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cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | now let 's practice some problems . problem 2 ben is a potato farmer . the function $ p ( a ) = 25 { , } 000a - 1000 $ gives the amount of potatoes , $ p $ , in kilograms , that he expects to produce from planting potatoes on $ a $ acres of land . | f ( x ) = 2x-1 g ( x ) =3x and h ( x ) =x^2+1 how would i find the answer f ( g ( h ( 2 ) ) ) ? |
cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | so , to find this expression , we can substitute $ \greend { c ( a ) } $ in for $ \goldd { c } $ in function $ m $ . $ \begin { align } m ( \goldd c ) & amp ; =0.9\goldd c-50\\ m ( { \greend { c ( a ) } } ) & amp ; =0.9 ( \greend { c ( a ) } ) -50\ \ & amp ; = 0.9 ( \greend { 7500a-1500 } ) -50~~~~~~~~~~\small { \gray ... | how does 6750a-1350-50 turn into 6750a-1400 instead of 6750a-1300 ? |
cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | visualizing the two methods here 's a visual to help interpret the above definition . using both functions $ c $ and $ m $ , function $ c $ —the corn function—takes two to 13,500 . then , function $ m $ —the money function—takes 13,500 to $ \ $ $ 12,100 . using the composite function , we see that function $ m\circ c $... | what is the difference between a regular function and a composing function ? |
cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | creating a new function we can indeed find the function that takes acres planted directly to expected earnings ! to find this new function , let 's think about the most general question : how much money does cam expect to make if he plants corn seed on $ a $ acres of land ? well , if cam plants corn on $ a $ acres , he... | how much money can ben expect to make if he sells all of the potatoes produced on the 3 acres ? |
cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | $ m ( c ( 2 ) ) =6750 ( 2 ) -1400=\ $ 12 { , } 100 $ cam can expect to make $ \ $ 12 { , } 100 $ from planting corn on two acres of land , which is consistent with our previous work ! defining composite functions we just found what is called a composite function . instead of substituting acres planted into the corn fun... | would the reverse of these functions be true ? |
cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | $ \begin { align } m ( \goldd c ) & amp ; =0.9\goldd c-50\\ m ( { \greend { c ( a ) } } ) & amp ; =0.9 ( \greend { c ( a ) } ) -50\ \ & amp ; = 0.9 ( \greend { 7500a-1500 } ) -50~~~~~~~~~~\small { \gray { \text { since } } } \small { \gray { c ( a ) =7500a-1500 } } \\ & amp ; = 6750a-1350-50\\ & amp ; =6750a-1400 \end ... | if we wanted to find the area needed to plant enough corn to make an x amount of money be a ( c ( m ) ) ? |
cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | $ \begin { align } m ( \goldd c ) & amp ; =0.9\goldd c-50\\ m ( { \greend { c ( a ) } } ) & amp ; =0.9 ( \greend { c ( a ) } ) -50\ \ & amp ; = 0.9 ( \greend { 7500a-1500 } ) -50~~~~~~~~~~\small { \gray { \text { since } } } \small { \gray { c ( a ) =7500a-1500 } } \\ & amp ; = 6750a-1350-50\\ & amp ; =6750a-1400 \end ... | would we need to create new functions ? |
cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | now let 's practice some problems . problem 2 ben is a potato farmer . the function $ p ( a ) = 25 { , } 000a - 1000 $ gives the amount of potatoes , $ p $ , in kilograms , that he expects to produce from planting potatoes on $ a $ acres of land . | what would be the difference between ( f o g ) ( 2 ) and ( g o f ) ( 2 ) ? |
cam is a farmer . each year he plants seeds that turn into corn . the function below gives the amount of corn , $ c $ , in kilograms ( kg ) , that he expects to produce if he plants corn on $ a $ acres of land . $ c ( a ) = 7500a - 1500 $ for example , if cam plants two , he expects to produce $ c ( 2 ) = 7500 ( 2 ) -1... | $ m ( c ( 2 ) ) =6750 ( 2 ) -1400=\ $ 12 { , } 100 $ cam can expect to make $ \ $ 12 { , } 100 $ from planting corn on two acres of land , which is consistent with our previous work ! defining composite functions we just found what is called a composite function . instead of substituting acres planted into the corn fun... | my question : when you speak of functions such as f ( x ) or g ( x ) and then define them as you do on the videos as , for example f ( x ) =9+x2 or g ( x ) +5x2 + 2x +1 , where do these equations come from ? |
this list links to videos , essays , images , and additional resources for the 250 required works of art for the ap* art history course and exam . smarthistory is adding new materials regularly . for more context on these works of art , please see the art history sections of khan academy . content area 1 global prehist... | for more context on these works of art , please see the art history sections of khan academy . content area 1 global prehistory 30,000-500b.c.e . 1 . | are the content areas supposed to be studied and completed every week on their own , or should they take longer than that ? |
this list links to videos , essays , images , and additional resources for the 250 required works of art for the ap* art history course and exam . smarthistory is adding new materials regularly . for more context on these works of art , please see the art history sections of khan academy . content area 1 global prehist... | acropolis a. parthenon ( video , essay , images , additional resources ) i. helios , horses , dionysus ( heracles ? ) , east pediment ( video , images , additional resources ) ii . frieze ( video , images ) , plaque of the ergastines ( video , images , additional resources ) b . victory adjusting her sandel , temple of... | why are pictures/images in flickr ? |
this list links to videos , essays , images , and additional resources for the 250 required works of art for the ap* art history course and exam . smarthistory is adding new materials regularly . for more context on these works of art , please see the art history sections of khan academy . content area 1 global prehist... | this list links to videos , essays , images , and additional resources for the 250 required works of art for the ap* art history course and exam . smarthistory is adding new materials regularly . | is there a website where i can take a mock multiple choice of ap art history ? |
this list links to videos , essays , images , and additional resources for the 250 required works of art for the ap* art history course and exam . smarthistory is adding new materials regularly . for more context on these works of art , please see the art history sections of khan academy . content area 1 global prehist... | smarthistory is adding new materials regularly . for more context on these works of art , please see the art history sections of khan academy . content area 1 global prehistory 30,000-500b.c.e . | do you think children must be denied access to such art ? |
this list links to videos , essays , images , and additional resources for the 250 required works of art for the ap* art history course and exam . smarthistory is adding new materials regularly . for more context on these works of art , please see the art history sections of khan academy . content area 1 global prehist... | smarthistory is adding new materials regularly . for more context on these works of art , please see the art history sections of khan academy . content area 1 global prehistory 30,000-500b.c.e . | are there any works of art from the philippines ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | the signs of the actual voltages always sort themselves out during calculations . kirchhoff 's voltage law - concept check problem 4 : what is $ v_ { r3 } $ ? reminder : check the first sign of each element voltage as you walk around the loop . | in the `` kirchhoff 's voltage law - concept check '' , why is the `` -1v '' negative ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | it 's okay . the voltage arrows and polarity signs are just reference directions for voltage . when the circuit analysis is complete , one or more of the element voltages around the loop will be negative with respect to its voltage arrow . | when i see the words `` voltage on each resistor '' - what does that mean ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | it 's okay . the voltage arrows and polarity signs are just reference directions for voltage . when the circuit analysis is complete , one or more of the element voltages around the loop will be negative with respect to its voltage arrow . | that voltage is getting eaten up or used by the resistor ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | kirchhoff 's voltage law can be written as , $ \large\displaystyle \sum_n v_n = 0 $ where $ n $ counts the element voltages around the loop . you can also state kirchhoff 's voltage law another way : the sum of voltage rises equals the sum of voltage drops around a loop . $ \large \displaystyle \sum v_ { rise } = \sum ... | what is the algebraic sum ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | $ \large \displaystyle \sum i_ { in } = \sum i_ { out } $ this form of the law requires you to do a little more bookkeeping on the current arrows . current arrows all in ? if you are wondering how all currents can add up to zero if they all point in the same direction , do not let this bother you . | what if all the current ( arrows ) are pointing inward , how is the sum of current zero in that case ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | to find $ \blued i $ , the four series resistors can be reduced to a single equivalent resistor : $ r_ { series } = 100 + 200 + 300 + 400 = 1000\ , \omega $ using ohm 's law , the current is : $ \blued i = \dfrac { v } { r_ { series } } = \dfrac { 20\ , \text v } { 1000\ , \omega } = 0.020\ , \text a = 20 \ , \text { m... | what if the resistors are in parallel ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | kirchhoff 's current law can be written as , $ \large\displaystyle \sum_n i_n = 0 $ the index $ n $ counts the branches attached to the node . kirchhoff 's current law is flexible . it can be stated other ways . | is kirchhoff 's law applicable for ac circuits ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | ( check the circuit diagram , make sure i got the last two $ - $ signs correct . ) done . we made it back home to node $ \greene { \text a } $ . | i mean when you see a diagram its usually done clock wise either way , correct ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | we can write the voltages for the resistors and the source on the schematic . these five voltages are referred to as element voltages . ( the circuit nodes get names , $ \greene { \text a } $ to $ \greene { \text e } $ , so we can talk about them . ) | and does in play a role in adding up of the voltages.. ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | how do we apply kirchhoff 's laws to parallel circuits ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | step 2 : pick a direction to travel around the loop ( clockwise or counterclockwise ) . step 3 : walk around the loop . include element voltages in a growing sum according to these rules : when you encounter a new element , look at the voltage sign as you enter the element . | how do you label the signs around each resistor based on what ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | let 's do a quick check . add up the voltages across the resistors , $ 2\ , \text { v } + 4\ , \text { v } + 6\ , \text { v } + 8\ , \text { v } = 20 \ , \text v $ the individual resistor voltages add up to the source voltage . this makes sense , and confirms our calculations . | if we calculate the sum of voltages with the answer 6v , we will get 5+3+6+ ( -1 ) = 13 and the source have 15 v. where are the two missing volts ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | if a circuit has multiple loops , kirchhoff 's voltage law is true for every loop . voltages all positive ? if you are wondering : how can the element voltages all be positive if they have to add up to zero ? | hello , normal electrical engineering problems are not labeled with positive and negative signs around the resistors , how would you solve problems with no labeling of positive and negative signs using kvl and kcl ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | the first step in solving the circuit is to compute the current . then we will compute the voltage across the individual resistors . we recognize this as a series circuit , so there is only one current flowing , $ \blued i $ , through all five elements . | why is there voltage difference across the resistors ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | if a circuit has multiple loops , kirchhoff 's voltage law is true for every loop . voltages all positive ? if you are wondering : how can the element voltages all be positive if they have to add up to zero ? | is resistance is ever positive ... ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | if a circuit has multiple loops , kirchhoff 's voltage law is true for every loop . voltages all positive ? if you are wondering : how can the element voltages all be positive if they have to add up to zero ? | while making up these problems , how do you decide which side of the resistor is the negative terminal and which one is the positive terminal ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | the voltage polarity on the resistors is arranged in a way you might not expect , with all the arrows pointing in the same direction around the loop . this reveals a cool property of loops . let 's take a walk around the loop , adding up voltages as we go . | could you also explain how this will apply to loops with parallel circuits ? |
kirchhoff 's laws for current and voltage lie at the heart of circuit analysis . with these two laws , plus the equations for individual component ( resistor , capacitor , inductor ) , we have the basic tool set we need to start analyzing circuits . this article assumes you are familiar with the definitions of node , d... | continue around the loop from node $ \greene { \text b } $ to $ \greene { \text c } $ to $ \greene { \text d } $ to $ \greene { \text e } $ , and finish back home at node $ \greene { \text a } $ . append resistor voltages to the loop sum along the way . the polarity labels on all the resistors are arranged so we encoun... | if we just connect battery with the couple of resistors will the resistor dissipate the energy or in other words will our battery end up after some time ? |
key points : primary producers ( usually plants and other photosynthesizers ) are the gateway for energy to enter food webs . productivity is the rate at which energy is added to the bodies of a group of organisms ( such as primary producers ) in the form of biomass . gross productivity is the overall rate of energy ca... | in this way , all the consumers , or heterotrophs ( `` other-feeding '' organisms ) of an ecosystem , including herbivores , carnivores , and decomposers , rely on the ecosystem 's producers for energy . if the plants or other producers of an ecosystem were removed , there would be no way for energy to enter the food w... | my name is jannah , my question is are the decomposer 's the main part of the food chain/ the food web ? |
key points : primary producers ( usually plants and other photosynthesizers ) are the gateway for energy to enter food webs . productivity is the rate at which energy is added to the bodies of a group of organisms ( such as primary producers ) in the form of biomass . gross productivity is the overall rate of energy ca... | numbers pyramids numbers pyramids show how many individual organisms there are in each trophic level . they can be upright , inverted , or kind of lumpy , depending on the ecosystem . as shown in the figure below , a typical grassland during the summer has a base of numerous plants , and the numbers of organisms decrea... | the pyramid of number for a marine ecosystem upright or inverted ? |
aesthetic refers to a type of human experience that combines perception , feeling , meaning making , and appreciation of qualities of produced and/or manipulated objects , acts , and events of daily life . aesthetic experience motivates behavior and creates categories through which our experiences of the world can be o... | aesthetic refers to a type of human experience that combines perception , feeling , meaning making , and appreciation of qualities of produced and/or manipulated objects , acts , and events of daily life . aesthetic experience motivates behavior and creates categories through which our experiences of the world can be o... | what is overlapping in an artwork ? |
aesthetic refers to a type of human experience that combines perception , feeling , meaning making , and appreciation of qualities of produced and/or manipulated objects , acts , and events of daily life . aesthetic experience motivates behavior and creates categories through which our experiences of the world can be o... | artistic traditions are norms of artistic production and artistic products . artistic traditions are demonstrated through art-making processes ( utilization of materials and techniques , mode of display ) , through interactions between works of art and audience , and within form and/or content of a work of art . artist... | how doe shadowing effect art ? |
aesthetic refers to a type of human experience that combines perception , feeling , meaning making , and appreciation of qualities of produced and/or manipulated objects , acts , and events of daily life . aesthetic experience motivates behavior and creates categories through which our experiences of the world can be o... | artistic traditions are norms of artistic production and artistic products . artistic traditions are demonstrated through art-making processes ( utilization of materials and techniques , mode of display ) , through interactions between works of art and audience , and within form and/or content of a work of art . artist... | can art /art culture survive with out art associations ? |
aesthetic refers to a type of human experience that combines perception , feeling , meaning making , and appreciation of qualities of produced and/or manipulated objects , acts , and events of daily life . aesthetic experience motivates behavior and creates categories through which our experiences of the world can be o... | style is a combination of unique and defining features that can reflect the historical period , geographic location , cultural context , and individual hand of the artist . techniques include art-making processes , tools , and technologies that accommodate and/or overcome material properties . techniques range from sim... | what are art making process tools ? |
aesthetic refers to a type of human experience that combines perception , feeling , meaning making , and appreciation of qualities of produced and/or manipulated objects , acts , and events of daily life . aesthetic experience motivates behavior and creates categories through which our experiences of the world can be o... | aesthetic refers to a type of human experience that combines perception , feeling , meaning making , and appreciation of qualities of produced and/or manipulated objects , acts , and events of daily life . aesthetic experience motivates behavior and creates categories through which our experiences of the world can be o... | what are the key factors to remember ? |
for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . how often do we stop to examine and contemplate its form and style ? stopping for that contemplation offers not only the opportunity to understand one ’ s dai... | tiered seats in the theatron provided space for spectators . two side aisles ( parados , pl . paradoi ) provided access to the orchestra . | is there any logic behind the fact that these two rather different structures share the same name ? |
for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . how often do we stop to examine and contemplate its form and style ? stopping for that contemplation offers not only the opportunity to understand one ’ s dai... | for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . | `` ... i hope it was only animals being sacrificed ... no people right ? |
for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . how often do we stop to examine and contemplate its form and style ? stopping for that contemplation offers not only the opportunity to understand one ’ s dai... | while altars did not necessarily need to be architecturalized , they could be and , in some cases , they assumed a monumental scale . the third century b.c.e . altar of hieron ii at syracuse , sicily , provides one such example . | in the third paragraph , were there other important types of columns ? |
for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . how often do we stop to examine and contemplate its form and style ? stopping for that contemplation offers not only the opportunity to understand one ’ s dai... | originally taught his stoic philosophy in the stoa poikile of athens . theater the greek theater was a large , open-air structure used for dramatic performance . theaters often took advantage of hillsides and naturally sloping terrain and , in general , utilized the panoramic landscape as the backdrop to the stage itse... | how greek theater is forerunner modern gymnasium ? |
for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . how often do we stop to examine and contemplate its form and style ? stopping for that contemplation offers not only the opportunity to understand one ’ s dai... | for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . how often do we stop to examine and contemplate its form and style ? | did the greeks sometimes use the golden numeral to build their structures ? |
for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . how often do we stop to examine and contemplate its form and style ? stopping for that contemplation offers not only the opportunity to understand one ’ s dai... | the third century b.c.e . altar of hieron ii at syracuse , sicily , provides one such example . at c. 196 meters in length and c. 11 m in height the massive altar was reported to be capable of hosting the simultaneous sacrifice of 450 bulls ( diodorus siculus history 11.72.2 ) . | i have found many photographs of the ruins of the altar of hieron ii similar to the one posted in the article , but are there any drawings or models of what it originally looked like ? |
for most of us , architecture is easy to take for granted . its everywhere in our daily lives—sometimes elegant , other times shabby , but generally ubiquitous . how often do we stop to examine and contemplate its form and style ? stopping for that contemplation offers not only the opportunity to understand one ’ s dai... | ( with the earliest extant stone architecture dating to the seventh century b.c.e . ) . greek architecture influenced roman architecture and architects in profound ways , such that roman imperial architecture adopts and incorporates many greek elements into its own practice . an overview of basic building typologies de... | how does greek architecture influence modern architecture ? |
coins have a unique significance in the history of aksum . they are particularly important because they provide evidence of aksum and its rulers . the inscriptions on the coins highlight the fact that aksumites were a literate people with knowledge of both ethiopic and greek languages . conversion to christianity it is... | they are particularly important because they provide evidence of aksum and its rulers . the inscriptions on the coins highlight the fact that aksumites were a literate people with knowledge of both ethiopic and greek languages . conversion to christianity it is generally thought that the first aksumite coins were inten... | were there people who carved the coins as their jobs ? |
coins have a unique significance in the history of aksum . they are particularly important because they provide evidence of aksum and its rulers . the inscriptions on the coins highlight the fact that aksumites were a literate people with knowledge of both ethiopic and greek languages . conversion to christianity it is... | the old religious symbols of the sun and the moon no longer appeared on coins and were replaced with a cross , which was enlarged over the years . the religious symbolism on these coins had strong political implications , as it aligned aksum 's religious identity with its main trading partners , rome and later byzantiu... | i mean like , if you carve coins based on religious events , would n't people who did n't believe in the religion get offended at all ? |
coins have a unique significance in the history of aksum . they are particularly important because they provide evidence of aksum and its rulers . the inscriptions on the coins highlight the fact that aksumites were a literate people with knowledge of both ethiopic and greek languages . conversion to christianity it is... | the coins also had a portrait of the ruler on the obverse and reverse of the coin along with teff , a local type of wheat . inscriptions were another form of information included on the coins . for the most part , gold coins were inscribed in greek and often intended for exports , while silver and copper coins were ins... | like , what if people who made the coins were a different religion , and they decided that they were gon na make their own coins the entire time , would n't they get punished and neglected ? |
coins have a unique significance in the history of aksum . they are particularly important because they provide evidence of aksum and its rulers . the inscriptions on the coins highlight the fact that aksumites were a literate people with knowledge of both ethiopic and greek languages . conversion to christianity it is... | they are particularly important because they provide evidence of aksum and its rulers . the inscriptions on the coins highlight the fact that aksumites were a literate people with knowledge of both ethiopic and greek languages . conversion to christianity it is generally thought that the first aksumite coins were inten... | were there people who carved the coins as their jobs ? |
maybe you can bring it with you…if you are rich enough . the elite men and women of the han dynasty ( china's second imperial dynasty , 206 b.c.e.–220 c.e . ) enjoyed an opulent lifestyle that could stretch into the afterlife . today , the well-furnished tombs of the elite give us a glimpse of the luxurious goods they ... | the moon and the sun are emblematic of a supernatural realm above the human world . dragons and other immortal beings populate the sky . in the lower register , beneath the mourning hall , we see the underworld populated by two giant black fish , a red snake , a pair of blue goats , and an unidentified earthly deity . | why are dragons used , what is the symbolism ? |
maybe you can bring it with you…if you are rich enough . the elite men and women of the han dynasty ( china's second imperial dynasty , 206 b.c.e.–220 c.e . ) enjoyed an opulent lifestyle that could stretch into the afterlife . today , the well-furnished tombs of the elite give us a glimpse of the luxurious goods they ... | today , the well-furnished tombs of the elite give us a glimpse of the luxurious goods they treasured and enjoyed . for instance , a wealthy official could afford beautiful silk robes in contrast to the homespun or paper garments of a laborer or peasant . their tombs also inform us about their cosmological beliefs . | did i read correctly that a chinese peasant might have worn `` paper '' garments ? |
`` discovery '' between 1933 and 1940 , camel corps officer lieutenant brenans of the french foreign legion completed a series of small sketches and hand written notes detailing his discovery of dozens of rock art sites deep within the canyons of the tassili n ’ ajjer . tassili n ’ ajjer is a difficult to access plat... | this ordering approach results in useful classification and dating systems , dividing the tassili paintings and engravings into periods of concurrent and overlapping traditions ( the running horned woman is estimated to date to approximately 6,000 to 4,000 b.c.e.—placing it within the `` round head period '' ) , but of... | were there any horned animals in that area that might have influenced the idea of horns on a person ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | } { = } 3\ 3 & amp ; = 3 \end { align } $ yes , $ p = \greend { 21 } $ is a solution ! summary of how to solve addition and subtraction equations cool , so we just solved an addition equation and a subtraction equation . let 's summarize what we did : type of equation | example | first step : - | : - : | : - : addition... | can these equations be as complex as 20 steps ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or counteract each other . here 's an example of how subtraction is the inverse operation of addition : if we start with seven , add three , then subtract th... | if addition and subtraction are of equal level in the order of operations , could n't another valid answer for 5 - 2 + 2 be 1 ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | \end { align } $ let 's check our work . $ \qquad $ $ \begin { align } p - 18 & amp ; = 3 \ \greend { 21 } - 18 & amp ; \stackrel { \large ? } { = } 3\ 3 & amp ; = 3 \end { align } $ yes , $ p = \greend { 21 } $ is a solution ! summary of how to solve addition and subtraction equations cool , so we just solved an addit... | after solving the equation p-18=3 why they have written k=21 is a solution instead of p=21 is a solution ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | } { = } 3\ 3 & amp ; = 3 \end { align } $ yes , $ p = \greend { 21 } $ is a solution ! summary of how to solve addition and subtraction equations cool , so we just solved an addition equation and a subtraction equation . let 's summarize what we did : type of equation | example | first step : - | : - : | : - : addition... | how will these equations become useful in people 's every day lives ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | \\ k & amp ; = \greend { 7 } ~~~~~~~~~~\small\gray { \text { simplify . } } \end { align } $ let 's check our work . it 's always a good idea to check our solution in the original equation to make sure we did n't make any mistakes : $ \qquad $ $ \begin { align } k +22 & amp ; = 29 \ \greend { 7 } +22 & amp ; \stackrel ... | check after applying the correct operation to each side , what is ttt ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? | how do we use pi in these questions ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | let 's try some problems . equation a : $ y + 6 = 52 $ equation b : $ 3 + y = 27 $ equation c : $ t - 13 = 35 $ equation d : $ 35 = t - 13 $ | why are equation c and d the same but on different ends of the equals sign ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | } { = } 3\ 3 & amp ; = 3 \end { align } $ yes , $ p = \greend { 21 } $ is a solution ! summary of how to solve addition and subtraction equations cool , so we just solved an addition equation and a subtraction equation . let 's summarize what we did : type of equation | example | first step : - | : - : | : - : addition... | how do we use pi in these equations ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | addition and subtraction are inverse operations inverse operations are opposite operations that undo or counteract each other . here 's an example of how subtraction is the inverse operation of addition : if we start with seven , add three , then subtract three , we get back to seven : $ 7 + 3 - 3 = 7 $ here 's an exam... | how do you get and keep the concept of knowing when to add and subtract from both sides ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | let 's try some problems . equation a : $ y + 6 = 52 $ equation b : $ 3 + y = 27 $ equation c : $ t - 13 = 35 $ equation d : $ 35 = t - 13 $ | why is equation c and d pretty much the same thing ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? | why are there so many letters in algebra ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? | who came up with rules of math ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | let 's try some problems . equation a : $ y + 6 = 52 $ equation b : $ 3 + y = 27 $ equation c : $ t - 13 = 35 $ equation d : $ 35 = t - 13 $ | is one step equation and two step equation have the same method ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | } { = } 3\ 3 & amp ; = 3 \end { align } $ yes , $ p = \greend { 21 } $ is a solution ! summary of how to solve addition and subtraction equations cool , so we just solved an addition equation and a subtraction equation . let 's summarize what we did : type of equation | example | first step : - | : - : | : - : addition... | can these equations be as complex as , even though it is unreasonable , 20 terms ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | let 's try some problems . equation a : $ y + 6 = 52 $ equation b : $ 3 + y = 27 $ equation c : $ t - 13 = 35 $ equation d : $ 35 = t - 13 $ | if the problem is t-13=35 , why do you leave 13 blank if you need to add 13 to each side ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | } { = } 3\ 3 & amp ; = 3 \end { align } $ yes , $ p = \greend { 21 } $ is a solution ! summary of how to solve addition and subtraction equations cool , so we just solved an addition equation and a subtraction equation . let 's summarize what we did : type of equation | example | first step : - | : - : | : - : addition... | how do we use pi in these equations ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | let 's summarize what we did : type of equation | example | first step : - | : - : | : - : addition equation | $ k + 22 = 29 $ | subtract 22 from each side . subtraction equation | $ p - 18 = 3 $ | add 18 to each side . let 's try some problems . | why are one of the qualifications to add a number to each side of the other number ? |
based on our understanding of the balance beam model , we know that we always have to do the same thing to both sides of an equation to keep it true . but how do we know what to do to both sides of the equation ? addition and subtraction are inverse operations inverse operations are opposite operations that undo or cou... | summary of how to solve addition and subtraction equations cool , so we just solved an addition equation and a subtraction equation . let 's summarize what we did : type of equation | example | first step : - | : - : | : - : addition equation | $ k + 22 = 29 $ | subtract 22 from each side . subtraction equation | $ p -... | 23+y=123 , 23 to the other side changing the sign ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . | who discovered / invented sohcahtoa ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | trigonometric functions input angles and output side ratios | |inverse trigonometric functions input side ratios and output angles : - : | : -| : - : $ \sin ( \theta ) =\dfrac { \text { opposite } } { \text { hypotenuse } } $ | $ \rightarrow $ | $ \sin^ { -1 } \left ( \dfrac { \text { opposite } } { \text { hypotenuse ... | so i know that arcsin ( sin ( x ) ) = x but ... what happens when you do arcsin ( x ) * sin ( x ) ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . | if the earth is really round , then why do commercial airliners going from south america to australia fly the long way over africa ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | in other words , the $ \small { -1 } $ is not an exponent . instead , it simply means inverse function . however , there is an alternate notation that avoids this pitfall ! | how to calculate the inverse function in a calculator ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | trigonometric functions input angles and output side ratios | |inverse trigonometric functions input side ratios and output angles : - : | : -| : - : $ \sin ( \theta ) =\dfrac { \text { opposite } } { \text { hypotenuse } } $ | $ \rightarrow $ | $ \sin^ { -1 } \left ( \dfrac { \text { opposite } } { \text { hypotenuse ... | sin ( 150 ) =0.5 and sin ( 30 ) =0.5 so for arcsin ( 0.5 ) which value should i take and why ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | this notation is common in computer programming languages , but not in mathematics . solving the introductory problem in the introductory problem , we were given the opposite and adjacent side lengths , so we can use inverse tangent to find the angle . $ \begin { align } { m\angle l } & amp ; =\tan^ { -1 } \left ( \dfr... | can you use pythagoras to find out the length of a missing side if you are given the other 2 lenghts ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | inverse tangent $ ( \tan^ { -1 } ) $ does the opposite of the tangent . in general , if you know the trig ratio but not the angle , you can use the corresponding inverse trig function to find the angle . this is expressed mathematically in the statements below . | what does the _m_ prefix mean before the angle ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | we need inverse trig functions ! the inverse trigonometric functions we already know about inverse operations . for example , addition and subtraction are inverse operations , and multiplication and division are inverse operations . | what is the difference between trigonometric ratios and trigonometric functions ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | in other words , the $ \small { -1 } $ is not an exponent . instead , it simply means inverse function . however , there is an alternate notation that avoids this pitfall ! | is there any way to calculate arcsine or any inverse function in the iphone calculator ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | inverse tangent $ ( \tan^ { -1 } ) $ does the opposite of the tangent . in general , if you know the trig ratio but not the angle , you can use the corresponding inverse trig function to find the angle . this is expressed mathematically in the statements below . | what button do i use to find the approximate values of non-integer square roots ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | they take angles and give side ratios , but we need functions that take side ratios and give angles . we need inverse trig functions ! the inverse trigonometric functions we already know about inverse operations . | do cosecant , secant , and cotangent also have inverse functions ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | they take angles and give side ratios , but we need functions that take side ratios and give angles . we need inverse trig functions ! the inverse trigonometric functions we already know about inverse operations . | what are the uses of inverse trig functions ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | trigonometric functions input angles and output side ratios | |inverse trigonometric functions input side ratios and output angles : - : | : -| : - : $ \sin ( \theta ) =\dfrac { \text { opposite } } { \text { hypotenuse } } $ | $ \rightarrow $ | $ \sin^ { -1 } \left ( \dfrac { \text { opposite } } { \text { hypotenuse ... | why do we need to use sin ( -1 when we could just use sin ( ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | trigonometric functions input angles and output side ratios | |inverse trigonometric functions input side ratios and output angles : - : | : -| : - : $ \sin ( \theta ) =\dfrac { \text { opposite } } { \text { hypotenuse } } $ | $ \rightarrow $ | $ \sin^ { -1 } \left ( \dfrac { \text { opposite } } { \text { hypotenuse ... | according to the inverse function that has been said here , if i were to have a function , say , f ( x ) = 2x+3 , then f^-1 ( 2x+3 ) = x ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . | what does m refers to ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . | do the trees moving cause the wind to blow ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | inverse tangent $ ( \tan^ { -1 } ) $ does the opposite of the tangent . in general , if you know the trig ratio but not the angle , you can use the corresponding inverse trig function to find the angle . this is expressed mathematically in the statements below . | how do i find the trig ratio of a number without a calculator ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | they take angles and give side ratios , but we need functions that take side ratios and give angles . we need inverse trig functions ! the inverse trigonometric functions we already know about inverse operations . | when and when not do we use the inverse of trig functions to calculate the answer , vice versa ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | in other words , the $ \small { -1 } $ is not an exponent . instead , it simply means inverse function . however , there is an alternate notation that avoids this pitfall ! | if it 's an inverse function , would n't tan be adjacent over opposite ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | \\ m\angle l & amp ; =\tan^ { -1 } \left ( \dfrac { \blued { 35 } } { \maroonc { 65 } } \right ) \quad\small { \gray { \text { substitute values . } } } \\ m\angle l & amp ; \approx 28.30^\circ \quad\small { \gray { \text { evaluate with a calculator . } } } \end { align } $ now let 's try some practice problems . | how do you convert to degrees if your calculator measures in radians ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | they take angles and give side ratios , but we need functions that take side ratios and give angles . we need inverse trig functions ! the inverse trigonometric functions we already know about inverse operations . for example , addition and subtraction are inverse operations , and multiplication and division are invers... | how do you solve an inverse problem in degrees ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | $ \begin { align } { m\angle l } & amp ; =\tan^ { -1 } \left ( \dfrac { \text { } \blued { \text { opposite } } } { \text { } \maroonc { \text { adjacent } } \text { } } \right ) \quad\small { \gray { \text { define . } } } \\ m\angle l & amp ; =\tan^ { -1 } \left ( \dfrac { \blued { 35 } } { \maroonc { 65 } } \right )... | how do you substitute the values ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? | how do you know when to use cosecant , secant , and cotangent instead of sine , cosine , and tangent ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we can write : $ \tan ( l ) = \dfrac { \text { opposite } } { \... | in the triangle has opp of 35 and adj of 65 , so what is the measure of angle l ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we can write : $ \tan ( l ) = \dfrac { \text { opposite } } { \... | i have question from in the previous lesson , called `` practice : solve for a side in right triangle '' from the triangle how do you know which one to divide or multiple ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | trigonometric functions input angles and output side ratios | |inverse trigonometric functions input side ratios and output angles : - : | : -| : - : $ \sin ( \theta ) =\dfrac { \text { opposite } } { \text { hypotenuse } } $ | $ \rightarrow $ | $ \sin^ { -1 } \left ( \dfrac { \text { opposite } } { \text { hypotenuse ... | is there any way to not use a calculator when finding out the sin , cos , tan , sin-1 , cos-1 , or tan-1 ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | inverse tangent $ ( \tan^ { -1 } ) $ does the opposite of the tangent . in general , if you know the trig ratio but not the angle , you can use the corresponding inverse trig function to find the angle . this is expressed mathematically in the statements below . | so im guessing for angle z you cant use 8.06/9 which would give you the arc sine any body know why ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . | how can you insert a square root sign ? |
let 's take a look at a new type of trigonometry problem . interestingly , these problems ca n't be solved with sine , cosine , or tangent . a problem : in the triangle below , what is the measure of angle $ l $ ? what we know : relative to $ \angle l $ , we know the lengths of the opposite and adjacent sides , so we c... | they take angles and give side ratios , but we need functions that take side ratios and give angles . we need inverse trig functions ! the inverse trigonometric functions we already know about inverse operations . for example , addition and subtraction are inverse operations , and multiplication and division are invers... | how to round for inverse sin ( 8/10 ) ? |
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