I've attached a plot of the intersection (highlighted in red) between the parabolic cylinder (orange) and the hyperbolic paraboloid (blue).
The arc length can be computed with a line integral, but first we'll need a parameterization for
. This is easy enough to do. First fix any one variable. For convenience, choose
.
Now,
, and
. The intersection is thus parameterized by the vector-valued function
where
. The arc length is computed with the integral
Some rewriting:
Complete the square to get
So in the integral, you can substitute
to get
Next substitute
, so that the integral becomes
This is a fairly standard integral (it even has its own Wiki page, if you're not familiar with the derivation):
So the arc length is
Answer:
42 square feet
Step-by-step explanation:
the smaller square at the bottom
3 x 2 = 6 square feet
the larger square
3 x11 = 36
add the two areas together
36+6 = 42
Answer:
d
Step-by-step explanation:
it's the only one that isn't a trend
The answer is 2 dawgy dawg
Answer
16/9
Step-by-step explanation:
I don't know if this is right or not and I'm sry if its wrong
but 16/9 divided by 4 = 9/4