Answer:
E; 8x9 is equal to 72 which estimated is 70
<em><u>The system of equations that represents this situation are:</u></em>
q + p = 2
4q + 5p = 8
<em><u>Solution:</u></em>
Let q be the number of hours it took Courtney to walk from her house to the beach
Let p be the number of hours it took her to walk from the beach to the park
<em><u>The entire walk took 2 hours</u></em>
Therefore,
q + p = 2 ------- eqn 1
<em><u>The total distance Courtney walked was 8 kilometers</u></em>
Total distance = 8 km
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour
Then walked from the beach to the park at a constant speed of 5 kilometers per hour
<em><u>Distance is given as:</u></em>
<em><u>From her house to the beach:</u></em>
<em><u>From the beach to the park:</u></em>
We know that,
Total distance = 8 km
Therefore,
4q + 5p = 8 ------ eqn 2
<em><u>Thus the system of equations that represents this situation are:</u></em>
q + p = 2
4q + 5p = 8
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!
Answer:
3.636 hour. dividing 200miles /55m/h =3.636h
Answer:
y = 0.375x
Step-by-step explanation:
Let there are two variables, one independent variable x and another dependent variable y which are in proportionality relation.
So, y ∝ x
⇒ y = kx ........... (1) {Where k is the proportionality constant}
Let us assume that the given values of 4 and 1.50 are values of x and y respectively.
Hence, from equation (1) we get, 1.5 = 4k
⇒ k = 0.375
So, the proportionality equation is y = 0.375x (Answer)
