The area of a rectangle is 352in2. If the width of the rectangle is x inches, write a function for the perimeter, P(x)

Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be

Travka [436]

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

$L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}$

When t = 0, A(0) = 0 (since the forest floor is initially clear)

$A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L$

$A = \frac{L}{k} - \frac{L}{k} e^{kt}$

So, D = R - A =

$D = \frac{L}{k} - \frac{L}{k} - \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{kt}$

when t = 0(at initial time), the initial value of D =

$D = \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{k0}\\D = \frac{L}{k} e^{0}\\D = \frac{L}{k}$

4 0

3 years ago

A set of cards contains cards numbered 1-10. Mrs. Jacobs class is conducting an experiment in which a card Is drawn from the pil

Olegator [25]

Answer:

a

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Simplify the expression -2x^2(4x − 3). -8x3 − 6x2 -8x3 + 6x2 8x3 − 6x2 8x3 + 6x2

Digiron [165]

To simplify the expression we are going to use the distributive property of multiplication: $a(b+c)=ab+ac$ .
We can infer from our problem that $a=-2x^2$ , $b=4x$ , and $c=-3$ . So lets apply the property to simplify our expression:
$-2x^2(4x-3)=(-2x^2)(4x)+(-2x^2)(-3)$
$(-2x^2)(4x)+(-2x^2)(-3)=-8x^3+6x^2$

We can conclude that the correct answer is -8x3 + 6x2

8 0

3 years ago

how many solutions does this equation have 15x-5 3=5x+4 a no solutions b. exactly one solution c. exactly two solution d. infini

velikii [3]

Answer:

one solution! & that would be be 57/10. hopefully that's correct.

Step-by-step explanation:

7 0

3 years ago

What is the perimeter of this shape?

Korvikt [17]

Answer:

59.4 km

Step-by-step explanation:

First you need to find the circumference of the circle. 20*3.14=62.8. Then, you divide this by two, because there is only half of a circle, to get 31.4.

Then you can just add 16 + 12 + 31.4 to get 59.4.

6 0

3 years ago