Answer:
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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
As x approaches infinity the value of the function Y approaches infinity. There is a vertical asymptote at x = 0 (Solve denominator for x) and since the degree of the numerator is greater than the denominator there are no horizontal asymptotes. You can simplify the limit by merging the expression into (x^4 + 1)/x^2 and dropping the one and simplifying to x^2 which in x^2 as x approaches infinity Y approaches infinity. Hope that helps!
Answer:
The measure of minor arc AD in degrees is = 42 degrees.
Step-by-step explanation:
The line AB is the diameter of the circle. This also implies that the line dive=ides the circle into two equal halves.
The angle subtended by the diameter of a circle is 180degrees.
This means that angle APD + DPG + CPB = 180 degrees
Already, we can infer that angle DPC = 90 degrees because of the rectangular symbol drawn around point P
Hence we can have
(7x + 1) + 90 +(9x - 7) = 180
16x = 96
the value of x is = 96/16 = 6
we can now plug the value of x into tha expression for the value of angle APD = (7(6) +1) = 42 degrees
Hence APD = 42 degrees.
The measure of minor arc AD in degrees is = 42 degrees.
The answer is A: because 3x • 4x = 12x^2; 3x • 3 and -2 • 4x make 9x-8x which is just x; and -2 • 3 is -6