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uranmaximum [27]
3 years ago
12

The difference of two numbers is 34 and their sum is 338

Mathematics
1 answer:
Assoli18 [71]3 years ago
4 0
X-y=34
x+y=338

We can use elimination in this problem.

2x=372
x=186

186+y=338
y=338-186
y=152
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A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so
Debora [2.8K]

Let A(t) = amount of salt (in pounds) in the tank at time t (in minutes). Then A(0) = 11.

Salt flows in at a rate

\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}

and flows out at a rate

\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}

which I'll solve with the integrating factor method.

\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95

-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}

\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}

Integrate both sides. By the fundamental theorem of calculus,

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)

\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}

\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}

\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}

After 1 hour = 60 minutes, the tank will contain

A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131

pounds of salt.

7 0
2 years ago
On a map, the scale shown is 1 inch : 3 miles. If an island is 0.5 square inches on the map, what is the actual area of the isla
gtnhenbr [62]

Answer:

4.5

Step-by-step explanation:

First we need to turn the ratio of 1 : 3 into a fraction

1:3 = 1/3

Next we need to square that fraction

1 x 1 = 1

3 x 3 = 9

Then we turn those numbers into a fraction

1/9

We turn the .5 into a fraction

.5/x

And cross multiply both fraction by each other

1/9 x .5/x

1 x X = X

9 x .5 = 4.5

So

4.5 = X

4 0
3 years ago
Here's another, Thanks. (3/5)
Pachacha [2.7K]

You are correct. The scale factor is 1/5 = 0.2

Nice work.

7 0
3 years ago
Pls pls help me I need it and the other one pls guys
snow_lady [41]

do u need all the answers?


3 0
3 years ago
Ok the first question confuses me what is the volume of the prisom show in the top?
Veronika [31]
Split the shape in to two this is the rectangular side.
15+6=21
21×7=147
147×4=588in
square shape
6+6=12
12×12=144
144×4=576in
then add the answers together
588+576=1164in
1164 is how many more inches greater
5 0
3 years ago
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