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3 years ago

A water tank is 1/8 full the tank is 3/4 full when 42 gallons are added to the tank how much water was originally in the tank

1 answer:

8 0

<span>A water tank is 1/8 full. The tank is 3/4 full when 42 gallons are added to the tank. How much water was originally in the tank? (I rewrote it, your wording was messed up)

3/4 = 6/8
1/8 + 6/8 = 7/8 = 42 gallons
42 divided by 8 = 5 1/4

So, the answer is 5 1/4. The tank originally 5.25 gallons of water.</span>

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At time t=0 sec, a tank contains 15 oz of salt dissolved in 50 gallons of water. Then brine containing 88oz of salt per gallon o

maria [59]

Answer:

a) $s(t) =400- 385 e^{-\frac{1}{10} t}$

b) $s(t=25min) =400- 385 e^{-\frac{1}{10}25}=368.397$

Step-by-step explanation:

Part a

Assuming that the original concentration of salt is 8 oz/gal and that the rate of in is equal to the rate out = 5 gal/min.

For this case we know that the rate of change can be expressed on this way:

$Rate change = In-Out$

And we can name the rate of change as $\frac{ds}{dt}=rate change$

And our variable s would represent the amount of salt for any time t.

We know that the brine containing 8oz/gal and the rate in is equal to 5 gal/min and this value is equal to the rate out.

For the concentration out we can assume that is $\frac{s}{50gal}$

And now we can find the expression for the amount of salt after time t like this:

$\frac{dS}{dt}= 8 \frac{oz}{gal}(5\frac{gal}{min}) -\frac{s}{50gal} 5 \frac{gal}{min} =40\frac{oz}{min}- \frac{s}{10} \frac{oz}{min}$

And we have this differential equation:

$\frac{dS}{dt} +\frac{1}{10} s = 40$

With the initial conditions y(0)=15 oz

As we can see we have a linear differential equation so in order to solve it we need to find first the integrating factor given by:

$\mu = e^{\int \frac{1}{10} dt }= e^{\frac{1}{10} t}$

And then in order to solve the differential equation we need to multiply with the integrating factor like this:

$e^{\frac{1}{10} t} s = \int 40 e^{\frac{1}{10} t} dt$

$e^{\frac{1}{10} t} s = 400 e^{\frac{1}{10} t} +C$

Now we can divide both sides by $e^{\frac{1}{25} t}$ and we got:

$s(t) =400 + C e^{-\frac{1}{10} t}$

Now we can apply the initial condition in order to solve for the constant C like this:

$15 = 400+C$

$C=-385$

And then our function would be given by:

$s(t) =400- 385 e^{-\frac{1}{10} t}$

Part b

For this case we just need to replace t =25 and see what we got for the value of the concentration:

$s(t=25min) =400- 385 e^{-\frac{1}{10}25}=368.397$

7 0

3 years ago

The diameter of the earth

Roman55 [17]

Answer:

25,132.74 miles

Step-by-step explanation:

Hello!

We are basically asked to find the circumference of the Earth's cross-section.

Circumference: $C = 2\pi r$

We can replace 2r with the diameter, because the diameter is 2 times the radius.

Multiply the Diameter by pi:

$C = \pi D$
$C = 8000\pi$
$C = 25,132.7412287183 \approx 25,132.74$

It is around 25,132.74 miles around.

6 0

2 years ago

Help me please, thx

crimeas [40]

90 degrees clockwise

5 0

3 years ago

Read 2 more answers

Help please, look The picture !

JulijaS [17]

Answer:

Ha ha what I was doing is just looking at the picture.

OK jokes aside

The correct answer should be

option d (-0.25)

6 0

3 years ago

There are two factories in the town of Lemming. Factory A has 4 times as many workers as Factory B. Factory A has 1,160 workers.

madreJ [45]

Anwser = Factory B has 290 workers. Because it says that Factory A has 4 times as many workers as Factory B you will have to do 4 times the amount of workers Factory B has and you will get 1,160 which is how much Factory A has .To do that you have to do the opposite which is dividing by 4 and 4÷1,160=290 which is the amount of workers that Factory B has.

7 0

3 years ago