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
15.6 oz i believe. 3/4 is equal to 75% .75x20.8oz = 15.6
Answer:
Step-by-step explanation:
Answer:
6,0
Step-by-step explanation:
the dilation moves points from A to B
in this case we're moving point T
point T has coordinates 2,0 to start with (A)
Now let's move it to B
To do so, we need to apply the calculation
(x,y) => (3x,3y)
Substitute in point T:
(2,0) => (3x,3y)
(2,0) => (3(2),3(0))
(2,0) => (6,0)
Answer:
(x + 12)² + (y + 32)² = 1031
Step-by-step explanation:
137 + 64y = -y² - x² - 24x
Arrange the terms in descending powers of x and y.
x² + 24x + y² + 64y = -137
Complete the squares for x and y
(x² + 24x + 144) + (y² + 64y + 1024) = -137 + 144 + 1024
Write the equation as the squares of binomials of x and y
(x + 12)² + (y + 32)² = 1031
This is the equation of a circle with centre at (-12, -32) and radius r = √1031.