I think the correct answer is 1/16
Let f(x) = p(x)/q(x), where p and q are polynomials and reduced to lowest terms. (If p and q have a common factor, then they contribute removable discontinuities ('holes').)
Write this in cases:
(i) If deg p(x) ≤ deg q(x), then f(x) is a proper rational function, and lim(x→ ±∞) f(x) = constant.
If deg p(x) < deg q(x), then these limits equal 0, thus yielding the horizontal asymptote y = 0.
If deg p(x) = deg q(x), then these limits equal a/b, where a and b are the leading coefficients of p(x) and q(x), respectively. Hence, we have the horizontal asymptote y = a/b.
Note that there are no obliques asymptotes in this case. ------------- (ii) If deg p(x) > deg q(x), then f(x) is an improper rational function.
By long division, we can write f(x) = g(x) + r(x)/q(x), where g(x) and r(x) are polynomials and deg r(x) < deg q(x).
As in (i), note that lim(x→ ±∞) [f(x) - g(x)] = lim(x→ ±∞) r(x)/q(x) = 0. Hence, y = g(x) is an asymptote. (In particular, if deg g(x) = 1, then this is an oblique asymptote.)
This time, note that there are no horizontal asymptotes. ------------------ In summary, the degrees of p(x) and q(x) control which kind of asymptote we have.
I hope this helps!
(12 - 2x)(15 - 2x) = 108
180 - 24x - 30x + 4x² = 108
180 - 54x + 4x² = 108
4x² - 54x + 72 = 0
2x² - 27x + 36 = 0
(2x - 3)(x - 12) = 0
2x - 3 = 0 x - 12 = 0
x = 3/2 x = 12
Since the length of the border must be less than the width, disregard the 12
x = 3/2 = 1.5
Answer: 1.5 ft
Answer:
The endpoints of the latus rectum are and .
Step-by-step explanation:
A parabola with vertex at point and whose axis of symmetry is parallel to the y-axis is defined by the following formula:
(1)
Where:
- Independent variable.
- Dependent variable.
- Distance from vertex to the focus.
, - Coordinates of the vertex.
The coordinates of the focus are represented by:
(2)
The <em>latus rectum</em> is a line segment parallel to the x-axis which contains the focus. If we know that , and , then the latus rectum is between the following endpoints:
By (2):
By (1):
There are two solutions:
Hence, the endpoints of the latus rectum are and .