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:
A. (-∞, ∞)
Step-by-step explanation:
f circle g (x) is another way of expressing f(g(x)). Basically, we have to plug g(x) into f(x) wherever we see x's.
f(x) = x^2 - 1
f(x) = (2x-3)^2 - 1
Now find the domain. I think the easiest way to do this is to graph it. I've attached the graph. You can also do it algebraically by thinking about it: it's a positive parabola (+x^2) and its minimum is -1, so its range will not be all real numbers, but its domain will certainly be. (The range would be answer choice B!)
Domain = (-∞, ∞)
Answer:
Here is your answer
Step-by-step explanation:
3.(x+3)(x+5)
4.(x-8)(x+8)
5.(x+6)^2
Answer:
€4.20
Step-by-step explanation:
the have a 5 in 26 chance in winning so 26(letters in alphabet) - 5(vowels) =21
21÷5 =4.2
Answer:
(147.50 - 22.5)/.25
Step-by-step explanation:
First subtract his portion of the $90. Which is $22.5, when subtracted from 147.5 you get $125. Now divide $125 by .25 cents and you get the amount of megabytes he downloaded.