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andreyandreev [35.5K]
4 years ago
15

You have taken up gardening for relaxation and have decided to fence in your new rectangular shaped masterpiece. The length of t

he garden is 2 meters and 46 meters of fencing is required to completely enclose it. What is the width of the garden ?
Mathematics
1 answer:
sineoko [7]4 years ago
3 0

Answer:

Step-by-step explanation:

It appears i cant answer your question but what i can do is provide this paragraph as a trade for points. Appreciate your help. :)

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Initially 15 grams of salt are dissolved into 25 liters of water. Brine with concentration of salt 4 grams per liter is added at
Alla [95]

Answer:

a) dx/dt = 600 - 6x

b) x = 100 - 4.12((e⁻ ⁽⁶ᵗ ⁻ ³•⁰²⁾)

c) The mass of salt in the tank attains the value of 20 g at time, t = 0.227 min = 13.62 s

Explanation:

Taking the overall balance, since the total Volume of the setup is constant, then flowrate in = flowrate out

Let the concentration of salt in the tank at anytime be C

Let the concentration of salt entering the tank be Cᵢ

Let the concentration of salt leaving the tank be C₀ = C (Since it's a well stirred tank)

Let the flowrate in be represented by Fᵢ

Let the flowrate out = F₀ = F

Fᵢ = F₀ = F = 6 L/min

a) Then the component balance for the salt

Rate of accumulation = rate of flow into the tank - rate of flow out of the tank

dx/dt = Fᵢxᵢ - Fx

Fᵢ = 6 L/min, C = 4 g/L, F = 6 L/min

dC/dt = 24 - 6C

dx/dt = 25 (dC/dt), (dC/dt) = (1/25) (dx/dt) and C = x/25

(1/25)(dx/dt) = 24 - (6/25)x

dx/dt = 600 - 6x

b) dC/dt = 24 - 6C

dC/(24 - 6C) = dt

∫ dC/(24 - 6C) = ∫ dt

(-1/6) In (24 - C) = t + k (k = constant of integration)

In (24 - 6C) = -6t - 6k

-6k = K

In (24 - 6C) = K - 6t

At t = 0, C = 15 g/25 L = 0.6 g/L

In (24 - 6(0.6)) = K

In 20.4 = K

K = 3.02

So, the equation describing concentration of salt at anytime in the tank is

In (24 - 6C) = K - 6t

In (24 - 6C) = 3.02 - 6t

24 - 6C = e⁻ ⁽⁶ᵗ ⁻ ³•⁰²⁾

6C = 24 - (⁻⁽⁶ᵗ ⁻ ³•⁰²⁾)

C = 4 - ((e⁻⁽⁶ᵗ ⁻ ³•⁰²⁾)/6

C = 4 - (e⁻ ⁽⁶ᵗ ⁻ ³•⁰²⁾)/6)

But C = x/25

x/25 = 4 - (e⁻ ⁽⁶ᵗ ⁻ ³•⁰²⁾)/6)

x = 100 - 4.12((e⁻ ⁽⁶ᵗ ⁻ ³•⁰²⁾)

c) when x = 20 g

20 = 100 - 4.12(e⁻ ⁽⁶ᵗ ⁻ ³•⁰²⁾)

80 = (e⁻ ⁽⁶ᵗ ⁻ ³•⁰²⁾)

- (6t - 3.02) = In 80

- (6t - 3.02) = 4.382

(6t - 3.02) = -4.382

6t = -4.382 + 3.02

t = 1.362/6 = 0.227 min = 13.62 s

4 0
4 years ago
3/4 x 5/6 plssssssssssss help
yan [13]

the answer is 5/8 :)

3 0
3 years ago
Read 2 more answers
Brandon made $47.00 in 2 hours. How much would he make in 9 hours?<br>​
Lerok [7]
9/2=4.5 47x4.5=$235
5 0
4 years ago
Read 2 more answers
Meaghan goes to the grocery store to buy hot dogs and hamburgers for a cookout. She buys a total of 12
Archy [21]

The system of equations is d+b=12 and 2.59d+5.49b=36.88 and Meaghan bought 10 packages of hot dogs and 2 packages of hamburgers.

Step-by-step explanation:

Cost of one package of hot dog = $2.59

Cost of one package of hamburgers = $5.49

Packages bought = 12

Cost of packages = $36.88

Let,

Packages of hot dogs = d

Packages of hamburger = b

According to given statement;

d+b=12     Eqn 1

2.59d+5.49b=36.88   Eqn 2

Multiplying Eqn 1 by 2.59

2.59(d+b=12)\\2.59d+2.59b=31.08\ \ \ Eqn\ 3

Subtracting Eqn 3 from Eqn 2

(2.59d+5.49b)-(2.59d+2.59b)=36.88-31.08\\2.59d+5.49b-2.59d-2.59b=5.80\\2.90b=5.80

Dividing both sides by 2.90

\frac{2.90b}{2.90}=\frac{5.80}{2.90}\\b=2

Putting b=2 in Eqn 1

d+2=12\\d=12-2\\d=10

The system of equations is d+b=12 and 2.59d+5.49b=36.88 and Meaghan bought 10 packages of hot dogs and 2 packages of hamburgers.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/8806598
  • brainly.com/question/8955867

#LearnwithBrainly

6 0
4 years ago
Please i meed help!!! im stuck and cant concentrate​
creativ13 [48]

Total outcomes=6 i.e{1,2,3,4,5,6 }

No.of favourable outcomes = 3 i.e {I, 3,5}

P(odd)=3/6=1/2

5 0
3 years ago
Read 2 more answers
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