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what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . and let me call this point down here -- let me call it point d. the angle bisector theo... | what does the angle bisector theorom prove ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | able ? ] to set up this one isosceles triangle , so these sides are congruent . now , let 's look at some of the other angles here and make ourselves feel good about it . | is n't it already pretty clear that if you get a isosceles triangle and bisect it down the middle perpendicular to the base that the two sides will have the same angle ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | we know that these two angles are congruent to each other , but we do n't know whether this angle is equal to that angle or that angle . we do n't know . we ca n't make any statements like that . so in order to actually set up this type of a statement , we 'll have to construct maybe another triangle that will be simil... | does n't a bisector always make right angles ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | and we could have done it with any of the three angles , but i 'll just do this one . i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . | can somebody please give me some hints as to how to make successful proofs ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . | going off of the angle bisector theorem , if you bisect a triangle and are told to prove the new angles congruent ( all 4 ) how would you go about doing so ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | the ratio of ab , the corresponding side is going to be cf -- is going to equal cf over ad . ad is the same thing as cd -- over cd . and so we know the ratio of ab to ad is equal to cf over cd . | how is ad same as cd ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | we know that these two angles are congruent to each other , but we do n't know whether this angle is equal to that angle or that angle . we do n't know . we ca n't make any statements like that . so in order to actually set up this type of a statement , we 'll have to construct maybe another triangle that will be simil... | i do n't get how to make statement-reason proofs , can someone please give me hints ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so these two angles are going to be the same . but this angle and this angle are also going to be the same , because this angle and that angle are the same . this is a bisector . | is there a an exterior angle inequality theorem video or explanation on this website ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so once you see the ratio of that to that , it 's going to be the same as the ratio of that to that . so that 's kind of a cool result , but you ca n't just accept it on faith because it 's a cool result . you want to prove it to ourselves . | could n't sal have used cross multiplication to get abcd = adbc and achieved the same result ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | and we 're done . we 've just proven ab over ad is equal to bc over cd . so there 's two things we had to do here is one , construct this other triangle , that , assuming this was parallel , that gave us two things , that gave us another angle to show that they 're similar and also allowed us to establish -- sorry , i ... | sal said that ratio of ab/ad=bc/cd is n't it the same thing as ab/bc=ad/dc and a much more simpler method to solve if we make a line ae parallel bd and do the exact same steps ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so these two angles are going to be the same . but this angle and this angle are also going to be the same , because this angle and that angle are the same . this is a bisector . | if the measure of angle a = angle c = 50 degrees , what is the measure of angle abd ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . | how can i bisect a triangle that has angles 50-103-27 and make two right triangles ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | the ratio of ab , the corresponding side is going to be cf -- is going to equal cf over ad . ad is the same thing as cd -- over cd . and so we know the ratio of ab to ad is equal to cf over cd . | why sal put ab/ad rather than ab/fc same cf/cd rather than ad/cd ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | and unfortunate for us , these two triangles right here are n't necessarily similar . we know that these two angles are congruent to each other , but we do n't know whether this angle is equal to that angle or that angle . we do n't know . | and if we know that we also know that the angle a and angle c are equal am i right ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . and let me call this point down here -- let me call it point d. the angle bisector theo... | what exactly is the angle bisector theorem ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so this is parallel to that right over there . and we could just construct it that way . and now we have some interesting things . | i 'm still confuse don how to make a statement-reason proofs chart could you explain than to me in simpler terms ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . | 9 what is an arbitrary triangle ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | if we want to prove it , if we can prove that the ratio of ab to ad is the same thing as the ratio of fc to cd , we 're going to be there because bc , we just showed , is equal to fc . but let 's not start with the theorem . let 's actually get to the theorem . so fc is parallel to ab , [ ? | what exactly is the hinge theorem ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . | is this theorem used to prove triangle similarities ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | and here , we want to eventually get to the angle bisector theorem , so we want to look at the ratio between ab and ad . similar triangles , either you could find the ratio between corresponding sides are going to be similar triangles , or you could find the ratio between two sides of a similar triangle and compare the... | i think triangle abd and bdc are not similar but only ratio of ab/bd and bd/dc is same , is n't it ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | this is a bisector . because this is a bisector , we know that angle abd is the same as angle dbc . so whatever this angle is , that angle is . | how would i solve an angle bisector question if it is not part of a shape and i do n't know the degree of the larger angle especially when all the numbers i have i need to solve for x first ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | and so you can imagine right over here , we have some ratios set up . so we 're going to prove it using similar triangles . and unfortunate for us , these two triangles right here are n't necessarily similar . | i am quite confused on how that rule can be used for all sorts of triangles ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | let 's actually get to the theorem . so fc is parallel to ab , [ ? able ? ] | sal used parallel lines to construct this proof , but would it still work if the line was n't parallel ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . and let me call this point down here -- let me call it point d. the angle bisector theo... | if the angle abc is bisected , will ad equal to dc ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | and unfortunate for us , these two triangles right here are n't necessarily similar . we know that these two angles are congruent to each other , but we do n't know whether this angle is equal to that angle or that angle . we do n't know . | in any given case , when an angle is bisected , are the two angles formed by that bisection always congruent ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . and let me call this point down here -- let me call it point d. the angle bisector theo... | what do you need to do to prove a line is an angle bisector of an angle ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | you want to make sure you get the corresponding sides right . we now know by angle-angle -- and i 'm going to start at the green angle -- that triangle b -- and then the blue angle -- bda is similar to triangle -- so then once again , let 's start with the green angle , f. then , you go to the blue angle , fdc . and he... | i thought sal proved in another video that when you drop an altitude from the vertex to the base that it is perpendicular to the base.would n't that be the same thing as the angle bisector in this particular case or does that only apply to an equilateral triangle ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . | in triangle abc , if p is the point where the bisectors of < b and < c meet , what is the measure of < bpc ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | we know that these two angles are congruent to each other , but we do n't know whether this angle is equal to that angle or that angle . we do n't know . we ca n't make any statements like that . | does anyone know how to find the length of bd when given the other side lengths ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so these two angles are going to be the same . but this angle and this angle are also going to be the same , because this angle and that angle are the same . this is a bisector . | hey , i think he could have easily abd congruent to a bdc ... since bd is an angle bisector of angle abc ... angle abd congruent to angle bdc.. also angle bda congruent to angle bdc.. ( 90 degrees ) and if two angles are congruent then third angle is also congruent to each other since sum of the angles are 180 degrees ... |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | if we want to prove it , if we can prove that the ratio of ab to ad is the same thing as the ratio of fc to cd , we 're going to be there because bc , we just showed , is equal to fc . but let 's not start with the theorem . let 's actually get to the theorem . so fc is parallel to ab , [ ? | is there any videos on triangle midsegment theorem and proportionality theorem ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . and let me call this point down here -- let me call it point d. the angle bisector theorem tells us that the ratio between the sid... | so technically the angle bisector forms a line that intersects the base and forms 2 right triangles ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | and we 're done . we 've just proven ab over ad is equal to bc over cd . so there 's two things we had to do here is one , construct this other triangle , that , assuming this was parallel , that gave us two things , that gave us another angle to show that they 're similar and also allowed us to establish -- sorry , i ... | what would happen if you put ad/ab first ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so i could imagine ab keeps going like that . fc keeps going like that . and line bd right here is a transversal . | when drawing segment fc do you have to construct that ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . | what is the proof that medians of a triangle are concurrent please tell me ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | and unfortunate for us , these two triangles right here are n't necessarily similar . we know that these two angles are congruent to each other , but we do n't know whether this angle is equal to that angle or that angle . we do n't know . | how do we know those two angles are equal ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . and let me call this point down here -- let me call it point d. the angle bisector theo... | is n't the angle bisector theorem same as the basic proportionality theorem by thales ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so by similar triangles , we know that the ratio of ab -- and this , by the way , was by angle-angle similarity . want to write that down . so now that we know they 're similar , we know the ratio of ab to ad is going to be equal to -- and we could even look here for the corresponding sides . | do you need to write a line over the letters ? |
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an... | so these two angles are going to be the same . but this angle and this angle are also going to be the same , because this angle and that angle are the same . this is a bisector . | what if the angle bisected is in a quadrangle ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | but anyway , now we are ready to add a significant entry into our table of laplace transforms . and that is that the laplace transform -- i had an extra curl , there . that was unecessary . | is it possible to do the laplace transform of tan at ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . | i still have n't seen the other laplace transform videos , but since the laplace transform is an integral operator , you can use some of it properties like : l { e^ ( iat ) } =l { cos ( at ) +i*sin ( at ) } =l { cos ( at ) } +il { sin ( at ) } , and solvig the real part for the cossine and the immaginary part for the s... |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | but anyway , now we are ready to add a significant entry into our table of laplace transforms . and that is that the laplace transform -- i had an extra curl , there . that was unecessary . | what laplace transform for tsin ( at ) ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | if this had a t here , i would have to somehow get them back on the other side . because the t 's are involved in evaluating the boundaries , since we 're doing our definite integral or improper integral . so let 's evaluate the boundaries now . | is n't the whole point of using y= ( the integral expression ) to avoid evaluating that entire integral ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | but anyway , now we are ready to add a significant entry into our table of laplace transforms . and that is that the laplace transform -- i had an extra curl , there . that was unecessary . | how can we solve [ t ] , the bracket function by using laplace transform ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . | is there a condition for the result to be true ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | so let 's backtrack . maybe this is n't a negative number ? let 's see , infinity , right ? | is it possible to figure out the laplace transform of n^t ( l { n^t } ) , where n is a positive integer ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | so let 's backtrack . maybe this is n't a negative number ? let 's see , infinity , right ? | could n't you solve using the complex expansion of sin x ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did integration by parts once , then i did integration by parts twice . i said , you know , do n't worry about the boundaries of the integral right now . | are there any specific signs when doing a laplace transform that would indicate that the problem requires two integration by parts ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | and if you 're curious , you can graph it . this kind of forms an envelope around these oscillations . so the limit , as this approaches infinity , is going to be equal to 0 . | why did the `` a '' dissapear in the equation in the brackets around ? |
welcome back . we were in the midst of figuring out the laplace transform of sine of at when i was running out of time . this was the definition of the laplace transform of sine of at . i said that also equals y . this is going to be useful for us , since we 're going to be doing integration by parts twice . so i did i... | and let 's see if we can simplify this . so let 's factor out an e to the minus st. actually , let 's factor out a negative e to the minus st . so it 's minus e to the minus st , times sine of -- well , let me just write 1 over s , sine of at , minus 1 over s squared , cosine of at . | why does sal factor out -e^ ( -st ) and not ( -e^ ( -st ) ) /s ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . | when do you write only one inequality out of the two inequalitys ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . | when would you ever use the compound inequalities ( or ) shown in the video ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | now , to isolate the z , we could just divide both sides of this inequality by negative 3 . but remember , when you divide or multiply both sides of an inequality by a negative number , you have to swap the inequality . so we could write negative 3z . | why do you have to flip the inequality sign when you multiply or divide by a negative number ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | so even 4 works . so it 's really the entire number line will satisfy either one or both of these constraints . | so sal is saying that the numbers that are on the section of the number line where the inequalities overlap can be used to satisfy both inequalities ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . | in terms of inequalities and compound inequalities , how do you define the terms `` constraint '' , `` condition '' , `` solution '' , and `` set '' ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | we 're going to divide it by negative 3 . but we 're going to swap the inequality . so the less than or equal will become greater than or equal to . | why does he swap the inequality ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . | has anyone ever seen compound inequalities on the new 2016 sat exam ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . | what is the difference between the union and the intersection of inequalities ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | so it 's everything greater than that . so what we see is we 've essentially shaded in the entire number line . every number will meet either one of these constraints or both of them . | how could the whole number line be shaded ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | look at ? ] the other one over here . we have negative 3z is less than or equal to 18 . | will 1 million fit one of the equalities ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . | are the circles in place of brackets and parenthesis ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . | and what is the symbol for indicating an average ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . | would it be appropriate to answer the question with z being ( - infinity , + infinity ) given all values can satisfy the condition of or ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . | can you show us an `` and inequalities '' instead of an `` or in equalities '' ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | and so we get z is less than 20/5 . z is less than 4 . now , this was only one of the conditions . | so is the answer technically either `` z < 4 or z > 6 '' or `` all values of x are solutions '' ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . | when i am solving compound inequalities , when do i flip the sign ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . | why does sal keep changing the colors ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | but we 're going to swap the inequality . so the less than or equal will become greater than or equal to . and so these guys cancel out . | how do i type a less than or equal too sign ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | we have negative 3z is less than or equal to 18 . now , to isolate the z , we could just divide both sides of this inequality by negative 3 . but remember , when you divide or multiply both sides of an inequality by a negative number , you have to swap the inequality . so we could write negative 3z . we 're going to di... | lets see -5y+7 > 27 or 7y-16 < = -34 that is a compound inequality now why are the rules like this multiply/divide positive by positive = do n't swap inequality multiply/divide negative by positive = do n't swap inequality multiply/divide positive by negative = swap inequality multiply/divide negative by negative = swa... |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . | so an or will always be all values of x ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | and then negative 6 . we have 1 , 2 , 3 , 4 , 5 , 6 . that 's negative 6 over there . | in how come we do n't multiply by -1 to make -3p a positive and flip the inequality ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | but remember , when you divide or multiply both sides of an inequality by a negative number , you have to swap the inequality . so we could write negative 3z . we 're going to divide it by negative 3 . | is there any way to write an or equation using interval notation ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | and so we get z is less than 20/5 . z is less than 4 . now , this was only one of the conditions . | are n't you supposed to put the lines in between the grader and less than signs ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . | when do schools usually do compound inequalities ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | but we 're going to swap the inequality . so the less than or equal will become greater than or equal to . and so these guys cancel out . | on a number line , would there be a combined open and closed circle if the solution was x is greater than or equal to 2 or x is less than 2 ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . | how would you solve a compound inequality when the two possible z intervals are separate ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | and then negative 6 . we have 1 , 2 , 3 , 4 , 5 , 6 . that 's negative 6 over there . | if 2 < a < 5 , and 3 < b < 6 , what are the possible values of a + b ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | let 's plot these . so there 's a number line right over there . let 's say that 0 is over here . | what does the number line have to do with the problem ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | let 's plot these . so there 's a number line right over there . let 's say that 0 is over here . | how do you use the number line ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | look at ? ] the other one over here . we have negative 3z is less than or equal to 18 . | what do you do if one of the numbers is irrational ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . | does the inequality still change ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | let 's plot these . so there 's a number line right over there . let 's say that 0 is over here . | how do we know when to include a number in plotting a number line ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | and this one boils down to this . so our solution set -- z is less than 4 or z is greater than or equal to negative 6 . so let me make this clear . | what is the solution in interval notation ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | we have 1 , 2 , 3 , 4 is right over there . and then negative 6 . we have 1 , 2 , 3 , 4 , 5 , 6 . that 's negative 6 over there . | i have ( -infinity,4 ) ; [ -6 , infinity ) , is there a union sign in between ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just look at this . | when do you know when to switch the sign ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | and so our left-hand side is just going to be 5z . plus 7 , minus 7 -- those cancel out . 5z is less than 27 minus 7 , is 20 . so we have 5z is less than 20 . | what do i do when 5z + 7 is in the middle of two inequality symbols ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . | can someone point out a real-life example of an `` or '' inequality ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | negative 3 times 4 is negative 12 , which is less than 18 . so it meets this constraint , but it wo n't meet this constraint . because you do 5 times 4 plus 7 is 27 , which is not less than 27 . | how does the first inequality not meet the constraint ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . | what is the interval notation for the or inequalities ? |
solve for z . 5z plus 7 is less than 27 or negative 3z is less than or equal to 18 . so this is a compound inequality . we have two conditions here . so z can satisfy this or z can satisfy this over here . so let 's just solve each of these inequalities . and just know that z can satisfy either of them . so let 's just... | so 4 meets this constraint . so even 4 works . so it 's really the entire number line will satisfy either one or both of these constraints . | is there even interval notation if it is an 'or ' problem ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | - [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . | why are we using the division sign ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | well this fraction has cheese , but it also has olives so we wo n't count that . then we have one , two , three , three fractions three of these equal pieces have only cheese so we could say three out of a total of four pieces of . . | how do you use division with fractions ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | and lets say on this fourth slice , i have cheese and , i do n't know , i have olives i have olives right over here . so we can ask ourselves , `` what fraction of this pizza has olives on it ? '' well , we have four total slices . they all are equal slices . | 2/3 scooter ,3/4cycle.total vehicles are 4836.what fraction of vehicle are cars ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | i have a lemon . just like that . and let 's say that i have an apple . | how would you divide a negative number as a fraction like -32 over 128 ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | - [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . | is 3/6 = to 9/18 ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? | what do you think of fractions ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | just like that . and let me divide it into let me divide it into 5 equal pieces 1 one , two , three , four that does n't look too equal . so the whole point is to do it equal , one , two , three , four that looks pretty close . | speaking of infinity , how many fractions are between 1 and 2 ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | .is yellow ? '' `` what fraction of my fruit as drawn is yellow ? '' well , we could say , we have a total of one , two , three , four , five pieces of fruit so there 's a total of five pieces of fruit . | how can you simplify a fraction ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | and let 's say that i have an apple . i 'll draw . . | what do you use to draw ? |
- [ sal ] what i want to do in this video is think about the idea of a fraction . and for the sake of this video as we just learn what a fraction is , you can really think of it as a part of a whole . later on we 'll think of it in even more ways . what do i mean by a part of a whole ? so let 's imagine that we have a ... | i 'm gon na try my best to draw a circle right over here . and let 's say that i divided into four equal parts so just like that i 've divided it into two equal parts and now i will divide it into four equal parts . so there 's a total of four slices , four equal slices of this pizza . | so why 25 equal parts ? |
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