The following graph represents the distance a commercial airplane travels over time, at cruising speed and an altitude of 35,000
feet. In fact, the distance the airplane travels at cruising speed is directly proportional to the time it travels. Using complete sentences, describe what the points (0, 0) and (4, 2268) represent.
1 answer:
Answer:
see the explanation
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Let
x ----> the time in hours
y ----> the distance in miles
<em>Find the value of k</em>
For the point (4,2268)
The slope represent the speed of the airplane
so
The linear equation is
Part 1 :
The point (0,0) represents the starting point of the aircraft, when the time and distance are equal to zero. The cruising starts when time t = 0.
Part 2 :
The point (4, 2268) represents the plane after 4 hours of cruise , and shows it has traveled a distance of 2268 miles after 4 hours
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Answer:
(a), (a,c), (a,d), (a,e), (a,c,d), (a,c,e), (a,d,e), (a,c,d,e)
Step-by-step explanation:
We are given the set (a,b,c,d,e).
Total number of subsets of the above set are = 32
Subsets:
φ
(a,b,c,d,e)
(a), (b), (c), (d), (e)
(a,b), (a,c), (a,d), (a,e), (b,c), (b,d), (b,e), (c,d), (c,e), (d,e)
(a,b,c), (a,b,d), (a,b,e), (a,c,d), (a,c,e), (a,d,e), ( b,c,d), (b,c,e), (b,d,e), (c,d,e)
(a,b,c,d), (a,b,c,e), (a,b,d,e), (a,c,d,e), (b,c,d,e)
Subset having a but not b :
(a), (a,c), (a,d), (a,e), (a,c,d), (a,c,e), (a,d,e), (a,c,d,e)
Answer:
D = L/k
Step-by-step explanation:
Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is
dA/dt = in flow - out flow
Since litter falls at a constant rate of L grams per square meter per year, in flow = L
Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow
So,
dA/dt = in flow - out flow
dA/dt = L - Ak
Separating the variables, we have
dA/(L - Ak) = dt
Integrating, we have
∫-kdA/-k(L - Ak) = ∫dt
1/k∫-kdA/(L - Ak) = ∫dt
1/k㏑(L - Ak) = t + C
㏑(L - Ak) = kt + kC
㏑(L - Ak) = kt + C' (C' = kC)
taking exponents of both sides, we have
When t = 0, A(0) = 0 (since the forest floor is initially clear)
So, D = R - A =
when t = 0(at initial time), the initial value of D =