context stringlengths 545 71.9k | questionsrc stringlengths 16 10.2k | question stringlengths 11 563 |
|---|---|---|
what does tension mean ? all physical objects that are in contact can exert forces on each other . we give these contact forces different names based on the types of objects in contact . if one of the objects exerting the force happens to be a rope , string , chain , or cable we call the force tension . ropes and cable... | what does tension mean ? all physical objects that are in contact can exert forces on each other . | in example 1 , the question was asking for the tension in the rope , how come the answer given here is the tension on the x-axis ? |
what does tension mean ? all physical objects that are in contact can exert forces on each other . we give these contact forces different names based on the types of objects in contact . if one of the objects exerting the force happens to be a rope , string , chain , or cable we call the force tension . ropes and cable... | this might sound obvious , but when it comes time to draw the forces acting on an object , people often draw the force of tension going in the wrong direction so remember that tension can only pull on an object . how do we calculate the force of tension ? unfortunately , there 's no special formula to find the force of... | why does tension force always act in the horizontal direction ? |
what does tension mean ? all physical objects that are in contact can exert forces on each other . we give these contact forces different names based on the types of objects in contact . if one of the objects exerting the force happens to be a rope , string , chain , or cable we call the force tension . ropes and cable... | there are tensions directed both vertically and horizontally , so again it 's a little unclear which direction to choose . however , since we know the force of gravity , which is a vertical force , we 'll start with newton 's second law in the vertical direction . $ a_y=\dfrac { \sigma f_y } { m } \quad \text { ( use n... | for example if you have a spring balance and attach an object to it , then is n't it exerting force in the vertical direction ? |
what does tension mean ? all physical objects that are in contact can exert forces on each other . we give these contact forces different names based on the types of objects in contact . if one of the objects exerting the force happens to be a rope , string , chain , or cable we call the force tension . ropes and cable... | however , since we know the acceleration horizontally , and since we know tension is the only force directed horizontally , we 'll use newton 's second law in the horizontal direction . $ a_x=\dfrac { \sigma f_x } { m } \quad \text { ( use newtons 's second law for the horizontal direction ) } $ $ 3.0\dfrac { \text { m... | on example # 2 solution , how did the formula go from 0=t2 sin 30 - fg / 0.25 kg to t2=fg/sin30 ? |
what does tension mean ? all physical objects that are in contact can exert forces on each other . we give these contact forces different names based on the types of objects in contact . if one of the objects exerting the force happens to be a rope , string , chain , or cable we call the force tension . ropes and cable... | this might sound obvious , but when it comes time to draw the forces acting on an object , people often draw the force of tension going in the wrong direction so remember that tension can only pull on an object . how do we calculate the force of tension ? unfortunately , there 's no special formula to find the force of... | the article wrote that the tension of t2 should be the same as the force of gravity so they can cancel out but isnt gravity 9.8m/s2 ? |
what does tension mean ? all physical objects that are in contact can exert forces on each other . we give these contact forces different names based on the types of objects in contact . if one of the objects exerting the force happens to be a rope , string , chain , or cable we call the force tension . ropes and cable... | there are tensions directed both vertically and horizontally , so again it 's a little unclear which direction to choose . however , since we know the force of gravity , which is a vertical force , we 'll start with newton 's second law in the vertical direction . $ a_y=\dfrac { \sigma f_y } { m } \quad \text { ( use n... | can example 1 be expanded to include the affect of the vertical force on the normal force , therefore decreasing the influence of friction on its movement in the horizontal direction ? |
what does tension mean ? all physical objects that are in contact can exert forces on each other . we give these contact forces different names based on the types of objects in contact . if one of the objects exerting the force happens to be a rope , string , chain , or cable we call the force tension . ropes and cable... | the tension in the rope causes the box to slide across the table to the right with an acceleration of $ 3.0\dfrac { \text { m } } { \text { s } ^2 } $ . what is the tension in the rope ? first we draw a force diagram of all the forces acting on the box . | what will be the tension in rope if two masses are attached on each end of the rope and hang with the help of fraction less pulley ? |
what does tension mean ? all physical objects that are in contact can exert forces on each other . we give these contact forces different names based on the types of objects in contact . if one of the objects exerting the force happens to be a rope , string , chain , or cable we call the force tension . ropes and cable... | we 'll use this problem solving strategy in the solved examples below . what do solved examples involving tension look like ? example 1 : angled rope pulling on a box a $ 2.0 \text { kg } $ box of cucumber extract is being pulled across a frictionless table by a rope at an angle $ \theta=60^o $ as seen below . | when i am working on problems which have diagrams that look like this : http : //sibor.physics.tamu.edu/teaching/phys218/images/image67.gif how do i know where acceleration is directed ? |
the intermediate value theorem ( ivt ) and the extreme value theorem ( evt ) are existence theorems . they guarantee that a certain type of point exists on a graph under certain conditions . the reason that we study ivt and evt together is that they share the exact same condition : that the function we 're working with... | points that are the highest or the lowest on that interval . the same reasoning we used to justify ivt applies for evt . if a graph is continuous on a specific interval ( i.e . | why is the evt and ivt studied in calculus ? |
the intermediate value theorem ( ivt ) and the extreme value theorem ( evt ) are existence theorems . they guarantee that a certain type of point exists on a graph under certain conditions . the reason that we study ivt and evt together is that they share the exact same condition : that the function we 're working with... | if we know the graph goes from $ ( a , f ( a ) ) $ to $ ( b , f ( b ) ) $ ... ... then it must pass through every $ y $ -value between $ f ( a ) $ and $ f ( b ) $ . but if a function is n't continuous , there 's no guarantee an intermediate value exists . for example , function $ g $ is n't continuous on $ [ a , b ] $ ... | for problem 3 , should n't the answer be kevin 's work is correct because the problem already stated that g was a continuous function ? |
augustus and the power of images today , politicians think very carefully about how they will be photographed . think about all the campaign commercials and print ads we are bombarded with every election season . these images tell us a lot about the candidate , including what they stand for and what agendas they are pr... | at the very bottom of the cuirass is tellus , the earth goddess , who cradles two babies and holds a cornucopia . tellus is an additional allusion to the pax romana as she is a symbol of fertility with her healthy babies and overflowing horn of plenty . not simply a portrait the augustus of primaporta is one of the way... | i had a question as to where the `` horn of plenty '' or the `` cornucopia '' originated from ? |
augustus and the power of images today , politicians think very carefully about how they will be photographed . think about all the campaign commercials and print ads we are bombarded with every election season . these images tell us a lot about the candidate , including what they stand for and what agendas they are pr... | in fact , in this portrait augustus shows himself as a great military victor and a staunch supporter of roman religion . the statue also foretells the 200 year period of peace that augustus initiated , called the pax romana . recalling the golden age of ancient greece in this marble freestanding sculpture , augustus st... | the pax romana is a period of peace right ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | consider function $ f $ , given in the graph and in a table of values . $ ~~~x $ | $ f ( x ) $ : - : | : - : $ -2 $ | $ \dfrac14 $ $ -1 $ | $ \dfrac12 $ $ ~~~0 $ | $ ~~~1 $ $ ~~~1 $ | $ ~~~2 $ $ ~~~2 $ | $ ~~~4 $ we can reverse the inputs and outputs of function $ f $ to find the inputs and outputs of function $ f^ { -... | how would i find the inverse function of a quadratic , such as 2x^2+2x-1 ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | but suppose we wanted an equation that did the reverse – that converted a temperature in degrees celsius to a temperature in degrees fahrenheit . this describes the function $ f=\dfrac95c+32 $ , or the inverse function . on a more basic level , we solve many equations in mathematics , by `` isolating the variable '' . | if c = 5/9 ( f-32 ) is the original function should n't c = f ( 9/5 ) +32 be the inverse function ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function $ f^ { -1 } $ takes $ x $ to $ 1 $ , $ y $ to $ 3 $ , and $ z $ to $ 2 $ . | why is the inverse always a reflection ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | this gives us these graph and table of values of $ f^ { -1 } $ . $ ~~~x $ | $ f^ { -1 } ( x ) $ : - : | : - : $ \dfrac14 $ | $ -2 $ $ \dfrac12 $ | $ -1 $ $ ~~~1 $ | $ ~~~0 $ $ ~~~2 $ | $ ~~~1 $ $ ~~~4 $ | $ ~~~2 $ looking at the graphs together , we see that the graph of $ y=f ( x ) $ and the graph of $ y=f^ { -1 } ( x... | is it simply two lines that have the same set of reversed relationships , because plugging in the answer does not make a full restitution , instead it gives the same original value of x in a different line ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | this gives us these graph and table of values of $ f^ { -1 } $ . $ ~~~x $ | $ f^ { -1 } ( x ) $ : - : | : - : $ \dfrac14 $ | $ -2 $ $ \dfrac12 $ | $ -1 $ $ ~~~1 $ | $ ~~~0 $ $ ~~~2 $ | $ ~~~1 $ $ ~~~4 $ | $ ~~~2 $ looking at the graphs together , we see that the graph of $ y=f ( x ) $ and the graph of $ y=f^ { -1 } ( x... | what is the f inverse of f ( x ) =x^2 ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . | why are the number in the order pairs have to be reversed ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | but suppose we wanted an equation that did the reverse – that converted a temperature in degrees celsius to a temperature in degrees fahrenheit . this describes the function $ f=\dfrac95c+32 $ , or the inverse function . on a more basic level , we solve many equations in mathematics , by `` isolating the variable '' . | would a function still be the inverse if it was reflected over y=-x or would it mean something different ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | but suppose we wanted an equation that did the reverse – that converted a temperature in degrees celsius to a temperature in degrees fahrenheit . this describes the function $ f=\dfrac95c+32 $ , or the inverse function . on a more basic level , we solve many equations in mathematics , by `` isolating the variable '' . | what is a function inverses ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | but suppose we wanted an equation that did the reverse – that converted a temperature in degrees celsius to a temperature in degrees fahrenheit . this describes the function $ f=\dfrac95c+32 $ , or the inverse function . on a more basic level , we solve many equations in mathematics , by `` isolating the variable '' . | if f ( x ) =4x-7 , what is the inverse function ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . | so , the domain is the opposite of the range and vice versa ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | this gives us these graph and table of values of $ f^ { -1 } $ . $ ~~~x $ | $ f^ { -1 } ( x ) $ : - : | : - : $ \dfrac14 $ | $ -2 $ $ \dfrac12 $ | $ -1 $ $ ~~~1 $ | $ ~~~0 $ $ ~~~2 $ | $ ~~~1 $ $ ~~~4 $ | $ ~~~2 $ looking at the graphs together , we see that the graph of $ y=f ( x ) $ and the graph of $ y=f^ { -1 } ( x... | what would be the inverse of f ( x ) =4^x and how do you solve it ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | $ ~~~x $ | $ f^ { -1 } ( x ) $ : - : | : - : $ \dfrac14 $ | $ -2 $ $ \dfrac12 $ | $ -1 $ $ ~~~1 $ | $ ~~~0 $ $ ~~~2 $ | $ ~~~1 $ $ ~~~4 $ | $ ~~~2 $ looking at the graphs together , we see that the graph of $ y=f ( x ) $ and the graph of $ y=f^ { -1 } ( x ) $ are reflections across the line $ y=x $ . this will be true ... | is the reflection of a function and its inverse always over the line y=x ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | $ ~~~x $ | $ f^ { -1 } ( x ) $ : - : | : - : $ \dfrac14 $ | $ -2 $ $ \dfrac12 $ | $ -1 $ $ ~~~1 $ | $ ~~~0 $ $ ~~~2 $ | $ ~~~1 $ $ ~~~4 $ | $ ~~~2 $ looking at the graphs together , we see that the graph of $ y=f ( x ) $ and the graph of $ y=f^ { -1 } ( x ) $ are reflections across the line $ y=x $ . this will be true ... | to graph the inverse of a function , does it have to be reflected over y = x ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | function $ f^ { -1 } $ takes $ x $ to $ 1 $ , $ y $ to $ 3 $ , and $ z $ to $ 2 $ . defining inverse functions in general , if a function $ f $ takes $ a $ to $ b $ , then the inverse function , $ f^ { -1 } $ , takes $ b $ to $ a $ . $ \quad $ from this , we have the formal definition of inverse functions : $ f ( a ) =... | after the first problem , near the top of the page , it says : `` in general , if a function f takes a to b , then the inverse function , takes b to a , '' when would this not be true ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | from the graph , we see that $ g ( -3 ) =-7 $ . therefore , $ g^ { -1 } ( -7 ) =-3 $ . check your understanding a graphical connection the examples above have shown us the algebraic connection between a function and its inverse , but there is also a graphical connection ! | why does g ( -1 ) ( 7 ) equals ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . | why is common core so dumb ? |
inverse functions , in the most general sense , are functions that `` reverse '' each other . for example , here we see that function $ f $ takes $ 1 $ to $ x $ , $ 2 $ to $ z $ , and $ 3 $ to $ y $ . the inverse of $ f $ , denoted $ f^ { -1 } $ ( and read as `` $ f $ inverse '' ) , will reverse this mapping . function... | but suppose we wanted an equation that did the reverse – that converted a temperature in degrees celsius to a temperature in degrees fahrenheit . this describes the function $ f=\dfrac95c+32 $ , or the inverse function . on a more basic level , we solve many equations in mathematics , by `` isolating the variable '' . | why we need inverse function ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | incised and engraved stone , bone , ochre and ostrich eggshell have been found at sites in southern africa . these marked objects share features in the expression of design , exhibiting patterns that have been classified as cross-hatching . one of the most iconic and well-publicised sites that have yielded cross-hatch ... | does idiosyncratic behavior here mean that given the same situation humans tend to make similar gestures , like the cross- hatching marks ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | incised and engraved stone , bone , ochre and ostrich eggshell have been found at sites in southern africa . these marked objects share features in the expression of design , exhibiting patterns that have been classified as cross-hatching . one of the most iconic and well-publicised sites that have yielded cross-hatch ... | if the cross-hatching marks are not idiosycratic behavior , what do they mean ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | 8000 b.c . ) cave stones on the metropolitan museum of art 's heilbrunn timeline of art history trust for african rock art © trustees of the british museum | i understand that language as a precursor to symbolic art is a logical assumption , but is it necessarily so that language was needed to convey the meanings of this art ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | the debate about when we became a symbolic species and acquired fully syntactical language – what archaeologists term ‘ modern human behaviour ’ – is both complex and contested . it has been proposed that these cross-hatch patterns are clear evidence of thinking symbolically , because the motifs are not representationa... | would it be impossible to think symbolically without explicit verbal explanation of a motif ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . | what does bp stand for ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cave he named apollo 11 , after nasa ’ s successful moon landing mission . seven painted stone slabs of brown-grey quartzite , depicting a variety of animals painte... | but i have to wonder ... were the eggshells painted , or do ostrich eggs really come in such fabulous and varied colors and patterns ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | 8000 b.c . ) cave stones on the metropolitan museum of art 's heilbrunn timeline of art history trust for african rock art © trustees of the british museum | where did art all begin you see nothing starts unless you discover because all the way back they did n't have paint brushes so where did they notice this stuff because people who are 4 5 6 7 8 9 10 ... were n't there so the earth is are clue really were was art set out ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | for many archaeologists , the incised pieces of ochre at blombos are the most complex and best-formed evidence for early abstract representations , and are unequivocal evidence for symbolic thought and language . the debate about when we became a symbolic species and acquired fully syntactical language – what archaeolo... | why is the modern idea of language so important ? |
rock art and the origins of art in africa the oldest scientifically-dated rock art in africa dates from around 26,000-28,000 years ago and is found in namibia . between 1969 and 1972 , german archaeologist , w.e . wendt , researching in an area known locally as `` goachanas , '' unearthed several painted slabs in a cav... | it has been proposed that these cross-hatch patterns are clear evidence of thinking symbolically , because the motifs are not representational and as such are culturally constructed and arbitrary . moreover , in order for the meaning of this motif to be conveyed to others , language is a prerequisite . the blombos engr... | it seems that even now we still make this a competitive issue for example the declaration of language vs dialect ? |
scholars often refer to the tang ( 618–906 ) and song ( 960–1279 ) dynasties as the `` medieval '' period of china . the civilizations of the tang ( 618–906 ) and song ( 960–1279 ) dynasties of china were among the most advanced civilizations in the world at the time . discoveries in the realms of science , art , philo... | china was divided into at least fifteen different independent political regimes , and peoples on the border areas set up their own states . the cultural glory of tang was eclipsed , surviving only among tiny warring states . however in the year 960 , another unified empire arose , the song . | was the tang before or after the warring states ? |
on the writing and language test , there are four key ways you can mark up the test : 1 ) circle or underline important elements of passages to do your best , you 'll need to read passages on the writing and language test just as actively as you read the passages on the reading test . that means underlining and circlin... | top tip : understand what the passage is saying ! contrary to what some people think , the sat writing and language test is not just about grammar . grammar-related questions ( also called `` standard english conventions '' ) make up just one part of your score on the writing and language test . | do i need sat for universities in canada ? |
on the writing and language test , there are four key ways you can mark up the test : 1 ) circle or underline important elements of passages to do your best , you 'll need to read passages on the writing and language test just as actively as you read the passages on the reading test . that means underlining and circlin... | top tip : understand what the passage is saying ! contrary to what some people think , the sat writing and language test is not just about grammar . grammar-related questions ( also called `` standard english conventions '' ) make up just one part of your score on the writing and language test . | what is the high score i should get for sat ? |
on the writing and language test , there are four key ways you can mark up the test : 1 ) circle or underline important elements of passages to do your best , you 'll need to read passages on the writing and language test just as actively as you read the passages on the reading test . that means underlining and circlin... | top tip : understand what the passage is saying ! contrary to what some people think , the sat writing and language test is not just about grammar . grammar-related questions ( also called `` standard english conventions '' ) make up just one part of your score on the writing and language test . | should you read the whole passage first when doing the writing and language portion of the sat ? |
overview the vietnam war was a prolonged military conflict that started as an anticolonial war against the french and evolved into a cold war confrontation between international communism and free-market democracy . the democratic republic of vietnam ( drv ) in the north was supported by the soviet union , china , and ... | president lyndon johnson dramatically escalated us involvement in the conflict , authorizing a series of intense bombing campaigns and committing hundreds of thousands of us ground troops to the fight . after the united states withdrew from the conflict , north vietnam invaded the south and united the country under a c... | or is it saying that the south fought the north with america or did america never ally with the south of vietnam ? |
overview the vietnam war was a prolonged military conflict that started as an anticolonial war against the french and evolved into a cold war confrontation between international communism and free-market democracy . the democratic republic of vietnam ( drv ) in the north was supported by the soviet union , china , and ... | heightened opposition to the war was one of the major factors in johnson ’ s decision not to run for re-election in 1968 . richard nixon and vietnam richard nixon campaigned for the presidency with a “ secret plan ” to end the war in vietnam . once in office , his administration sought to achieve “ peace with honor. ” ... | did nixon realize the intervention would just get them in a hole ? |
overview the vietnam war was a prolonged military conflict that started as an anticolonial war against the french and evolved into a cold war confrontation between international communism and free-market democracy . the democratic republic of vietnam ( drv ) in the north was supported by the soviet union , china , and ... | overview the vietnam war was a prolonged military conflict that started as an anticolonial war against the french and evolved into a cold war confrontation between international communism and free-market democracy . the democratic republic of vietnam ( drv ) in the north was supported by the soviet union , china , and ... | and why using birth defect chemicals ? |
overview the vietnam war was a prolonged military conflict that started as an anticolonial war against the french and evolved into a cold war confrontation between international communism and free-market democracy . the democratic republic of vietnam ( drv ) in the north was supported by the soviet union , china , and ... | were they correct ? was the war in vietnam a civil war or a global cold war confrontation ? | was thailand ever involved in the war ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | what is your favorite multiplication quution ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | the expression $ \goldd { 3 } \times \maroond { 5 } $ means $ \goldd { 3 } $ groups with $ \maroond { 5 } $ items in each group . arrays we can also use arrays to show multiplication . an array is an arrangement of objects in equal sized rows . | what can you use multiplication for in daily life ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | we can also use repeated addition to find the total number of treats . there are $ 4 $ groups of $ 3 $ , so we can add $ 3+3+3+3 $ . whether we multiply or use repeated addition , we are finding the total of $ 4 $ groups of $ 3 $ treats . | christiano has 3 water bottles , his friend santa has 7x 's more water bottles.how many water bottles does santa have ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | the expression $ \goldd { 3 } \times \maroond { 5 } $ means $ \goldd { 3 } $ groups with $ \maroond { 5 } $ items in each group . arrays we can also use arrays to show multiplication . an array is an arrangement of objects in equal sized rows . | why do we use arrays in multiplication sometimes ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | if we count the treats one by one we get a total of $ 12 $ . we can also use repeated addition to find the total number of treats . there are $ 4 $ groups of $ 3 $ , so we can add $ 3+3+3+3 $ . | if multiplying is repeated addition , is division repeated subtraction ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | for this problem , we have $ 5 $ $ \text { \blued { groups of } } $ $ 2 $ dog treats . we can use the $ \blued\times $ symbol to write the problem : $ 5 \text { \blued { groups of } } 2 = 5 \blued\times 2 $ let 's try another one this week you visited tuffy $ 4 $ times . you thought he looked too skinny so you gave him... | what is 675 times 980 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | for this problem , we have $ 5 $ $ \text { \blued { groups of } } $ $ 2 $ dog treats . we can use the $ \blued\times $ symbol to write the problem : $ 5 \text { \blued { groups of } } 2 = 5 \blued\times 2 $ let 's try another one this week you visited tuffy $ 4 $ times . you thought he looked too skinny so you gave him... | what is 132 times 486 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | for this problem , we have $ 5 $ $ \text { \blued { groups of } } $ $ 2 $ dog treats . we can use the $ \blued\times $ symbol to write the problem : $ 5 \text { \blued { groups of } } 2 = 5 \blued\times 2 $ let 's try another one this week you visited tuffy $ 4 $ times . you thought he looked too skinny so you gave him... | what is 567 times 8653 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | so there are $ 5 $ equal sized groups . we can use multiplication to find out how many total treats you gave tuffy . the symbol for multiplication is $ \blued { \times } $ . | how many stars are there in the universe ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | we learned that $ 4 $ groups with $ 3 $ treats in each group is the same as $ 4 \times 3 $ . if we count the treats one by one we get a total of $ 12 $ . we can also use repeated addition to find the total number of treats . | is khana acdmey for evey one ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | for this problem , we have $ 5 $ $ \text { \blued { groups of } } $ $ 2 $ dog treats . we can use the $ \blued\times $ symbol to write the problem : $ 5 \text { \blued { groups of } } 2 = 5 \blued\times 2 $ let 's try another one this week you visited tuffy $ 4 $ times . you thought he looked too skinny so you gave him... | what is 5689 times 38 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | there are $ 4 $ groups of $ 3 $ , so we can add $ 3+3+3+3 $ . whether we multiply or use repeated addition , we are finding the total of $ 4 $ groups of $ 3 $ treats . $ 4 \times 3 = 12 $ $ 3 + 3 + 3 + 3 = 12 $ there are $ 12 $ total treats . | can we multiply fractions , decimals and negative numbers too , or only positive numbers ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | what is 7 x 7 x 7 x 7 x 7 x 7 x 7 then ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | what 's 23 x 32 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | how old exactly is multiplication ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | we can think of this as $ \goldd { 3 } $ flowers with $ \maroond { 5 } $ petals on each flower . the expression $ \goldd { 3 } \times \maroond { 5 } $ means $ \goldd { 3 } $ groups with $ \maroond { 5 } $ items in each group . arrays we can also use arrays to show multiplication . | why is 1 x 7 expression is correct for 1 group of 7 fishes are there or in an aquarium there are 7 fishes rather than 7 x 1 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | we can think of this as $ \goldd { 3 } $ flowers with $ \maroond { 5 } $ petals on each flower . the expression $ \goldd { 3 } \times \maroond { 5 } $ means $ \goldd { 3 } $ groups with $ \maroond { 5 } $ items in each group . arrays we can also use arrays to show multiplication . an array is an arrangement of objects ... | is 7 x 1 expression also correct ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | is there 5th grade levels ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | how can you add big numbers in multiplication ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | so is n't like division is the opposite of multiplication and multiplication is the opposite of division and addition is the opposit of subtraction and subtraction is the opposite of addition ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | for this problem , we have $ 5 $ $ \text { \blued { groups of } } $ $ 2 $ dog treats . we can use the $ \blued\times $ symbol to write the problem : $ 5 \text { \blued { groups of } } 2 = 5 \blued\times 2 $ let 's try another one this week you visited tuffy $ 4 $ times . you thought he looked too skinny so you gave him... | what is 26 times 9 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | could we match divison plus multiplication ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | let 's use an array to show how this works . the array shows $ 4 $ rows with $ 5 $ dots in each row . this is the same as $ 4 \times 5 $ or $ 5 + 5 + 5 + 5 $ . | there are 6 rows of dots and 3 dots in each row how many are all together ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | tip : what is 4x7x2 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | why ca n't we divide 0 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . | what 's 118 x 118 ? |
getting started with multiplication multiplication helps us find the total number of items quickly . for multiplication we will think about the number of equal sized groups and the number of items in each group . let 's take a look at an example : each time you visit your neighbor 's dog tuffy , you give him two dog tr... | the expression $ \goldd { 3 } \times \maroond { 5 } $ means $ \goldd { 3 } $ groups with $ \maroond { 5 } $ items in each group . arrays we can also use arrays to show multiplication . an array is an arrangement of objects in equal sized rows . | why do we use multiplication instead of using adding those numbers ? |
a miracle at a burial don gonzalo ruíz , who died in 1323 ( and was later known by the title , count of orgaz ) , is not likely someone you know— and while you may not know ruíz , chances are you ’ ve seen a reproduction of el greco ’ s painting—it is one of the world ’ s most recognizable and often reproduced painting... | the figures are arranged as a frieze that moves across the bottom half of the painting with the heads forming a straight horizontal line , giving an impression of stability . this differs from the heavenly realm , where the clouds arc upwards to create a sense of motion and flux . these clouds , and the way that el gre... | why would the artist choose to paint the heavens in a `` loose '' way that portrays the heavens in a more `` chaotic '' sense ? |
a miracle at a burial don gonzalo ruíz , who died in 1323 ( and was later known by the title , count of orgaz ) , is not likely someone you know— and while you may not know ruíz , chances are you ’ ve seen a reproduction of el greco ’ s painting—it is one of the world ’ s most recognizable and often reproduced painting... | the lower half of the canvas has a darker , more earth-tone palette ( except saints stephen and augustine ) , giving it a more naturalistic appearance . differences also exist between the way the figures in each realm are painted . christ , mary , and john the baptist are more angular and elongated than those below . | especially given the contrast on the same painting where the `` earthly figures '' are painted with tighter and more controlled brushwork which we read indicates `` stability '' ? |
a miracle at a burial don gonzalo ruíz , who died in 1323 ( and was later known by the title , count of orgaz ) , is not likely someone you know— and while you may not know ruíz , chances are you ’ ve seen a reproduction of el greco ’ s painting—it is one of the world ’ s most recognizable and often reproduced painting... | mary and john the baptist gather at christ ’ s feet , leaning inwards—not unlike saints stephen and augustine holding the count of orgaz ’ s body . counter-reformation artist the mid-to-late sixteenth century was the era of the counter reformation , with toledo as a staunch bastion of catholic christendom . at the coun... | would n't a `` staunch bastion of catholic christendom '' seek to promote the heavens as stable and the earth as more chaotic or disorderly ( realistic ) ? |
work is a measurement of energy , so it may seem odd to think that a work can be negative — but it can ! work is how much energy is done by a force over a distance . suppose we needed to set up ice hockey goal nets . initially the nets are standing still with zero velocity at the edge of the ice hockey rink . when you ... | from drawing a free body force diagram , we can see the tension force is equal the gravity force , so t=mg . $ w=fd = td = ( mg ) ( 10 ) = 4900 n $ this is positive work . the tension force is in the same direction as the movement . | is n't the unit for work supposed to be joules instead of newtons ? |
work is a measurement of energy , so it may seem odd to think that a work can be negative — but it can ! work is how much energy is done by a force over a distance . suppose we needed to set up ice hockey goal nets . initially the nets are standing still with zero velocity at the edge of the ice hockey rink . when you ... | if the crate is moving upwards at a constant velocity , what is the net work done on the crate as it is hoisted up 10 feet ? $ w=fd = ( fg+t ) d = ( -490 n+490 n ) *d= 0 $ the net work is zero because there is no increase or decrease in kinetic energy : the crate is moving at a constant velocity . | is n't potential energy being put into the crate of snakes if it 's higher than it initially started ? |
work is a measurement of energy , so it may seem odd to think that a work can be negative — but it can ! work is how much energy is done by a force over a distance . suppose we needed to set up ice hockey goal nets . initially the nets are standing still with zero velocity at the edge of the ice hockey rink . when you ... | the phrase “ constant velocity ” always translates to zero acceleration . from drawing a free body force diagram , we can see the tension force is equal the gravity force , so t=mg . $ w=fd = td = ( mg ) ( 10 ) = 4900 n $ this is positive work . | from the last example if both works done by tension and gravity are equal to each other and they cancel out how is there still movement ? |
work is a measurement of energy , so it may seem odd to think that a work can be negative — but it can ! work is how much energy is done by a force over a distance . suppose we needed to set up ice hockey goal nets . initially the nets are standing still with zero velocity at the edge of the ice hockey rink . when you ... | because the direction of the push and the movement of the net are in the same direction , there is now positive energy : the goalie net went from zero energy to some amount of positive kinetic energy . this is an example of positive work . suppose at the end of an ice hockey game an assistant helps put the goalie nets ... | if work is equal to f times distance d and there is still displacement going upwards , how is work zero ? |
work is a measurement of energy , so it may seem odd to think that a work can be negative — but it can ! work is how much energy is done by a force over a distance . suppose we needed to set up ice hockey goal nets . initially the nets are standing still with zero velocity at the edge of the ice hockey rink . when you ... | $ w=fd = ( -mg ) d = ( -9.850 ) 10 = -4900 n $ this is negative work ! gravity does negative work here because gravity goes in the opposite direction as the displacement . if the crate is moving upwards at a constant velocity , what is the work done by the tension in the rope as it is hoisted up 10 feet ? | if a boy moving on straight road against the frictional force of 5n , lost his way in a circular path after walking 1km and goes round the circular path of radius 100m for 1.5 cycles then finally continues his journey at the correct path , what is the displacement and work here ? |
background single variable chain rule the gradient derivatives of vector valued functions what we 're building to given a multivariable function $ f ( x , y ) $ , and two single variable functions $ x ( t ) $ and $ y ( t ) $ , here 's what the multivariable chain rule says : $ \underbrace { \dfrac { d } { dt } f ( \blu... | the derivative $ \vec { \textbf { v } } ' ( t_0 ) $ at a particular value $ t_0 $ gives a vector in the input space of $ f $ : $ \begin { align } \quad \vec { \textbf { v } } ' ( t_0 ) = \left [ \begin { array } { c } x ' ( t_0 ) \ y ' ( t_0 ) \end { array } \right ] \end { align } $ if $ \vec { \textbf { v } } ( t ) $... | if i have something like p ( s ( t ) , t ) , then would the derivative of p with respect to t be just the partial derivative of p with respect to s multiplied by the derivative of s with respect to t , or is it a bit more complicated than that ? |
background single variable chain rule the gradient derivatives of vector valued functions what we 're building to given a multivariable function $ f ( x , y ) $ , and two single variable functions $ x ( t ) $ and $ y ( t ) $ , here 's what the multivariable chain rule says : $ \underbrace { \dfrac { d } { dt } f ( \blu... | likewise the term $ \redd { \dfrac { dy } { dt } } $ represents how a tiny change in $ t $ influences the second intermediate output $ y ( t ) $ . the term $ \blued { \dfrac { \partial f } { \partial x } } $ represents how a tiny change to the $ x $ -component of an input to $ f $ influences its output , and similarly ... | total change in f ( x , y ) = lim ( f ( x ( t+h ) , y ( t+h ) ) - f ( x ( t ) , y ( t ) ) ) / h h- > 0 also , what this expression tells ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | the product rule : $ \log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ this property says that the logarithm of a product is the sum of the logs of its factors . we can use the product rule to rewrite logarithmic expressions . example 1 : expanding logarithms for our purposes , expanding a logarithm means writing it as the s... | where will we use logarithms in our real life ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | || : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | why is n't there a base in question 4 ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | now let 's use the power rule to rewrite log expressions . example 1 : expanding logarithms for our purposes in this section , expanding a single logarithm means writing it as a multiple of another logarithm . let 's use the power rule to expand $ \log_2\left ( x^3\right ) $ . | why the base cant be 1 of a logarithm ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | this article explores three of those properties . let 's take a look at each property individually . the product rule : $ \log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ this property says that the logarithm of a product is the sum of the logs of its factors . | is there any property we can use when multiplying logs with same bases ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | now let 's use the power rule to rewrite log expressions . example 1 : expanding logarithms for our purposes in this section , expanding a single logarithm means writing it as a multiple of another logarithm . let 's use the power rule to expand $ \log_2\left ( x^3\right ) $ . | what if there is square root or cube root in the logarithm ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | || : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | how do you install minecraft mods ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | now let 's use the power rule to rewrite log expressions . example 1 : expanding logarithms for our purposes in this section , expanding a single logarithm means writing it as a multiple of another logarithm . let 's use the power rule to expand $ \log_2\left ( x^3\right ) $ . | which logarithm do we apply the most- common logarithm or natural logarithm ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | $ \begin { align } \log_2\left ( x^\maroonc3\right ) & amp ; =\maroonc3\cdot \log_2 ( x ) & amp ; & amp ; \small { \gray { \text { power rule } } } \ \ & amp ; =3\log_2 ( x ) \end { align } $ example 2 : condensing logarithms for our purposes in this section , condensing a multiple of a logarithm means writing it as a ... | how come in challenge problem 1 , you are supposed to bring the power to the front , and in challenge problem 2 , you are supposed to bring the power to the back ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | $ \begin { align } \log_6 ( \blued5\greend y ) & amp ; =\log_6 ( \blued5\cdot \greend y ) \ \ & amp ; =\log_6 ( \blued5 ) +\log_6 ( \greend y ) & amp ; & amp ; ~~~~~~~~\small { \gray { \text { product rule } } } \end { align } $ example 2 : condensing logarithms for our purposes , compressing a sum of two or more logar... | when there is no given base for the log are n't you supposed to automatically suppose that the base is 10 ? |
|| : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | || : - | : - the product rule | $ \large\log_b ( mn ) =\log_b ( m ) +\log_b ( n ) $ the quotient rule | $ \large\log_b\left ( \frac { m } { n } \right ) =\log_b ( m ) -\log_b ( n ) $ the power rule | $ \large\log_b ( m^p ) =p\log_b ( m ) $ ( these properties apply for any values of $ m $ , $ n $ , and $ b $ for which e... | for challenge problem # 1 : i see that the correct answer is c ) , but why is that not the same as a ) first : log_b ( ( 2x^3 ) /5 -- > log_b ( 2x^3 ) - log_b ( 5 ) then : log_b ( 2x^3 ) -- > 3log_b ( 2x ) is that not true ? |
in the table below , $ a $ and $ b $ are matrices of equal dimensions , $ c $ and $ d $ are scalars , and $ o $ is a zero matrix . property | example - | - associative property of multiplication | $ ( cd ) a=c ( da ) $ distributive properties | $ c ( a+b ) =ca+cb $ | $ ( c+d ) a=ca+da $ multiplicative identity property... | for example , $ \blued2 ( \greend5+\goldd3 ) =\blued2 \cdot \greend5+\blued2 \cdot \goldd3 $ . thus the original two expressions must be equivalent as well ! $ ( c+d ) a=ca+da $ this property states that a matrix can be distributed over scalar addition . | 1 ) which of the following are equivalent to c ( 1a+b ) all options must be true is n't it ? |
in the table below , $ a $ and $ b $ are matrices of equal dimensions , $ c $ and $ d $ are scalars , and $ o $ is a zero matrix . property | example - | - associative property of multiplication | $ ( cd ) a=c ( da ) $ distributive properties | $ c ( a+b ) =ca+cb $ | $ ( c+d ) a=ca+da $ multiplicative identity property... | so , for example , if $ a= \left [ \begin { array } { rr } { 2 } & amp ; 5 \ 1 & amp ; 7 \end { array } \right ] $ , then we have : $ \begin { align } \greend1 \left [ \begin { array } { rr } { 2 } & amp ; 5 \ 1 & amp ; 7 \end { array } \right ] & amp ; =\left [ \begin { array } { rr } { \greend1\cdot { 2 } } & amp ; \... | why is n't commutative property written in the above table ? |
in the table below , $ a $ and $ b $ are matrices of equal dimensions , $ c $ and $ d $ are scalars , and $ o $ is a zero matrix . property | example - | - associative property of multiplication | $ ( cd ) a=c ( da ) $ distributive properties | $ c ( a+b ) =ca+cb $ | $ ( c+d ) a=ca+da $ multiplicative identity property... | thus the original two expressions must be equivalent as well ! $ ( c+d ) a=ca+da $ this property states that a matrix can be distributed over scalar addition . here 's an example where $ \blued c=\blued2 $ , $ \greend d=\greend3 $ , and $ \goldd a=\left [ \begin { array } { rr } { \goldd6 } & amp ; \goldd9 \ \goldd7 & ... | just making sure , you ca n't add a vector to a scalar , right ? |
key points : transcription is the process in which a gene 's dna sequence is copied ( transcribed ) to make an rna molecule . rna polymerase is the main transcription enzyme . transcription begins when rna polymerase binds to a promoter sequence near the beginning of a gene ( directly or through helper proteins ) . rna... | the region of opened-up dna is called a transcription bubble . transcription uses one of the two exposed dna strands as a template ; this strand is called the template strand . the rna product is complementary to the template strand and is almost identical to the other dna strand , called the nontemplate ( or coding ) ... | what is the benefit of the coding strand if it does n't get transcribed and only the template strand gets transcribed ? |
key points : transcription is the process in which a gene 's dna sequence is copied ( transcribed ) to make an rna molecule . rna polymerase is the main transcription enzyme . transcription begins when rna polymerase binds to a promoter sequence near the beginning of a gene ( directly or through helper proteins ) . rna... | the rna transcript is nearly identical to the non-template , or coding , strand of dna . however , rna strands have the base uracil ( u ) in place of thymine ( t ) , as well as a slightly different sugar in the nucleotide . so , as we can see in the diagram above , each t of the coding strand is replaced with a u in th... | why does rna have the base uracil instead of thymine ? |
key points : transcription is the process in which a gene 's dna sequence is copied ( transcribed ) to make an rna molecule . rna polymerase is the main transcription enzyme . transcription begins when rna polymerase binds to a promoter sequence near the beginning of a gene ( directly or through helper proteins ) . rna... | this , coupled with the stalled polymerase , produces enough instability for the enzyme to fall off and liberate the new rna transcript . what happens to the rna transcript ? after termination , transcription is finished . | how does histone acetylation contribute to the genesis of the primary transcript ? |
key points : transcription is the process in which a gene 's dna sequence is copied ( transcribed ) to make an rna molecule . rna polymerase is the main transcription enzyme . transcription begins when rna polymerase binds to a promoter sequence near the beginning of a gene ( directly or through helper proteins ) . rna... | however , there is one important difference : in the newly made rna , all of the t nucleotides are replaced with u nucleotides . the site on the dna from which the first rna nucleotide is transcribed is called the $ +1 $ site , or the initiation site . nucleotides that come before the initiation site are given negative... | the fourth paragraph , under transcription overview , is the +1 site , or the initiation site and the promoter the same thing ? |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.