00:01
So in this question, they say that the formula for wind chill c in degrees fahrenheit is given by c equals 35 .74 plus 0 .6215t minus 35 .75 v to the point 16 power plus 0 .275 tv to the power of 0 .16, where v is the wind speed in miles per hour and t is the temperature in degrees fahrenheit.
00:27
The wind speed is 19 plus or minus 3 miles per hour, and the temperature is 8 degrees plus or minus 1 degree.
00:37
I want to use dc to estimate the maximum possible propagated error and relative error in calculating the windshield, everything rounded to 4 decimal places for dc and 2 decimal places for dc oversee.
00:55
So let's start with dc.
00:58
What's my formula for dc? my formula for dc is the partial derivative of c with respect to t times dt, plus the partial derivative of c with respect to v times dv.
01:17
So what's my partial derivative of c with respect to t? that would be 0 .6215 plus my derivative with respect to t.
01:33
0 .4275 v to the power of 0 .16, and this is times d t.
01:44
Plus what's my partial derivative with respect to v? well i'm going to have to multiply down.
01:51
So 35 .75 times 0 .16 is 5 .72.
01:58
So negative 5 .72 v to the power of negative 0 .72 of negative 0 .84.
02:08
And then it's plus i need 0 .4275 times 0 .16 and i'm getting 0 .0684.
02:20
So 0 .0684 t v to the power of negative 0 .84, all of this dv.
02:34
So now i'm going to start plugging in.
02:37
My v this.
02:38
Time is 19 and my t is 8.
02:45
So let's see, what does that make this first piece? i'm getting 0 .6215 plus 0 .4275 times my v was 19, so times 19 raised to the power of 0 .16.
03:09
1 .3062.
03:12
So i'm getting 1 .3062 times dt.
03:20
Plus, now what do we have? we've got, and by the way, let me store that number as a, just so i can bring it back later.
03:30
I'm going to store that guy as a.
03:33
Now my second number is going to be negative 5 .72 times v.
03:40
My v is 19 raised to the power of negative 0 .84 and then it's going to be plus 0 .0684 times t t is 8 times 19 raised to the power of negative 0 .84 so that's negative 0 .436 negative 0 .436 follow this dv.
04:18
Now i'm going to store that number as b.
04:25
Now, if i want my maximum propagated error, what's my dt? well, they said that the maximum error in the temperature was 1 degree celsius.
04:39
And the maximum error in the velocity of the wind was 3 miles per hour.
04:45
But i don't want to make this 3...