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3 years ago

What is a conversion factor that you can use to convert gallons into pints?

1 answer:

7 0

There are four quarts in a gallon and two pints in a quart. Therefore, there are eight pints in a gallon because we need 2(4). Eight would be the conversion factor :)

I hope I helped!

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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

How you would find the empirical probability of rolling a 2 on a die?

harkovskaia [24]

Answer:

it's a 1 in 6 chance/possibility

3 0

4 years ago

Karen is 6 years older than her sister Michelle, and Michelle is 2 years younger than their brother David. If the sum of their a

ale4655 [162]

$K\ \rightarrow\ the\ Karen's\ age\\M\ \rightarrow\ the\ Michelles\ age \\D\ \rightarrow\ the\ David's\ age\\\\K=M+6\\M=D-2\ \ \ \Rightarrow\ \ \ D=M+2\\K+M+D=62\\\\(M+6)+M+(M+2)=62\\3M+8=62\\3M=54\ /:3\\M=18\ \ \ \Rightarrow\ \ \ K=18+6=24\ \ \ and\ \ \ D=18+2=20\\\\Ans.\ Michelle\ is\ 18,\ David\ is\ 20,\ Karen\ is\ 24.$

6 0

3 years ago

To the nearest tenth, what is the y-coordinate for point A? 4.5 4.6 4.7 4.8

fomenos

the complete question is
<span>Point A has an x coordinate of −2 and lies in a circle with a center at (0, 0) and a radius of 5.
To the nearest tenth, what is the y-coordinate for point A?
A: 4.5
B: 4.6
C: 4.7
D: 4.8
see the attached figure

we know that
the equation of the circle is
(x-h)</span>²+(y-k)²=r²
(h,k) is the center---------> (h,k) is the point (0,0)
r=5 units
so
(x-h)²+(y-k)²=r²--------> (x-0)²+(y-0)²=5²------> x²+y²=25

substitute the value of x=-2 in the equation
(-2)²+y²=25------> y²=25-4------> y=(+/-)√21
the y coordinate of point A is positive----> see the picture
therefore
y=√21-----> 4.58-----> y=4.6

the answer is
the y-coordinate for point A is 4.6

3 0

3 years ago

Read 2 more answers

Oh a number line what is the distance between -54 and 73

Ghella [55]

The correct answer is 127.

5 0

4 years ago

Read 2 more answers