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
No because there are 20 multiplied by 3 is 60. So the answer would be 60+144=204x12=2448 but the last answer was still correct
Answer:
P = 1 3
Q = 1 6 8 3
Step-by-step explanation:
through factorization of 21879
You need to up your points if you want anyone to answer.
Answer:
d. 72 in³
Step-by-step explanation:
To find the volume of a cylinder that a cone of volume 24 cubic inches fits in exactly inside of, we will follow the steps below:
From the question volume of the cone = 24 cubic inches
volume of a cone = πr²h
and volume of a cylinder = πr²h
This implies
volume of a cone = πr²h
= (volume of a cylinder)
volume of a cone = (volume of a cylinder)
24 = (volume of a cylinder)
multiply both-side of the equation by 3
24×3 = (volume of a cylinder)
72 =volume of a cylinder
Therefore volume of the cylinder that the cone fits exactly inside of is 72 cubic inches