Answer:
y'(t) = k(700,000-y(t)) k>0 is the constant of proportionality
y(0) =0
Step-by-step explanation:
(a.) Formulate a differential equation and initial condition for y(t) = the number of people who have heard the news t days after it has happened.
If we suppose that news spreads through a city of fixed size of 700,000 people at a time rate proportional to the number of people who have not heard the news that means
<em>dy/dt = k(700,000-y(t)) </em>where k is some constant of proportionality.
Since no one has heard the news at first, we have
<em>y(0) = 0 (initial condition)
</em>
We can then state the initial value problem as
y'(t) = k(700,000-y(t))
y(0) =0
Answer:
A = 14.2/1.1 hours
B = 5.091 hours
Step-by-step explanation:
Formulate 2 simultaneous equations
5.7A + 6.8B = 111.40..........(1)
A +B =18...............................(2)
Multiply each item in (2) by 5.7 to get
5.7A + 5.7B = 97.2............(3)
subtract (1) - (3) on each side
5.7A -5.7A + 6.8B - 5.7B = 111.40 -97.2
1.1B = 14.2
B = 14.2 /1.1
to get A use equation (2)
A = 18 - B
A = 18 - 14.2/1.1 = 5.091
Answer:
Step-by-step explanation:
8 I think
9514 1404 393
Answer:
(x, y, z) = (1, 2, 3)
Step-by-step explanation:
The equations that result from reduction to row-echelon form are ...
x = 0.4 +0.2t
y = 5.6 -1.2t
z = t
Then t must have a value 5n+3 for 0 ≤ n < 1. That is, t=3.
x = 0.4 +0.2(3) = 1
y = 5.6 -1.2(3) = 2
z = 3
The integers that satisfy are (x, y, z) = (1, 2, 3).
A plausible guess might be that the sequence is formed by a degree-4* polynomial,
From the given known values of the sequence, we have
Solving the system yields coefficients
so that the n-th term in the sequence might be
Then the next few terms in the sequence could very well be
It would be much easier to confirm this had the given sequence provided just one more term...
* Why degree-4? This rests on the assumption that the higher-order forward differences of eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of by . Then
• 1st-order differences:
• 2nd-order differences:
• 3rd-order differences:
• 4th-order differences:
From here I made the assumption that is the constant sequence {15, 15, 15, …}. This implies forms an arithmetic/linear sequence, which implies forms a quadratic sequence, and so on up forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.