The sum of interior angles in a triangle is 180°
42° + 67° + other angle = 180°
109° + other angle = 180°
other angle = 180° - 109°
other angle = 71°
The measure of the other angle is 71 degrees
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:
Step-by-step explanation:
another way to express 52+24 is 4(13+6)
The answer is 492.307
The number after the thousandths is 9 - greater than 5 - so we round 6 up to 7.
Bracelet
There are 2 bracelets and she possibly picks three. :)