In a certain tropical forest, litter (mainly dead vegetation such as leaves and vines) forms on the ground at the rate of 10 grams per square centimeter per year. At the same time, however, the litter is decomposing at the rate of 80% per year. Let f(t) be the amount of litter (in grams per square centimeter) present at time t. Find a differential equation satisfied by f(t).

Answers

Answer 1

Answer:

df(t)/dt = 10 - 0.8f(t)

Step-by-step explanation:

The net rate of change, df(t)/dt = rate in - rate out

The rate in = rate litter forms on ground = 10 g/cm²/yr

Since f(t) is the amount of litter present at time, t, in g/cm² the rate out = rate of decomposition = the percentage rate × f(t) = 80% per year × f(t) = 0.8f(t) g/cm²/yr

Since df(t)/dt = rate in - rate out

df(t)/dt = 10 - 0.8f(t)

So the desired differential equation is

df(t)/dt = 10 - 0.8f(t)


Related Questions

factorise x^{2} +2x-24[/tex]

Answers

Answer:

(x + 6)(x - 4)

Step-by-step explanation:

x² + 2x - 24

(x + 6)(x - 4)

-4 and +6 multiply to 24 and add to +2.

Please help!! No links

Answers

9514 1404 393

Answer:

  10.5

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so ...

  ZX/ZY = CA/CB

  ZX = Zy(CA/CB) = 14(3/4)

  ZX = 10.5

Angle A and Angle B are vertical angles. If Angle A measures 45 degrees,
what does Angle B measure.

Answers

Answer:

135

Step-by-step explanation:

135+45=180

What is the volume of the figure shown below?

Answers

Answer:

31 in

Step-by-step explanation:

Answer:

The volume of the figure shown below is 31 inches

Step-by-step explanation:

Just trust me ;)

The expression (g^2)^4 is equivalent to g^m. What is the value of m?

^ means exponents

Answers

Answer:

m = 8

Step-by-step explanation:

4 x 2

you just have to multiply exponents

Calculate the volume of this triangular prism?

Answers

Answer:

960 sq cm

Step-by-step explanation:

(16*12*10)/2

5th grade math. correct answer will be marked brainliest

Answers

Answer:

8 1/12 boxes

Step-by-step explanation:

Your first step to solve this problem is to convert those fractions to a common denominator. I would choose 12. So your first would be 4 4/12 and your second would be 3 9/12. You would then add those up and get 8 1/12 boxes of muffins bought at the bake sale.

If a pizza pie had
a diameter of 12
inches, what
would be its
circumference?

Answers

circumference = π x d
= π x 12
= 37.699
Rounded off is 37.70

Answer:

37.7 inches

Step-by-step explanation:

Formula of circumference:

[tex]2\pi r[/tex]

r = radius

In the current case,

radius is 6 inches

Hence,

circumference=

[tex]2*\pi *6\\= 12\pi\\= 37.6991118431[/tex]

≅ 37.7 inches

Feel free to mark it as brainliest

(x+6)/(x+1)=6/2
Solving proportions

Answers

Answer:

[tex]x = \frac{3}{2} [/tex]

Step-by-step explanation:

[tex] \frac{x + 6}{x + 1} = \frac{6}{2} [/tex]

[tex] \frac{6}{2} = 3[/tex]

so, the solution of the equation will be as follows:

[tex] \frac{x + 6}{x + 1} = 3[/tex]

3(x+1) = x + 6

3x + 3 = x + 6

3x - x = 6 - 3

[tex]x = \frac{3}{2} [/tex]

so, the answer will be x = 3/2

Let X and Y be the following sets:
X = {10,20,30}
Y = {5, 10, 15, 20}
Which of the following is the set XY?

Answers

Answer:

{10;20}

Step-by-step explanation:

X & Y = {10;20}

El precio de cada acción de una empresa de tecnología ha presentado a través del tiempo un comportamiento dado por la siguiente función:



Donde t es el tiempo dado en días y A es el precio de la acción inicial cuando t = 0. Un inversionista desea conocer el número de días para el cual el valor de la acción se duplica. Para conocer este resultado, el proceso que se debe realizar es reemplazar f(t) por


A.
A/2, luego, expresar la ecuación en forma de logaritmo natural y ahora despejar t.

B.
2A, luego, expresar la ecuación en forma de logaritmo natural y ahora despejar t.

C.
2A, luego, dividir ambos lados de la ecuación por e y ahora despejar t.

D.
A/2, luego, dividir ambos lados de la ecuación por e y ahora despejar t.

Answers

I will ask you to turn it in english instead of española.

Ryan's Study Schedule
Subject Subject (Hours)
2
Math
2
3
1
Science
1-
2
1
English
3
1
Social Studies
1
4
What is the closest amount to the hours Ryan spends studying?
7 hours
8 hours
0 5 hours
O 9 hours

Answers

math and english give you a total of 4 hours. and social studies and science gives you a total of 2 3/4 hours. add them up, and the closest he will spend to studying is 7 hours

At a Beirut market, oranges are priced at $1.29/KG. Ms. X buys 10 oranges that have a total weight of 4.82 kgs. What is the average price per orange that she pays?

Answers

Answer:

The average price of each orange is $0.62.

Step-by-step explanation:

Given that at a Beirut market, oranges are priced at $ 1.29 per kilo, and Ms. X buys 10 oranges that have a total weight of 4.82 kilograms, to determine what is the average price per orange that she pays must perform the following calculation:

(4.82 x 1.29) / 10 = X

6.21 / 10 = X

0.62 = X

Thus, the average price of each orange is $ 0.62.

I need a answer ASAP​

Answers

Answer:

8

Step-by-step explanation:

y = (10x^2 + 3x^4)/ 2x^2

where x is not equal to 0

(20x + 12x)/4x

32x / 4x

= 8

When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is "the drug is unsafe." What is the Type II Error? ( Select the one, correct letter option below) :

Answers

Answer:

Not to conclude that the drug is safe, when, in fact, it is safe.

Step-by-step explanation:

A type ii error is an error that occurs in a hypothesis testing when a person goes ahead to accept a null hypothesis when it is actually false and should be rejected.

To continue, here are the hypothesis:

H0: the drug is unsafe

H1: drug is safe.

A type ii error was committed here because H0, which is the null was accepted and it was concluded that the drug was unsafe, When in fact it should have been rejected. The conclusion should have been that the drug was safe.

can someone help me with this please​

Answers

Answer:

4

This figure has 4 lines of symmetry.

Find the unit rate.. If a family travels in their mini-van for 465 miles and uses 15 gallons of gas what is the mileage per gallon?
10 points

Answers

465 miles 15 galons
x miles 1 gallon
x=465•1/15
x=465/15
x=31
Rate is 31 mirage per gallon

9 and 11 need help
Mark brainlist

Answers

I will do 9 only. You can do 11.

Question 9

sin(60) = x/8

sin(60)(8) = x

4•sqrt{3} = x

x^2 + y^2 = 8^2

(4•sqrt{3})^2 + y^2 = 64

16(3) + y^2 = 64

48 + y^2 = 64

y^2 = 64 - 48

y^2 = 16

sqrt{y^2} = sqrt{16}

y = 4

Do 11 the same way.

PLZZZZ HELPPP MEE!!!!!

Answers

Answer:

-60

Explanation:

6x(2x-5) always do what's in the parentheses first

6x(-10)

= -60

simplify the expression by using the distributive property 3(7y+4)​

Answers

Answer:

3(7y+4) multiply the inner to 3 so, 21y+12

Hi there!

Let’s distribute 3 by multiplying it by everything inside the parentheses:

3 * 7y = 21

3 * 4 = 12

21y+12 (Answer)

Hope you find it helpful.

Feel free to ask if you have any doubts.

-Sparkle-

Please help me and happy april fools day! B)

Answers

Answer:

A,C,D,F

Step-by-step explanation:

jeremiah has a total of 144 pokemon cards 40 out of every 48 cards are not holographic cards at this rate how many of jeremiah cards are holographic

Answers

Answer:

120

Step-by-step explanation:

rate of a holographic card= 40/48=5/6.

Total number of holographic cards = 144*rate =144*5/6=120

Need help with this asap!!

Answers

Answer:

≈ 53.7° (Option 3)

Step-by-step explanation:

In the figure given above , the lengths of other two sides (excluding hypotenuse) are known to us. So , it would be convenient to use 'tan'.

Length of side opposite to angle 'x' = 15 cm

Length of side adjacent to angle 'x' = 11 cm

Using 'tan' formula - [tex]\tan x = \frac{Side \: opposite \: to \: x}{Side \: adjacent \: to \: x}[/tex] , lets solve this.

[tex]=> \tan x = \frac{15}{11}[/tex]

Using inverse tan function , lets find x.

[tex]=> x = {\tan}^{-1}(\frac{15}{11} )[/tex] ≈ 53.74°

Please help me with this

Answers

Angle c is equal to 34 degrees. Explanation: if a=73 and b is the same as a. 73+73=146, the sum of the interior angles of a triangle is 180 degrees so 180-146= 34 degrees. Angle c is 34 degrees.

Select the measures that are equal to 3 gallons. Mark all that apply.

6 quarts

12 quarts

6 pints

12 pints

24 pints

20 cups

Answers

Answer:

12 quarts 24 pints

Step-by-step explanation:

change all measurements to gallons and solve.

1 quart= 2 pints

1 galllon = 8 pints

Answer:

12 quarts 24 pints

Step-by-step explanation:

change all measurements to gallons and solve.

1 quart= 2 pints

1 gallon = 8 pints

The large rectangle below represents one whole.

What percent is represented by the shaded area????

Answers

40% is shaded :))))))

Answer:

40%

Step-by-step explanation:

Because there are 5 rectangle total, we can dive 100% into 5 parts.

Each part is then 20%, there are 2 shaded rectangles thus the answer is 40%.

Help shefeejhrhrhhtuy

Answers

Answer:

c. 80,360

Step-by-step explanation: multiply the number of cases they make each day by the amount of pastries each case contains

Find the perimeter of the figure. due today

Answers

Answer:

24 in

Step-by-step explanation:

5in + 4in + 9in + 5in + (4in - 3in) = 24in


Jacque was selling bottles of water at the golf tournament Between 7 am and 8 am he sold 2 bottles of water, between 8 am and 9 am he sold 8 bottles, and between 9 am and 10 am he sold 32 bottles. If this trend
continues, how many bottles of water will he sell between 10 am and 11 am?
32
64
128
256

Answers

Answer:

128

Step-by-step explanation:

becuase 7-8 he sold 2

8-9 he sold 8

9-10 he sold 32

4*2= 8

4*2=32

4*32=128

Find the measure of 41.
{
839
41
4 1 = [?]
Enter

Answers

<1=97°

Answer:

<1+83=180 co interior angle

<1=180-83=97°

Answer:

solution given:

<1+<83°=180°[co- interior angle]

<1=180°-<83°=97°

<1=97° is your answer

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