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( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . dr. zucker : we 're in this long room th... | ( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . | how old are these buildings ? |
( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . dr. zucker : we 're in this long room th... | look , for instance , at the large male figure in the lower left , and the way his shoulder comes out towards us . that 's not something that you would see in those more decorative paintings by botticelli . so , i think we should n't be taking these paintings too seriously . i mean , they 're a beautiful expression , o... | how old are the paintings ? |
( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . dr. zucker : we 're in this long room th... | dr. harris : the figures in the background move in opposing directions . dr. zucker : for all that movement , this is not a baroque painting . this is a high renaissance painting , and so there is still a sense of clarity and order . | where is polyphemus in the painting ? |
( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . dr. zucker : we 're in this long room th... | i think `` fabulously wealthy '' would be more appropriate . the most famous painting in the villa is by raphael : galatea . dr. harris : galatea was a sea nymph . she was chased in the scene by polyphemus , the one-eyed giant who makes an appearance in homer 's odyssey , but also in other mythic stories . | what was galatea doing on the island of polyphemus ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and i go in the future , and in 40 years , they tell me it 's actually gone up . my blood pressure is now 150 over 90 . and in fact , i go again , when i 'm 101 , and they say it 's 180 over , let 's say , 105 . | why is keeping our blood pressure in normal range so important for our health ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . | what is the main cause ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and that 's based on the fact that i 'm about 70 kilos . and my heart rate is about 70 , very relaxed heart rate . and let 's assume , just as we did with the mean venous pressure , that that does n't change . | really heart rate desnt change over time ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | so blood , as it 's flowing through , is having a tougher time getting through because the radius is smaller in these spots . and , as you know , if you calculate total resistance -- and that 's what , actually , this is , total resistance -- the total resistance will start to slowly climb up . and in this case , maybe... | as plaque builds up in the circulatory system and reduces the radius part of the resistance equation , can the body adjust other variables in the resistance equation to try and maintain a specific resistance ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and right now , i have , let 's say , a stroke volume -- i 'll write it up here -- stroke volume , meaning each time my heart beats , about 70 milliliters of blood go out . so each time my heart beats , it sends out to the rest of the body 70 ml of blood . and that 's based on the fact that i 'm about 70 kilos . | for example will the body reduce blood viscosity ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and so , because it 's filled up the vessels , now here , my radius got smaller . my vessel radius in here got smaller . and over here , it got smaller . | or will the body increase the radius of other capillaries or arterioles to try and offset the effects of a plaque ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and i go in the future , and in 40 years , they tell me it 's actually gone up . my blood pressure is now 150 over 90 . and in fact , i go again , when i 'm 101 , and they say it 's 180 over , let 's say , 105 . | doesnt the tissues like muscles or fat around the vessel apply pressure on ir , blocking it or increasing blood pressure ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | so blood , as it 's flowing through , is having a tougher time getting through because the radius is smaller in these spots . and , as you know , if you calculate total resistance -- and that 's what , actually , this is , total resistance -- the total resistance will start to slowly climb up . and in this case , maybe... | is the viscosity of the blood also a factor when talking about resistance , or is it irrelevant ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | i 've got the future me with a cane at the age of 71 . and i 've got the really old version of myself living at a ripe , old age of 101 , waving , in fact . so three versions of myself . | does age really matter as much ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and that 's why my resistance was 18 . blood is flowing through very smoothly . it 's going out this way to feed the kidney and maybe to my ears and my eyes and my foot . | do your blood vessels stretch the tissue over timer ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | now let me change colors to figure out my q , my flow . and right now , i have , let 's say , a stroke volume -- i 'll write it up here -- stroke volume , meaning each time my heart beats , about 70 milliliters of blood go out . so each time my heart beats , it sends out to the rest of the body 70 ml of blood . | the stroke volume / body weight ratio can be applied so easily to 100 years old people ( no change in this relationship ) or was that a simplification ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and i go in the future , and in 40 years , they tell me it 's actually gone up . my blood pressure is now 150 over 90 . and in fact , i go again , when i 'm 101 , and they say it 's 180 over , let 's say , 105 . | does blood pressure really change over time ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | now let me change colors to figure out my q , my flow . and right now , i have , let 's say , a stroke volume -- i 'll write it up here -- stroke volume , meaning each time my heart beats , about 70 milliliters of blood go out . so each time my heart beats , it sends out to the rest of the body 70 ml of blood . | why does blood volume in pregnancy increase but the systolic and diastolic bp drop ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | so blood , as it 's flowing through , is having a tougher time getting through because the radius is smaller in these spots . and , as you know , if you calculate total resistance -- and that 's what , actually , this is , total resistance -- the total resistance will start to slowly climb up . and in this case , maybe... | does n't the resistance go up even if you do exercise and eat healthfully , or do some 101 year olds have the same resistance as when they were 31 ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | i 've got the future me with a cane at the age of 71 . and i 've got the really old version of myself living at a ripe , old age of 101 , waving , in fact . so three versions of myself . | if the resistance is higher in the healthy 101 year old , is the cause still plaque ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and i go in the future , and in 40 years , they tell me it 's actually gone up . my blood pressure is now 150 over 90 . and in fact , i go again , when i 'm 101 , and they say it 's 180 over , let 's say , 105 . | what is the blood pressure of people over 50 suppose to be ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . | are you implying that atherosclerosis is the cause to hypertension ? |
let 's imagine that i 'm here . and this is me at the age -- actually , i 'll do this right now -- so let 's say at the age of 31 . and then i go into the future . so this is a line for the present . and then i go into the future . and this is me again . and this is now at the age of 71 . so i 've got 40 extra years . ... | and in the previous slide here , we actually can see now that as the resistance goes up , assuming that the other things kind of stay the same , your blood pressure can go up . and so when you hear , in the doctor 's office , that you have a blood pressure of a certain number over a certain number , that 's one thing t... | what causes the diastolic number to increase above 60 ? |
jill just received $ 40 . the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . then we can use that table to actua... | so let 's make that our y-axis , or in this case it 's the number of dollars she has . and let 's make this my x-axis . this is our x-axis . and we only need to focus on the first quadrant . | when sal makes the graph , does n't the x and y-axis have to have the same increments ? |
jill just received $ 40 . the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . then we can use that table to actua... | the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . | but taking the graph takes much time than substituting the value of `` x '' in the equation.so , what is the use of solving with graph ? |
jill just received $ 40 . the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . then we can use that table to actua... | so this is -- let me do it , i 'll do that same yellow color -- so this is after 2 days , this is 4 days , this is 6 days , this is 8 days . we could keep going if we like . so after 0 days , so this right over here , after 0 days , she has $ 40 . | is there anyway i can know which way is easier like sal always does ? |
jill just received $ 40 . the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . then we can use that table to actua... | we could actually just , if we had a nice ruler , we could just connect two of those , and we would have the line . but our line looks something -- let me do this in a new color -- our line would look something like that . that shows how much she has after every day . | do you stop the line at the constraint with a circle or dot instead of putting the arrow at the end of the line ? |
jill just received $ 40 . the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . then we can use that table to actua... | so then at 2 days , how much money will she have ? well , it 's going to be 40 minus 2 times -- i 'll do the same order -- minus 2.5 times 2 . 2.5 times 2 is 5 . so 40 minus 5 is $ 35 . after 4 days , it 's going to be 40 -- let me do this in a different color , so when i plot the points , you 'll see where i got my in... | so i know the 40 is from the $ 40 dollars , where is the 2.5 from ? |
jill just received $ 40 . the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . then we can use that table to actua... | let 's actually graph the equation , see it visually . so let me draw some axes here . this will be a hand-drawn graph , but i think it 'll get the job done . | when sal drew the graph , why is it okay to draw different values for the tick marks on the x and y axes ? |
jill just received $ 40 . the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . then we can use that table to actua... | well , it 's going to be 40 minus 2 times -- i 'll do the same order -- minus 2.5 times 2 . 2.5 times 2 is 5 . so 40 minus 5 is $ 35 . | how do you calculate simple things like 2.5 x 6 and 2.5 x 8 in your head ? |
jill just received $ 40 . the number of dollars she has left , y , after x days , is approximated by the formula y is equal to 40 minus 2.5x . graph the equation and use the graph to estimate how much money jill will have 8 days later . so let 's just make a table of x and y values . then we can use that table to actua... | let me mark off the y-axis in increments of 10 first . so this would be $ 10 , this would be $ 20 , this would be $ 30 , this would be $ 40 . and then i could do the $ 35 , the $ 25 , the $ 15 , and then the $ 5 . | if you had not told me what was x and what was y , how would i know ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . | the narrators voice belongs to whom ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | it refers to the bluish tinge of the vagina and the cervix . and eventually , actually , an examiner can feel the presence of the fetus . so , there is this maneuver where the examiner can insert their finger through the vagina and gently tap upwards , which causes the fetus to rise . | what would make the answering bounce on the examiner when ballottmenting if not the fetus ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | so there have been a few studies that have shown that a urine pregnancy test is pretty much as accurate as a blood test , but it 's improper usage or not correctly following instructions at home that tend to result in an inaccurate home pregnancy test . and you might be wondering why a positive pregnancy test is n't a ... | why is n't the ballottement a positive sign of pregnancy ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | what is the scientific explanation for how ( in 70 % of all cases according to the study mentioned in the video ) pregnant women 's urine makes either barley or wheat sprout depending on the unborn child 's sex ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | but that 's not necessarily true . so there have been a few studies that have shown that a urine pregnancy test is pretty much as accurate as a blood test , but it 's improper usage or not correctly following instructions at home that tend to result in an inaccurate home pregnancy test . and you might be wondering why ... | so you can then use a pregnancy test to test if you have cancer ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | and you might be wondering why a positive pregnancy test is n't a positive sign of pregnancy . why is it a probable sign of pregnancy ? and it 's because you can actually have a false positive pregnancy test . | why is the chadwick 's and goodell 's sign considered a probable sign and not a positive sign ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | and that event , that event where the follicle ruptures and releases the egg inside of it , is referred to as ovulation . after ovulation , the egg that 's released travels down the fallopian tube , hopefully to find a sperm to fertilize it . but meanwhile , this ruptured follicle that 's left behind over here , which ... | what is fallopian tube cancer ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | so there have been a few studies that have shown that a urine pregnancy test is pretty much as accurate as a blood test , but it 's improper usage or not correctly following instructions at home that tend to result in an inaccurate home pregnancy test . and you might be wondering why a positive pregnancy test is n't a ... | will the pregnancy test be positive when done with male urine sample ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | but meanwhile , this ruptured follicle that 's left behind over here , which is now referred to as the corpus luteum , so the corpus luteum takes this sort of waiting period while it 's sitting around waiting for the egg to be fertilized to start producing lots of progesterone . so progesterone is another hormone that ... | in the corpus luteum , how are the hormones ( estrodiol and progesterone ) produced ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | after ovulation , the egg that 's released travels down the fallopian tube , hopefully to find a sperm to fertilize it . but meanwhile , this ruptured follicle that 's left behind over here , which is now referred to as the corpus luteum , so the corpus luteum takes this sort of waiting period while it 's sitting aroun... | also , is the corpus luteum a living , dying , or dead structure during this period ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . | why can periods be light or heavy ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | so one of these follicles is selected to grow and develop . and as it does that , as it grows and develops , it secretes hormones , specifically estradiol , so it specifically secretes estradiol , which is a type of estrogen . and that estradiol acts on the uterus and it causes this inner lining of the uterus , the end... | does the estradiol sometimes makes more than usual ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | so the hyper pigmentation of the face is called melasma , and a lot of people refer to it as the mask of pregnancy . so you can see dark , blotchy spots on the face which typically go away within a year after the pregnancy is over , but still it can be a sign early on in the pregnancy . linea nigra is another manifesta... | but why do some pregnancy go unnoticed ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | so there have been a few studies that have shown that a urine pregnancy test is pretty much as accurate as a blood test , but it 's improper usage or not correctly following instructions at home that tend to result in an inaccurate home pregnancy test . and you might be wondering why a positive pregnancy test is n't a ... | a woman has taken two pregnancy tests at home and they both were positive , can this be considered a false positive ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | but that 's not necessarily true . so there have been a few studies that have shown that a urine pregnancy test is pretty much as accurate as a blood test , but it 's improper usage or not correctly following instructions at home that tend to result in an inaccurate home pregnancy test . and you might be wondering why ... | if the urine pregnancy test can have a false result because of some cancers that produce hcg , can it be used as a cancer test ? |
in ancient egypt , women who questioned whether they were pregnant or not were told to urinate on bags of wheat and barely over the course of several days . and if the wheat sprouted , the woman was having a girl and if the barley sprouted , she was having a boy , and if neither sprouted , she was n't pregnant . so i ... | so if the examiner feels an enlarged uterus , that 's a pretty big clue that the woman might be pregnant . and of course a positive pregnancy test is another big sign . so most pregnancy tests , whether they 're blood tests or whether they 're urine tests , detect beta hcg , they detect that human chorionic gonadotropi... | and is there another cause for false positive tests besides cancer and wrong usage ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | but you 're having , at least at the coastline , the air is roughly the same temperature over both and , although there will be some variation , and they 're getting the same amount of sunlight . but since water has a higher specific heat , that heat is going to warm up water less . so this is going to get less hot . | why does water radiate less heat ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | that 's because water has a higher specific heat . so higher , higher , relatively higher specific heat . specific heat . | why is spacific gravity of liquids is higher than the spacific gravity of solids ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so the last thing you might be wondering is , well why does water have such a high specific heat ? well that goes back to our good old friend , the hydrogen bond . because , if we 're talking about a solid substance , if we 're talking about a solid substance , and i 'll just draw a generic solid substance . | is there a possibility that the former hydrogen electron goes to the more electronegative atom , thus making them separate ionized atoms instead of a single polar molecule ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . lower specific heat . so two ways you could think about it . | so , how is it possible that sand has a lower specific heat than water , when sand is thicker ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | i 'm going to need more heat here to raise this one degree celsius than to raise that . that 's because water has a higher specific heat . so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | i 'm not sure i understand this , so basically , water has a higher specific heat because the bonds between the oxygen and hydrogen are more temporary than the molecules in sand ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | but you 're having , at least at the coastline , the air is roughly the same temperature over both and , although there will be some variation , and they 're getting the same amount of sunlight . but since water has a higher specific heat , that heat is going to warm up water less . so this is going to get less hot . | when you increase the heat of water does n't it lessen the amount of water , so how is it possible to add calories to it to raise the heat , if it keeps getting smaller ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | but you 're having , at least at the coastline , the air is roughly the same temperature over both and , although there will be some variation , and they 're getting the same amount of sunlight . but since water has a higher specific heat , that heat is going to warm up water less . so this is going to get less hot . | if sand molecules are more polar than water molecules , should n't it take more heat to break up those bonds and cause the molecules to vibrate , resulting in a higher specific heat for sand than water ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | i dont get the intuition of the calories in the food , how can an ice cream molecules can become heat ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | and that 's actually what temperature is . it 's really average kinetic energy . when you touch something and go ooh , that 's hot , it 's really because those things are just vibrating super super super super fast . | heat is the average amount of kinetic energy in a system right ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so , for example . for example , water , water . if i wan na raise that one degree celsius , so if i wan na raise that one degree celsius , i would have to put in , i would have to put in a certain amount of , i would have to put in a certain amount of heat , which would be different than , say if i had sand . | so the sun is heating up a greater volume of water than sand per area ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so , 500 calories you see on a food label , that 's really 500 kilocalories , and that 's enough energy to raise 500,000 grams of water , remember 500 kilograms , 500,000 grams of water , one degree celsius , or 50,000 grams of water 10 degrees celsius . but anyway , water has a special name , it 's calorie . it 's nea... | what 's the difference between calorie and kilocalorie ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | why is specific heat in this case similar when gaining and losing temperature ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so , for example . for example , water , water . if i wan na raise that one degree celsius , so if i wan na raise that one degree celsius , i would have to put in , i would have to put in a certain amount of , i would have to put in a certain amount of heat , which would be different than , say if i had sand . | i wan na to ask are wierd question , if solid like metal for example , the partical inside dosnt move , and liquid like water for example the partical is moving around , when kinetic energy add in to make partical move faster to erup eachother to produce heat , will solid metal heat faster or liquid water heat faster ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | and sand , or at least relative to water , has a lower specific heat . lower specific heat . so two ways you could think about it . | if the sand has a lower specific heat , shouldnt it turn to gas or at least turn to liquid since at the same temperature , water with a greater specific heat is liquid ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | there 's one clarification . the calorie that people talk about when they 're talking about nutritional labels or how many calories are actually in food , that 's actually kilocalories . so if you see , if someone hands you a , let 's say a bowl of ice cream . | what is calorie important for in food substances ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | does specific heat have to do with metal feeling colder than wood ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | what is the value of the specific heat of water ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | you can imagine if this water molecule wants to move in this direction , it has to break this hydrogen bond , it 's gon na form another hydrogen bond , it 's got ta break that . so it needs energy to keep breaking those hydrogen bonds , overcoming the friction of those hydrogen bonds and i 'll use the friction in quote... | am i correct in thinking bonds breaking and reforming are what causes a liquid state ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | whereas , the solid substances bonds are more difficult to break , so all the heat goes towards causing vibration ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | and sand , or at least relative to water , has a lower specific heat . lower specific heat . so two ways you could think about it . | if a substance say a has lower specific heat than another substance say b , then will 10 g of a have lesser or more heat content than 10 g of b ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so , for example . for example , water , water . if i wan na raise that one degree celsius , so if i wan na raise that one degree celsius , i would have to put in , i would have to put in a certain amount of , i would have to put in a certain amount of heat , which would be different than , say if i had sand . | how does water `` know '' that it should vibrate rather than to move with ke to break the hydrogen bonds that are keep breaking and reforming ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | i do n't know what this is , let 's say it 's some type of structure that looks something like this . as it gets energy , as it gets heat energy , the heat energy just increases the kinetic energy of the actual particles . it actually just makes them vibrate more . | is there some kind of a property of atom or molecule that drives itself to behave differently when ( same amount of ) energy is received ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | but you 're having , at least at the coastline , the air is roughly the same temperature over both and , although there will be some variation , and they 're getting the same amount of sunlight . but since water has a higher specific heat , that heat is going to warm up water less . so this is going to get less hot . | why does the water store more heat as sal says at the end of the video ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | and so it 's nice to live near the water . it 's going to be less cold in the coastal areas than it would be if you 're further inland . and this phenomenon , this is frankly anywhere where you might see water , but it 's very pronounced where i live . | but why would my reaction be the same ( pulling away in pain ) when something is freezing cold ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | and sand , or at least relative to water , has a lower specific heat . lower specific heat . so two ways you could think about it . | how would some of the ways we produce and lose body heat change if water had a lower specific heat ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | but you 're having , at least at the coastline , the air is roughly the same temperature over both and , although there will be some variation , and they 're getting the same amount of sunlight . but since water has a higher specific heat , that heat is going to warm up water less . so this is going to get less hot . | why does water lose less heat ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | ok so ... the amount of heat needed to raise the temperature of one gram of a substance 1 degree c is specific heat ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | what is the difference between heat and temperature ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | one gram of a substance , one degree celsius . so this is telling us , well how much energy do i have to put into something to heat it up ? so , for example . | why does a vibrating molecule hurt us ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . | is there a chemical/physiological theory ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | can someone explain the difference between heat and temperature to me ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | you can almost imagine the friction of a hydrogen bond . you can imagine if this water molecule wants to move in this direction , it has to break this hydrogen bond , it 's gon na form another hydrogen bond , it 's got ta break that . so it needs energy to keep breaking those hydrogen bonds , overcoming the friction of... | could n't the forming of hydrogen bonds actually provide something like a magnetic force and help water molecules gain kinetic energy and break free ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | but you 're having , at least at the coastline , the air is roughly the same temperature over both and , although there will be some variation , and they 're getting the same amount of sunlight . but since water has a higher specific heat , that heat is going to warm up water less . so this is going to get less hot . | if a water molecule vibrates slower , it loses heat , but is the hydrogen bond not an all or nothing response ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . | does vibration in the molecules of a substance produce heat ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | if i wan na raise that one degree celsius , i would need a different amount . it actually turns out that i need less heat , i need less heat to raise the sand one degree celsius than i need to raise the temperature of the water or one gram of the water one degree celsius . so let 's say this is a gram of water and this... | why do you need less heat to raise the sand ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | let me write that down . this is 500 calories . if we 're thinking of it in terms of specific heat , it 's actually 500 kilocalories . | so what would be the difference of localities and calories then ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . | does vibration in the molecules of a substance produce heat ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | is having a high specific heat the same as having a high heat capacity ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so , for example . for example , water , water . if i wan na raise that one degree celsius , so if i wan na raise that one degree celsius , i would have to put in , i would have to put in a certain amount of , i would have to put in a certain amount of heat , which would be different than , say if i had sand . | in geography i saw in rise sea level saying water rise because water expend when heat , i though it expand when cold like become a ice , ice expand , but why water will expand when heat ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so it 's going to get colder here . so the land is going to get colder and the water is going to get less cold . because it works in both directions . | how warm blood animals get warm like human so our enzyme work normal , but how come there is cold blood animal ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | well that goes back to our good old friend , the hydrogen bond . because , if we 're talking about a solid substance , if we 're talking about a solid substance , and i 'll just draw a generic solid substance . so solid substance right over here . i do n't know what this is , let 's say it 's some type of structure tha... | while for molecules of solid , are the bonds also have to be broken in order to for solid molecules to move around ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so higher , higher , relatively higher specific heat . specific heat . and sand , or at least relative to water , has a lower specific heat . | is having a high specific heat the same as having a high heat capacity ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | so , for example . for example , water , water . if i wan na raise that one degree celsius , so if i wan na raise that one degree celsius , i would have to put in , i would have to put in a certain amount of , i would have to put in a certain amount of heat , which would be different than , say if i had sand . | 0 , why is the water colder than in the air ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | you can almost imagine the friction of a hydrogen bond . you can imagine if this water molecule wants to move in this direction , it has to break this hydrogen bond , it 's gon na form another hydrogen bond , it 's got ta break that . so it needs energy to keep breaking those hydrogen bonds , overcoming the friction of... | could n't the forming of hydrogen bonds actually provide something like a magnetic force and help water molecules gain kinetic energy and break free ? |
in chemistry , there 's a very valuable concept called specific heat , and specific heat is particular to a given substance . every substance has a different specific heat . it 's defined as the amount of heat , the amount of heat energy needed to raise one gram of a substance one degree celsius . sometimes the defini... | but you 're having , at least at the coastline , the air is roughly the same temperature over both and , although there will be some variation , and they 're getting the same amount of sunlight . but since water has a higher specific heat , that heat is going to warm up water less . so this is going to get less hot . | why does water radiate less heat ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | we have x plus 6 , and i 'm going to distribute this negative 1 . if i distribute the negative 1 , i have negative 1 times x is negative x . negative 1 times negative 6 is plus 6 . and then i have a negative 1 out here . | why did the negative one only go to a part of the numerator instead of being distributed onto the entire one ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | this is the exact same thing as 6 minus x if you just rearrange the two terms . negative x plus 6 is the same thing as 6 plus negative x , or 6 minus x . now you could cancel them out . | if you take ( x+6 ) ( -x+6 ) times negative one twice , wo n't you have to take ( x+6 ) times negative one twice ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | so , x could be all real numbers except 6 , because if x is 6 then you 're dividing by 0 , and then this expression is undefined . we 've stated the domain , now let 's do the simplifying the rational expression . let me rewrite it over here . | is simplifying rational expressions the same as simplifying rational equations ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | try it out . let 's multiply by negative 1 and then by negative 1 again . think of it that way . | what was the second -1 for ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | why can the domain not be imaginary number ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | let me rewrite the whole expression . we have x plus 6 , and i 'm going to distribute this negative 1 . if i distribute the negative 1 , i have negative 1 times x is negative x . negative 1 times negative 6 is plus 6 . | why do you not have to distribute the ( -1 ) onto the denominator ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | think of it that way . if i multiply by negative 1 times negative 1 , obviously , i 'm just multiplying the numerator by 1 , so i 'm not in any way changing the numerator . what happens if we just multiply the x minus 6 by that first negative 1 ? | does the rule `` what you do to the denominator , you do to the numerator '' not apply ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | the domain is a set of all x values that you could input into this function and get something that is well-defined . the one x value that would make this undefined is the x value that would make the denominator equal 0 -- the x value that would make that equal 0 . so when does that happen ? | would n't the domain be everything but -9 and -3 ? |
simplify the rational expression and state the domain . let 's see if we can start with the domain part of the question , if we can start with stating the domain . now , the domain is the set of all of the x values that you can legitimately input into this if you view this as a function , if you said this is f of x is ... | now you could cancel them out . 6 minus x divided by 6 minus x , and all you 're left with is a negative 1 -- i 'll write it out front -- times x plus 6 . if you want , you can distribute it and you would get negative x minus 6 . | could i just take the -1 out of the ( 6-x ) , and turn it into a -1* ( x-6 ) , instead of multiplying the whole equation time -1 twice ? |
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