To compare fractions you need a common denominator, then you can make a
comparison. You would divide the number line between 0 and 1 (or any 2
whole numbers on the number line) based on that common denominator. For
example... if you were trying to compare 3/4 and 2/8, you would find
the common denominator (in this case 8) and convert the fractions...
3/4 = 6/8
2/8 stays as 2/8
Now
you would go to the number line between 0 and 1 and divide it into 8
equal pieces. 3/4 would go over the 6th division and 2/8 would go over
the second division.
That would give you a good visual that 2/8 < 3/4
[ / / / / / / / ]
0 2/8 3/4 1
Stokes' theorem equates the line integral of 
along the curve to the surface integral of the curl of over any surface with the given curve as its boundary. The simplest such surface is the triangle with vertices (1,0,1), (0,1,0), and (0,0,1).
Parameterize this triangle (call it 
) by
with 
and 
. Take the normal vector to to be
Divide this vector by its norm to get the unit normal vector. Note that this assumes a "positive" orientation, so that the boundary of is traversed in the counterclockwise direction when viewed from above.
Compute the curl of :
Then by Stokes' theorem,
where
The integral thus reduces to
Answer: 13 units is the distance between the points.
Answer:
About 3.36 feet or about 40.3 inches
Step-by-step explanation:
The tangent ratio tells you ...
Tan = Opposite/Adjacent
In this geometry, we want ...
tan(50°) = (4 ft)/(distance)
Solving for distance gives ...
distance = (4 ft)/tan(50°) ≈ 3.3564 ft ≈ 40.28 in
The steps need to start about 3.36 feet, or about 40.3 inches, out from the house.
