case of an endangered species , like the red pandas in our example . life tables a life table records matters of life and death for a population—literally ! it summarizes the likelihood that organisms in a population will live , die , and/or reproduce at different stages of their l... | instead of a life-table , could you have used just the number of deaths at each age ( in a particular year ) , to come up with a distribution of life-expectancy ? |
key points to predict if a population will grow or shrink , ecologists need to know birth and death rates for organisms at different ages as well as the current age and sex makeup of the population . life tables summarize birth and death rates for organisms at different stages of their lives . survivorship curves are g... | that makes for a death , or mortality , rate of 54/1000 , or 0.054 , which is recorded in the far-right column . age interval in years| number surviving at beginning of age interval out of 1000 born |number dying in age interval out of 1000 born |age-specific mortality rate—fraction of individuals alive at beginning of... | for instance , if 20 out of 100 people die in their first year and 80 die in the next year , then , can i ( roughly ) say that the average life-expectancy is 0.2* ( 0.5 years ) +0.8* ( 1.5 years ) = 1.3 years ? |
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 . we have seen several examples of factoring already . however , for this article , you should be especially familiar with taking common factors... | this is because we can rewrite the expression as follows : $ 2x^2+\blued7x+3=2x^2+\blued1x+\blued6x+3 $ then we can use grouping to factor $ 2x^2+\blued1x+\blued6x+3 $ as $ ( x+3 ) ( 2x+1 ) $ . for more on factoring quadratic trinomials like these using the grouping method , check out our next article . | this may sound a bit dumb , but is there any significant difference between factoring , grouping trinomials , difference of squares , and gcf ? |
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 . we have seen several examples of factoring already . however , for this article , you should be especially familiar with taking common factors... | we can factor these out to obtain the following expression : $ 2x ( x+4 ) +3 ( x+4 ) $ notice that this reveals yet another common factor between the two terms : $ \goldd { x+4 } $ . we can use the distributive property to factor out this common factor . since the polynomial is now expressed as a product of two binomia... | my only question is , when finding the common factor why can you just take one out then multiply that common factor by what was being multiplied on each one ? |
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 . we have seen several examples of factoring already . however , for this article , you should be especially familiar with taking common factors... | check your understanding example 3 : factoring $ 3x^2-6x-4x+8 $ extra care should be taken when using the grouping method to factor a polynomial with negative coefficients . for example , the steps below can be used to factor $ 3x^2-6x-4x+8 $ . $ \begin { align } \phantom { 0 } & amp ; & amp ; & amp ; \phantom { = } 3x... | but , is there a way to recognize this un-factorability without going through the computational steps in order to find out whether or not the expression can be factored ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | we ended up at 0 so $ 8 \text { mod } 4 = \bf { 0 } $ . $ 7 \text { mod } 2 = ? $ with a modulus of 2 we make a clock with numbers 0 , 1 . | -17 mod 7 -7*2=-14 -17 '= ' -7 *2 +-3 -7 *2 +-3=-17 why does the site say 4 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \text { mod } 10 = 3 \ 33 \text { mod } 10 = 3 \ \end { eqnarray } $ notes to the reader mod in programming languages and calculators many programming languages , and calculators , have a mod operator , typically represented with ... | what happens if the modulus is negative ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | can someone explain the concept of calculating mod with out the circles ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | for these cases there is an operator called the modulo operator ( abbreviated as mod ) . using the same $ a $ , $ b $ , $ q $ , and $ r $ as above , we would have : $ a \text { mod } b = r $ we would say this as $ a $ modulo $ b $ is equal to $ r $ . where $ b $ is referred to as the modulus . | at line number 5 above , for where a mod b = r and you have said that a modulo b is congruent to r. is n't this more correct to say that a modulo b is equal to r ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | for example : $ \begin { eqnarray } \dfrac { 13 } { 5 } & amp ; = & amp ; 2 \text { remainder } \bf { 3 } \ 13 \text { mod } 5 & amp ; = & amp ; \bf { 3 } \ \end { eqnarray } $ visualize modulus with clocks observe what happens when we increment numbers by one and then divide them by 3 . $ \begin { eqnarray } \frac { 0... | so remainder always has to be positive ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | ( if the number is positive we step clockwise , if it 's negative we step counter-clockwise . ) examples $ 8 \text { mod } 4 = ? $ with a modulus of 4 we make a clock with numbers 0 , 1 , 2 , 3 . | *5=30 in the case of mod : 8 mod 4=0 , but can we do 0 'some operation ' 4 =8 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | how does the modulus operator work when both the dividend and the divisor are negative numbers ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | what is a negativ number mod itself ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | we ended up at 0 so $ 8 \text { mod } 4 = \bf { 0 } $ . $ 7 \text { mod } 2 = ? $ with a modulus of 2 we make a clock with numbers 0 , 1 . | what is the correct result of -34 % 7 in c language ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \text { mod } 10 = 3 \ 33 \text { mod } 10 = 3 \ \end { eqnarray } $ notes to the reader mod in programming languages and calculators many programming languages , and calculators , have a mod operator , typically represented with ... | in other words , ca n't you just pull out '' the negative sign on the modulus expression in the first place ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | why do we use modular arithmetic ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | what is the practical application of modular arithmetic ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | why does a student need to understand modular arithmetic ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | what happens if a is less than b ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | what is dividend and divisor ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | $ with a modulus of 2 we make a clock with numbers 0 , 1 . we start at 0 and go through 7 numbers in a clockwise sequence 1 , 0 , 1 , 0 , 1 , 0 , 1 . we ended up at 1 so $ 7 \text { mod } 2 = \bf { 1 } $ . $ -5 \text { mod } 3 = ? | what will be answer of ( x*x ) =1 mod ( 6 ) in range of [ 1,8 ] interger solution of x and how ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \text { mod } 10 = 3 \ 33 \text { mod } 10 = 3 \ \end { eqnarray } $ notes to the reader mod in programming languages and calculators many programming languages , and calculators , have a mod operator , typically represented with ... | can a modulus of a statement be negative ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | does a ti 84+ have a mod button ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | for example , a clock with the 12 replaced by a 0 would be the circle for a modulus of 12 . to find the result of $ a \text { mod } b $ we can follow these steps : construct this clock for size $ b $ start at 0 and move around the clock $ a $ steps wherever we land is our solution . ( if the number is positive we step ... | here 's a solution to easily find the positive congruence of a negative number : what is -2017 mod 9 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | to find the result of $ a \text { mod } b $ we can follow these steps : construct this clock for size $ b $ start at 0 and move around the clock $ a $ steps wherever we land is our solution . ( if the number is positive we step clockwise , if it 's negative we step counter-clockwise . ) examples $ 8 \text { mod } 4 = ? | what if we made the modulus a negative number , and applied a positive value to a ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | for these cases there is an operator called the modulo operator ( abbreviated as mod ) . using the same $ a $ , $ b $ , $ q $ , and $ r $ as above , we would have : $ a \text { mod } b = r $ we would say this as $ a $ modulo $ b $ is equal to $ r $ . where $ b $ is referred to as the modulus . | both a and b being negative , would we move clockwise ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | for these cases there is an operator called the modulo operator ( abbreviated as mod ) . using the same $ a $ , $ b $ , $ q $ , and $ r $ as above , we would have : $ a \text { mod } b = r $ we would say this as $ a $ modulo $ b $ is equal to $ r $ . where $ b $ is referred to as the modulus . | would you also be able to use this as a way to quickly discern mods of odds ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | what happens to the quotient when formatting the basis of modular arithmetic in the first equation ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | $ with a modulus of 2 we make a clock with numbers 0 , 1 . we start at 0 and go through 7 numbers in a clockwise sequence 1 , 0 , 1 , 0 , 1 , 0 , 1 . we ended up at 1 so $ 7 \text { mod } 2 = \bf { 1 } $ . | i want to encrypt my name to practice my key is 20 , h a s a n 7 0 18 0 13 20 20 20 20 20 ( 27 20 38 20 33 ) mod 26 please what is next ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | congruence modulo you may see an expression like : $ a \equiv b\ ( \text { mod } c ) $ this says that $ a $ is congruent to $ b $ modulo $ c $ . it is similar to the expressions we used here , but not quite the same . in the next article we will explain what it means and how it is related to the expressions above . | how is modular arithmetic used ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | -5 % 3 = -2 . congruence modulo you may see an expression like : $ a \equiv b\ ( \text { mod } c ) $ this says that $ a $ is congruent to $ b $ modulo $ c $ . it is similar to the expressions we used here , but not quite the same . | in the section called congruence modulo , what does `` a is congruent to b modulo c '' mean ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | is it possible that a mod b = b mod a ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | is there any similarity between modulus ( which reurns absolute value of a number ) and this modulo operator ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | how do you really break the code with all these clues ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | after that , the sequence repeats . by noticing this , we can visualize the modulo operator by using circles . we write 0 at the top of a circle and continuing clockwise writing integers 1 , 2 , ... up to one less than the modulus . | is there any way to determine the modulo of a number without drawing all those circles around the clock ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | we ended up at 0 so $ 8 \text { mod } 4 = \bf { 0 } $ . $ 7 \text { mod } 2 = ? $ with a modulus of 2 we make a clock with numbers 0 , 1 . | i mean , if i am given a problem like 123456 to the power 7 mod 89 , is there an easier way to solve it than to do all the multiplication ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | we start at 0 and go through 7 numbers in a clockwise sequence 1 , 0 , 1 , 0 , 1 , 0 , 1 . we ended up at 1 so $ 7 \text { mod } 2 = \bf { 1 } $ . $ -5 \text { mod } 3 = ? $ with a modulus of 3 we make a clock with numbers 0 , 1 , 2 . | how do i find the residue of 1/21 mod 26 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \text { mod } 10 = 3 \ 33 \text { mod } 10 = 3 \ \end { eqnarray } $ notes to the reader mod in programming languages and calculators many p... | is n't 3 mod 10 supposed to be 1 because the remainder when 10 is divided by 3 is 1 , and mod is supposed to be the remainder right ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | e.g . -5 % 3 = -2 . congruence modulo you may see an expression like : $ a \equiv b\ ( \text { mod } c ) $ this says that $ a $ is congruent to $ b $ modulo $ c $ . | what is the remainder when 2 raised to the power 1990 is divided by 1990 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | can a be bigger than the mod ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | $ with a modulus of 2 we make a clock with numbers 0 , 1 . we start at 0 and go through 7 numbers in a clockwise sequence 1 , 0 , 1 , 0 , 1 , 0 , 1 . we ended up at 1 so $ 7 \text { mod } 2 = \bf { 1 } $ . | another question , by the help of clock we precise our starting point 0.but while counting , shall we start by 0 or 1 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | how to determine unit digits of large powers using mod ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | we ended up at 1 so $ 7 \text { mod } 2 = \bf { 1 } $ . $ -5 \text { mod } 3 = ? $ with a modulus of 3 we make a clock with numbers 0 , 1 , 2 . | why does -5 mod 3 equal to 1 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | -5 % 3 = -2 . congruence modulo you may see an expression like : $ a \equiv b\ ( \text { mod } c ) $ this says that $ a $ is congruent to $ b $ modulo $ c $ . it is similar to the expressions we used here , but not quite the same . | in a mod b = c , if a is a negative number , is c always a positive number ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | congruence modulo you may see an expression like : $ a \equiv b\ ( \text { mod } c ) $ this says that $ a $ is congruent to $ b $ modulo $ c $ . it is similar to the expressions we used here , but not quite the same . in the next article we will explain what it means and how it is related to the expressions above . | only integers can be used in modular arithmetic ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | i still do n't understand this : a mod b = ( a + k * b ) mod b for any integer k. could somebody please explain it to me ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | what is the connection between range and arithmatic mean ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | conclusion if we have $ a \text { mod } b $ and we increase $ a $ by a multiple of $ \bf { b } $ , we will end up in the same spot , i.e . $ a \text { mod } b = ( a + k \cdot b ) \text { mod } b $ for any integer $ \bf { k } $ . for example : $ \begin { eqnarray } 3 \text { mod } 10 = 3 \ 13 \text { mod } 10 = 3 \ 23 \... | does mod stand for something ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | we ended up at 1 so $ 7 \text { mod } 2 = \bf { 1 } $ . $ -5 \text { mod } 3 = ? $ with a modulus of 3 we make a clock with numbers 0 , 1 , 2 . | how to proof if n mod 5=2 and m mod 5=3 then mn mod 5=1 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | $ 7 \text { mod } 2 = ? $ with a modulus of 2 we make a clock with numbers 0 , 1 . we start at 0 and go through 7 numbers in a clockwise sequence 1 , 0 , 1 , 0 , 1 , 0 , 1 . | how do you compute modular arithmetic without showing the diagram and with larger numbers ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | $ with a modulus of 2 we make a clock with numbers 0 , 1 . we start at 0 and go through 7 numbers in a clockwise sequence 1 , 0 , 1 , 0 , 1 , 0 , 1 . we ended up at 1 so $ 7 \text { mod } 2 = \bf { 1 } $ . | why does the clock start with 0 instead of 1 ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | how can we find modulo in such cases ? |
an introduction to modular math when we divide two integers we will have an equation that looks like the following : $ \dfrac { a } { b } = q \text { remainder } r $ $ a $ is the dividend $ b $ is the divisor $ q $ is the quotient $ r $ is the remainder sometimes , we are only interested in what the remainder is when w... | to find the result of $ a \text { mod } b $ we can follow these steps : construct this clock for size $ b $ start at 0 and move around the clock $ a $ steps wherever we land is our solution . ( if the number is positive we step clockwise , if it 's negative we step counter-clockwise . ) examples $ 8 \text { mod } 4 = ? | may i know the relation between the modular nomber , composite number , prime number and real number in example and venn diagram ? |
overview trading cities played an important role in the spread of goods on the silk road and indian ocean trade routes . with their large populations , access to major resources like food and goods , and complex networks of roads and trade , big cities were natural centers of urbanization and development that contribut... | with their large populations , access to major resources like food and goods , and complex networks of roads and trade , big cities were natural centers of urbanization and development that contributed to the growth of trade . a few examples of major trading cities are hangzhou , timbuktu , and malacca . all are strate... | what made those cities mentioned different from constantinople ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | visualizing these functions is all about thinking of space with multiple dimensions ( typically just two or three if we do n't want our brains to explode ) . what are multivariable functions ? when i first learned about functions , and maybe this is true for you too , i remember always thinking about them as taking in ... | how does multivariable functions helps in your everyday life ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | integrals , which study how to add together infinitely many infinitesimal quantities that make up a function 's output . multivariable calculus extends these ideas to functions with higher-dimensional inputs and/or outputs . with respect to the examples above , rates of change could refer to the following : how tempera... | can ka add ''the calculus of functions f : r^n- > r^m '' ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | note : some authors and teachers use the word multivariable for functions with multiple-number inputs , not outputs . lists of numbers $ \leftrightarrow $ points in space what makes multivariable calculus beautiful is that visualizing functions , along with all the new calculus you will learn to manipulate them , invol... | it is hard for me to read the content on this page , can the academy makes the font size larger or allow customize font size on this document ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | $ t $ is time . $ f $ is a vector-valued function . alternatively , you might break down components of the vector-valued function into separate scalar-valued functions $ x ( t ) $ and $ y ( t ) $ , which indicate the coordinates of x and y as functions of time : $ \begin { align } x ( t ) & amp ; = \dots ( \text { some... | why would you want to break down components of vector values into scalar values ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | when i first learned about functions , and maybe this is true for you too , i remember always thinking about them as taking in a number and outputting a number . a typical example would be something like this : $ f ( x ) = x^2 $ or this : $ f ( x ) = \sin ( x ) +2\sqrt { x } $ . and if you think back to the first time ... | the solution is z = a ( y*dx + x*dy ) = a d ( xy ) = -axy + c i got that we use the product rule identity in this ( y*dx + x*dy ) = a d ( xy ) but how is a d ( xy ) = -axy ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | but really , functions do n't just have to take in and spit out numbers , they can take in any thing and spit out any thing . in multivariable calculus , that thing can be a list of numbers . that is to say , the input and/or output can consists of multiple numbers . | what level of math is multivariable calculus ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | when i first learned about functions , and maybe this is true for you too , i remember always thinking about them as taking in a number and outputting a number . a typical example would be something like this : $ f ( x ) = x^2 $ or this : $ f ( x ) = \sin ( x ) +2\sqrt { x } $ . and if you think back to the first time ... | when i get to draw a function of x and y how can i draw it in 2 dimentional cartisian axes ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | when i first learned about functions , and maybe this is true for you too , i remember always thinking about them as taking in a number and outputting a number . a typical example would be something like this : $ f ( x ) = x^2 $ or this : $ f ( x ) = \sin ( x ) +2\sqrt { x } $ . and if you think back to the first time ... | so if we use square brackets for rectangular vectors , with the x above the y ( and possibly z ) , how do we denote vectors in polar , cylindrical , or spherical form ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | visualizing these functions is all about thinking of space with multiple dimensions ( typically just two or three if we do n't want our brains to explode ) . what are multivariable functions ? when i first learned about functions , and maybe this is true for you too , i remember always thinking about them as taking in ... | can i form a multivariable function given two individual functions ? |
what we 're building to a function is called multivariable if its input is made up of multiple numbers . if the output of a function consists of multiple numbers , it can also be called multivariable , but these ones are also commonly called vector-valued functions . visualizing these functions is all about thinking of... | here are just a few examples of where multivariable functions arise . example 1 : from location to temperature to model varying temperatures in a large region , you could use a function which takes in two variables—longitude and latitude , maybe even altitude as a third—and outputs one variable , the temperature . writ... | in the example of location to temperature , i can understand latitude as a variable , but why longitude ? |
a sacred object out of context the art of medieval india , like the art of medieval europe , was primarily in the service of religion . the devotee ’ s spiritual experience was enhanced by meditation inspired by works of art and architecture . just as the luminous upper chapel of the sainte chapelle dazzled and overwhe... | in hindu religious philosophy all things must come to a natural end so they can begin anew , and shiva is the agent that brings about this end so that a new cycle can begin . the metropolitan museum 's shiva nataraja was made some time in the eleventh century during the chola dynasty ( 9th-13th centuries c.e . ) in sou... | what kind of statues were made in the 19th centuries ? |
a sacred object out of context the art of medieval india , like the art of medieval europe , was primarily in the service of religion . the devotee ’ s spiritual experience was enhanced by meditation inspired by works of art and architecture . just as the luminous upper chapel of the sainte chapelle dazzled and overwhe... | one of the longest lasting empires of south india , the chola dynasty heralded a golden age of exploration , trade , and artistic development . a great area innovation within the arts of the chola period was in the field of metalwork , particularly in bronze sculpture . the expanse of the chola empire stretched south-e... | did the british rule affect the sculpture arts of india in any way ? |
a sacred object out of context the art of medieval india , like the art of medieval europe , was primarily in the service of religion . the devotee ’ s spiritual experience was enhanced by meditation inspired by works of art and architecture . just as the luminous upper chapel of the sainte chapelle dazzled and overwhe... | in these processions the shiva nataraja may have had its legs wrapped with a white and red cloth , adorned with flowers , and surrounded by candles . in a religious hindu context , the statue is the literal embodiment of the divine . when the worshiper comes before the statue and begins to pray , faith activates the di... | i know artist for this sculpture is unknown , but do you if it was n't created for religious purposes or by a religious institution ? |
a sacred object out of context the art of medieval india , like the art of medieval europe , was primarily in the service of religion . the devotee ’ s spiritual experience was enhanced by meditation inspired by works of art and architecture . just as the luminous upper chapel of the sainte chapelle dazzled and overwhe... | just as the luminous upper chapel of the sainte chapelle dazzled and overwhelmed worshipers in france , the looming bronze statues of shiva and parvati in , for example , the inner halls of the meenakshi temple in madurai , in south india would have awed a hindu devotee . its important to keep in mind that the bronze s... | when and how were the shiva as the lord of the dance statues made ? |
a sacred object out of context the art of medieval india , like the art of medieval europe , was primarily in the service of religion . the devotee ’ s spiritual experience was enhanced by meditation inspired by works of art and architecture . just as the luminous upper chapel of the sainte chapelle dazzled and overwhe... | bronzes of the chola period such as shiva as lord of the dance ( nataraja ) arose out of a need to transmute the divine into a physical embodiment of beauty . essay by farisa khalid additional resources : this sculpture at the metropolitan museum of art shiva nataraja from the smithsonian this sculpture on the metropol... | were artists of the art works in hindu art usually unknown ? |
a sacred object out of context the art of medieval india , like the art of medieval europe , was primarily in the service of religion . the devotee ’ s spiritual experience was enhanced by meditation inspired by works of art and architecture . just as the luminous upper chapel of the sainte chapelle dazzled and overwhe... | the expanse of the chola empire stretched south-east towards sri lanka and gave the kingdom access to vast copper reserves that enabled the proliferation of bronze work by skilled artisans . during this period a new kind of sculpture is made , one that combines the expressive qualities of stone temple carvings with the... | how is that possible if he were already the god of destruction ? |
a sacred object out of context the art of medieval india , like the art of medieval europe , was primarily in the service of religion . the devotee ’ s spiritual experience was enhanced by meditation inspired by works of art and architecture . just as the luminous upper chapel of the sainte chapelle dazzled and overwhe... | arms were to be long like stalks of bamboo , faces round like the moon , and eyes shaped like almonds or the leaves of a lotus . the shastras were a primer on the ideals of beauty and physical perfection within ancient hindu ideology . a dance within the cosmic circle of fire here , shiva embodies those perfect physica... | which is the ancient technique by which the shaping and mixing of alloys was acheived with great perfection ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | multiplication as a transformation the idea of a `` transformation '' can seem more complicated than it really is at first , so before diving into how $ 2 \times 2 $ matrices transform $ 2 $ -dimensional space , or how $ 3 \times 3 $ matrices transform $ 3 $ -dimensional space , let 's go over how plain old numbers ( a... | why does the two vectors that when transform , can deduce where others go have to be ( 1 0 ) and ( 0 1 ) ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | multiplication as a transformation the idea of a `` transformation '' can seem more complicated than it really is at first , so before diving into how $ 2 \times 2 $ matrices transform $ 2 $ -dimensional space , or how $ 3 \times 3 $ matrices transform $ 3 $ -dimensional space , let 's go over how plain old numbers ( a... | is there a particular reason why you chose green for x or [ 1 | 0 ] and red for y or [ 0 | 1 ] ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | in fact , once we know where $ \left [ \begin { array } { c } 1 \ 0 \end { array } \right ] $ and $ \left [ \begin { array } { c } 0 \ 1 \end { array } \right ] $ land , we can deduce where every point on the plane must go . for example , let 's follow the point $ \left [ \begin { array } { c } -1 \ 2 \end { array } \r... | it 'll make much better correspondence for xyz , ijk , rgb coding , the right-hand rule , and the physical progression of colour energies ( 1st red = low ; 2nd green = medium ; 3rd blue = high ) ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | representing two dimensional linear transforms with matrices in general , since each vector $ \left [ \begin { array } { c } x \ y \end { array } \right ] $ can be broken down as $ \left [ \begin { array } { c } x \ y \end { array } \right ] = x\greend { \left [ \begin { array } { c } 1 \ 0 \end { array } \right ] } + ... | what is av in the last part of the page ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | in fact , once we know where $ \left [ \begin { array } { c } 1 \ 0 \end { array } \right ] $ and $ \left [ \begin { array } { c } 0 \ 1 \end { array } \right ] $ land , we can deduce where every point on the plane must go . for example , let 's follow the point $ \left [ \begin { array } { c } -1 \ 2 \end { array } \r... | i understand multiplying the green arrow by the x component -1 ; but , how did you get the `` 3 '' digit you are using to multiply by the `` y '' component ( 2 ) ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | here are some examples : for our purposes , what makes a transformation linear is the following geometric rule : the origin must remain fixed , and all lines must remain lines . so all the transforms in the above animation are examples , but the following are not : following specific vectors during a transformation ima... | in the first example in the section `` following specific vectors during a transformation '' , is n't there an error ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | as before , our use of the word “ transformation ” indicates we should think about smooshing something around , which in this case is $ 2 $ -dimensional space . here are some examples : for our purposes , what makes a transformation linear is the following geometric rule : the origin must remain fixed , and all lines m... | what does analog mean in the following explanation ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | one way to visualize this is as follows : we keep a copy of the original line for reference , then slide each number on the line to $ 2 $ times that number . similarly , multiplication by $ \dfrac { 1 } { 2 } $ could be visualized like this : and so that negative numbers do n't feel neglected , here is multiplication b... | why do n't we prefer row vectors ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | in this case , $ 1 $ lands where $ -3 $ started off , so you can tell that the animation represents multiplication by $ -3 $ . what do linear transformations in $ 2 $ dimensions look like ? a $ 2 $ -dimensional linear transformation is a special kind of function which takes in a $ 2 $ -dimensional vector $ \left [ \beg... | is it not sufficient to use 2-tuple vector to denote the transformation ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | representing two dimensional linear transforms with matrices in general , since each vector $ \left [ \begin { array } { c } x \ y \end { array } \right ] $ can be broken down as $ \left [ \begin { array } { c } x \ y \end { array } \right ] = x\greend { \left [ \begin { array } { c } 1 \ 0 \end { array } \right ] } + ... | how we transform a vector in 3d ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | in this case , $ 1 $ lands where $ -3 $ started off , so you can tell that the animation represents multiplication by $ -3 $ . what do linear transformations in $ 2 $ dimensions look like ? a $ 2 $ -dimensional linear transformation is a special kind of function which takes in a $ 2 $ -dimensional vector $ \left [ \beg... | what is the transformation matrice used in the video `` tricky examples of nonlinear two dimensional transformations '' ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . | is there an intuitive explanation for why you multiply the vector matrix ( v ) by the transformation matrix ( a ) , and not the other way around ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | what do linear transformations in $ 2 $ dimensions look like ? a $ 2 $ -dimensional linear transformation is a special kind of function which takes in a $ 2 $ -dimensional vector $ \left [ \begin { array } { c } x \ y \end { array } \right ] $ and outputs another $ 2 $ -dimensional vector . as before , our use of the w... | but how to make sense for higher dimensional matrix transformation ? |
introduction if we think about a matrix as a transformation of space it can lead to a deeper understanding of matrix operations . this viewpoint helps motivate how we define matrix operations like multiplication , and , it gives us a nice excuse to draw pretty pictures . this material touches on linear algebra ( usuall... | representing two dimensional linear transforms with matrices in general , since each vector $ \left [ \begin { array } { c } x \ y \end { array } \right ] $ can be broken down as $ \left [ \begin { array } { c } x \ y \end { array } \right ] = x\greend { \left [ \begin { array } { c } 1 \ 0 \end { array } \right ] } + ... | am i right thinking about unit vectors refering to how a vector can be broken as shown in this article ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | vacuoles plants cells do not have lysosomes . instead , they have another type of organelle called the vacuole . the large central vacuole stores water and wastes wastes , isolates hazardous materials , and has enzymes that can break down macromolecules and cellular components , like those of a lysosome. $ ^3 $ plant v... | what 's the difference between a vesicle and a vacuole ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | instead , they have another type of organelle called the vacuole . the large central vacuole stores water and wastes wastes , isolates hazardous materials , and has enzymes that can break down macromolecules and cellular components , like those of a lysosome. $ ^3 $ plant vacuoles also function in water balance and may... | what 's the difference between a lipid and a phospholipid ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | some of these vesicles deliver their contents to other parts of the cell where they will be used , such as the lysosome or vacuole . others fuse with the plasma membrane , delivering membrane-anchored proteins that function there and releasing secreted proteins outside the cell . cells that secrete many proteins—such a... | and why are proteins so important ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | these patches serve as exit sites for vesicles budding off from the rough er and are called transitional er $ ^1 $ . the golgi apparatus when vesicles bud off from the er , where do they go ? before reaching their final destination , the lipids and proteins in the transport vesicles need to be sorted , packaged , and t... | how do the vesicles know where to go - for example when a vesicle leaves the er how does it know to go to the golgi apparatus ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | the phagosome then fuses with a lysosome , forming a combined compartment where digestive enzymes destroy the pathogen . vacuoles plants cells do not have lysosomes . instead , they have another type of organelle called the vacuole . | i know there are vacuoles in plants and animals cells , are there any major differences between the two other than the size ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | as these ribosomes make proteins , they feed the newly forming protein chains into the lumen . some are transferred fully into the er and float inside , while others are anchored in the membrane . inside the er , the proteins fold and undergo modifications , such as the addition of carbohydrate side chains . | why is the inner membrane of the lysosome not affected by the enzymes present inside it ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | the phagosome then fuses with a lysosome , forming a combined compartment where digestive enzymes destroy the pathogen . vacuoles plants cells do not have lysosomes . instead , they have another type of organelle called the vacuole . | why are lysosomes found only in animal cells , not in plant cells ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | instead , they have another type of organelle called the vacuole . the large central vacuole stores water and wastes wastes , isolates hazardous materials , and has enzymes that can break down macromolecules and cellular components , like those of a lysosome. $ ^3 $ plant vacuoles also function in water balance and may... | and , do prokaryotes recycle macromolecules ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . | what is a pancreatic cell ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | cells that secrete many proteins—such as salivary gland cells that secrete digestive enzymes , or cells of the immune system that secrete antibodies—have many golgi stacks . in plant cells , the golgi apparatus also makes polysaccharides ( long-chain carbohydrates ) , some of which are incorporated into the cell wall .... | how does protein travel through the cell wall in plant cell ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | after a moment of panic in which you consider calling the postal service , you relax , having remembered : i have an endomembrane system ! what is the endomembrane system ? the endomembrane system ( endo- = “ within ” ) is a group of membranes and organelles in eukaryotic cells that works together to modify , package ,... | is the endomembrane system located in both plants and animal cells , or just one ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | importantly , peroxisomes—unlike lysosomes—are are not part of the endomembrane system . that means they do n't receive vesicles from the golgi apparatus . you can learn more about how proteins are shipped to the peroxisome in the article on protein targeting . | why would a vesicle take a protein straight from the golgi apparatus to the lysosome ? |
introduction let ’ s imagine you are a pancreatic cell . your job is to secrete digestive enzymes , which travel into the small intestine and help break down nutrients from food . in order to carry out this job , you somehow have to get those enzymes shipped from their site of synthesis—inside the cell—to their place o... | importantly , peroxisomes—unlike lysosomes—are are not part of the endomembrane system . that means they do n't receive vesicles from the golgi apparatus . you can learn more about how proteins are shipped to the peroxisome in the article on protein targeting . | is n't it kinda a waste of energy for your body to create a protein just to have it be recycled ? |
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