Solve this system of linear equations. Separatethe x- and y-values with a comma.13x = -21 - 6y- 8x = 36 + 6yEnter the correct an
1 answer:
Solution:
Let:
To get the value of x, we add the Equation 1 and 2.
13x = -21 - 6y
+ - 8x = 36 + 6y
We will get:
5x=15
Calculate:
x= 3
Since x= 3, we plug in what we know:
13x = -21 - 6y
13(3) = -21 - 6y
39 = -21 - 6y
Simplify and rearrange:
-6y = 39 + 21
-6y= 60
Calculate:
y= -10
Therefore, the values are x= 3, y= -10 or (3,-10).
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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 =