Answer:
5 1/2 miles per 1 hr
Step-by-step explanation:
biked 1 3/8 miles in 1/ of an hour
1 3/8 miles = 11/8 miles in 1/4 of hour
11/8 miles divided by 1/4 hr
11/8 ÷ 1/4
11/8 * 4/1 =44/8 = 5 4/8 miles in 1 hr or 5 1/2 miles per 1 hr
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!
4inches = 1/3 of a foot (4inches x 3 = 12 inches) - so she can cut 3 out of each foot
1 yard = 3 feet - so she can cut 3 x 3 = 9 out of each yard
18 x 9 = 162 pieces
