Hello, I need help graphing with y = x+4,

Answer:

a. [tex]dA(t)/dt = 50 - \frac{7A(t)}{400} where A(0) = 400[/tex]

b. [tex]A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}[/tex]

c. 3.717 kg

Step-by-step explanation:

a) Write the differential equation that represents the problem.

Let A(t) be the amount of dissolved oxygen in the tank at any time, t.

The net flow rate dA(t)/dt = mass flow in - mass flow out

Since 10 g/l of oxygen flows in at a rate of 5 l/min, the mass flow in is 10 g/l × 5 l/min = 50 g/min

Since A(t) is the amount of oxygen present in the tank at time, t, and the volume of the tank is 400 liters. The concentration of oxygen in the tank is thus A(t)/400 g/l.

Also, water is being pumped out at a rate of 7 l/min. So, the mass flow out is thus concentration × flow rate out = A(t)/400 g/l × 7 l/min = 7A(t)/400 g/min

So, dA(t)/dt = mass flow in - mass flow out

dA(t)/dt = 50 - 7A(t)/400 with A(0) = 400 l × 1 g/l = 400 g since the tank initially contains 1 g/l of dissolved oxygen and has a volume of 400 l

So, the differential equation is

dA(t)/dt = 50 - 7A(t)/400  where A(0) = 400 g

[tex]dA(t)/dt = 50 - \frac{7A(t)}{400} where A(0) = 400[/tex]

b) Solve the differential equation

To solve the equation, we use separation of variables, so

dA(t)/dt = 50 - 7A(t)/400  where A(0) = 400 g

dA(t)/(50 - 7A(t)/400) = dt

Integrating both sides, we have

∫dA(t)/(50 - 7A(t)/400) = ∫dt

-7/400 ÷ -7/400∫dA(t)/(50 - 7A(t)/400) = ∫dt

1/ (-7/400)∫-7/400dA(t)/(50 - 7A(t)/400) = ∫dt

(-400/7)㏑(50 - 7A(t)/400) = t + C

㏑(50 - 7A(t)/400) = -7t/400 + (-7/400)C

㏑(50 - 7A(t)/400) = -7t/400 + C'     (C' = (-7/400)C)

taking exponents of both sides, we have

50 - 7A(t)/400 = exp[(-7t/400) + C']

50 - 7A(t)/400 = exp(-7t/400)expC'

[tex]50 - \frac{7A(t)}{400} = e^{-7t/400}e^{C'} \\50 - \frac{7A(t)}{400} = Ae^{-7t/400} A = e^{C'}\\ \frac{7A(t)}{400} = 50 - Ae^{-7t/400} \\A(t) = \frac{400}{7} X 50 - \frac{400}{7} Ae^{-7t/400} \\A(t) = \frac{20000}{7} - \frac{400}{7} Ae^{-7t/400}[/tex]

when t = 0 , A(0) = 400. So,

[tex]A(t) = \frac{20000}{7} - \frac{400}{7} Ae^{-7t/400} \\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{-7(0)/400}\\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{0/400}\\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{0}\\A(0) = \frac{20000}{7} - \frac{400}{7} A\\400 = \frac{20000}{7} - \frac{400}{7} A\\\frac{400}{7} A = 400 - \frac{20000}{7}\\\frac{400}{7} A = \frac{2800}{7} - \frac{20000}{7}\\\frac{400}{7} A = -\frac{17200}{7}\\\\A = -\frac{17200}{7} X \frac{7}{400} \\A = -43[/tex]

So,

[tex]A(t) = \frac{20000}{7} - \frac{400}{7} X -43e^{-7t/400} \\A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}[/tex]

c) At 1 p.m., what is the amount of dissolve oxygen in the fish tank.

At 1 p.m, t = 60 min

So, the amount of dissolved oxygen in the fish tank is A(60)

So,

[tex]A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-7X60/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-420/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-1.05}\\A(60) = \frac{20000}{7} + \frac{17200}{7} X 0.3499\\A(60) = \frac{20000}{7} + \frac{6018.93}{7} \\A(60) = \frac{26018.93}{7} \\A(60) = 3716.99 g[/tex]

A(60) ≅ 3717 g

A(60) ≅ 3.717 kg

Answer:

Naomi and Pierre

Step-by-step explanation:

Answer:

I don't no

Step-by-step explanation:

sorry friend

Answer:

72cm

Step-by-step explanation:

Area = b times h / 2

so 12 times 12 /2

144 / 2

72

Answer:

Step-by-step explanation:

25

Answer:

Step-by-step explanation:

6x3 +4x2y + 10xy2 + 3x2y + 2xy2+ 5y3

Solving like terms

6x3 + 7x2y + 12xy2 + 5y3

The simplified form of the expression is 6x³+5y³+12xy²+7x²y

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, (2x+y)(3x²+2xy+5y²)​, we need to simplify it,

(2x+y)(3x²+2xy+5y²)​

= 6x³+4x²y+10xy²+3x²y+2xy²+5y³

= 6x³+5y³+12xy²+7x²y

Hence, the simplified form of the expression is 6x³+5y³+12xy²+7x²y

Learn more about expression, click;

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Answer:

109440

Step-by-step explanation:

1750 boxes of water bottles with 48 bottles of water each: 1750 x 48 = 84000

plus the other 530 boxes at the warehouse which alone are: 530 x 48 = 25440

adding up 84000 + 25440 = 109440

The total number of bottles of water in the warehouse will be 27,190.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A warehouse has 1,750 boxes of water bottles.

A truck unloaded another 530 boxes at the warehouse.

Each box holds 48 bottles of water.

Then the number of bottles that were unloaded by truck will be

⇒ 530 x 48

⇒ 25,440

Then the total number of bottles of water in the warehouse will be

⇒ 25,440 + 1,750

⇒ 27,190

The total number of bottles of water in the warehouse will be 27,190.

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Answer:

Step-by-step explanation:

$21.75/(3 crabs) = $7.25/crab

Answer:

I would have to say A

Step-by-step explanation:

B has 2 of the same variables while A has to different variables and C&D have no variables there for the answer is A

Answer:

10/22

10 blue marbles/22 total marbles

(simplified = 5/11)

Answer:

10.3m

Step-by-step explanation:

area of a rectangle is width times length, so you have to rearrange the equation

55.929 ÷ 5.43 = 10.3

Answer:

10.3 meters

Step-by-step explanation:

Area = length x width

55.929 = ? x 5.43

Divide 5.43 from 55.929

55.929/5.43 = 10.3 meters

Check = 10.3 x 5.43 = 55.929

Answer:

$100

Step-by-step explanation:

1L has 1000ml, so 1000/20=50x$2.00=$100

I think

Hope this helps

:)

Answer:

18x - 30

Step-by-step explanation:

in order to expand the expression, you need to use the distributive property to simplify 6(3x - 5).

first, distribute 6 to 3x, which is just 6 • 3x.

now distribute 6 to -5, which is just 6 • -5.

therefore, 6(3x - 5) expanded is 18x - 30 :) i hope this helps!! have a lovely rest of your day <3

Answer:

b.5 hours

520-195=325

325/65=5

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

........................ .....

the answer is 80 ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

you take 9 x 8 and get 72 then you just add 8 to it and get 80.

Answer:

first 1 is 5.7 2 is the 4.6 3 is the 3 is the middle and the 4 is the last

Step-by-step explanation:

jus use the internet XD

Answer:

[tex]\displaystyle dy = 25e^{5x}dx\\dy = 3.27 \cdot 10^7[/tex]

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Calculus

Derivatives

Derivative Notation

Differentials

Basic Power Rule:

eˣ Derivative: [tex]\displaystyle \frac{dy}{dx}[e^u] = u'e^u[/tex]

Step-by-step explanation:

Part A

Step 1: Define

[tex]\displaystyle y = 5e^{5x}[/tex]

Step 2: Differentiate

Part B

Step 1: Define

[Differential] [tex]\displaystyle dy = 25e^{5x}dx[/tex]

[Given] x = 3, dx = 0.4

Step 2: Evaluate

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Differentials

Book: College Calculus 10e

Answer:

X=3 y=-1

Step-by-step explanation:

X+y=2

X-y=4

so that means

y=X-4

substitute it in

X+X-4=2

2x-4=2

2x=2+4

2x=6

x=3

3+y=2

3+-1=2

y=-1

ways to check

3--1=4

double minus equal plus

3+1=4

Answer:

3

Step-by-step explanation:

To find the mean add them up and divide by # of sets

soit =24 ÷8=3

Answer:

im am Santiago i am from Brazil, i live in a favela, i play soccer in the jungle and the beach with the monkeys, i speak brazilian.

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

one number = x

another = 3x

x+3x = 12

4x = 12

x = 12/4 = 3

units place = 3x = 9

tens place= x = 3

number = 39

Answer:

[tex]y = -2x -1[/tex]

Step-by-step explanation:

Given

Passes through: (0, -1)

Parallel to: y = -2x + 7

Required

Determine the line equation

If the line is parallel to y = -2x + 7, then it has the same slope as y = -2x + 7.

For an equation of form: [tex]y = mx + b[/tex]

The slope is m

By comparison:

[tex]m = -2[/tex]

So, the slope of the extorted is -2.

The equation is then calculated using:

[tex]y = m(x - x_1)+ y_1[/tex]

[tex]y = -2(x - 0)-1[/tex]

[tex]y = -2(x )-1[/tex]

[tex]y = -2x -1[/tex]

Answer:

8/55

Step-by-step explanation:

4/5 DIVIDED 5 1/2 = 8/55

Answer: A

Explanation:

Answer:

A. (–4, –3)

Step-by-step explanation:

This is in case any one else had the answer on a different letter.

Answer:

26 inches

Step-by-step explanation:

You find out that 1 foot equals 12 inches

times 2 by 12 equaling 24

24 added by 2 is 26

1/6 as a decimal is 1.83 infinitive 3 which is rounded to 2 as the whole number

makes your answer 26 inches

Hope that helps

Answer:

An inequality sign is like an equal sign with a line through it

so, like, if you put = and / together

Answer:

<, >, =>, =<

Step-by-step explanation:

Answer:

12000

Step-by-step explanation:

3000x2^(140/70)

Answer:

The answer is 3.)

Step-by-step explanation:

Answer:

3. 12p = 48

Step-by-step explanation:

Start with 12p = 48

Your goal is to find the number of photos, p, that can go on each page. To do this, you need to isolate p (in other words, get p by itself)

Divide both sides by 12 and you end up with:

p = 4

martemat 20 e7 72gsys y3823 485 u

Answer:

x = -10

Step-by-step explanation:

First, determine the slope of the answer. The x-axis is a horizontal line, thus the new line must be vertical. All vertical lines are represented by the equation x = a number. That number represents the x-value of all the points the vertical line passes through.

So, since the line passes through (-10, -1), take the x-value of that point and put it into that equation. Thus, x = -10.