00:01
Number 60, the body mass index, bmi, is a number that can be calculated for any individuals as follows.
00:10
Multiply a person's weight by 703 and divided by the person's height squared, that is v equals 703w over h square where w is in pounds and h is in inches.
00:24
The national hurt longs and blood institute uses the body mass index to determine where the person is, overweight where b is bigger or equal than 25 and smaller than 30.
00:40
You call it overweight and if b is bigger or equals than 30 is abyss.
00:45
So first calculate the body mass index for st.
00:49
Louis rams offensive taco jackal.
00:53
This guy's name is long.
00:55
Who weighs 317 pound and is 6, 5, 7, 7 ,000.
01:02
Inches tall okay we just need to plug that into the formula right so a we have seven hundred wait three hundred seventeen pounds sorry and six food seven inches tall which is six multiple twelve plus seven equals seventy light inches so the body index for this guy is 703 multiplied pound 317 divided by 709 square so we got 703 703 multiply 7 317 divided by 709 divided by 70 lie equals 35 .7076 so that's his body mass which is it's bigger than 30, way bigger actually.
02:15
So this guy, you're obese.
02:18
Okay, so problem two, part b, we want to find parts of derivatives with respect to doubling and h.
02:25
So this part, so db over dw, recall b equals 7 over 3 w over h square.
02:37
So h is constant now.
02:39
You've got this constant, multiply w so parts derivative is this part.
02:47
So db over the h.
02:50
Now this equals constant, this part.
02:54
So h negative 2, if we write it like this.
02:58
So 703w, this part derivative is negative 2h to the negative 3.
03:04
So negative 1 ,400 .6wh negative okay, this is part b.
03:16
For part c, use the fact that one inch equals 0 .0254 meter and 1 pound equals 0 .453, 6 kilograms.
03:30
Transfer this formula to handle metric units.
03:33
Okay, so we got 1 inch equals 0 .0254 meter...