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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 ?