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prohojiy [21]
3 years ago
7

3 Find the slope from the table. X -8 0 4 8 у -7 2 5

Mathematics
1 answer:
nikitadnepr [17]3 years ago
4 0

Answer:

m = 3/4

Step-by-step explanation:

take two coordinate points and use the formula:

rise/run or y2-y1/x2-x1

x1,y1 being the first point

x2,y2 being the second point chosen off of the chart.

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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
1 year ago
The size of the angle of a triangle are are in the ratio 2:4:9 calculate the size of the three angles in degree
solmaris [256]
Total Unit of Triangle = 2+4+9 = 15
Value of one unit = 180/15 = 12

So, Angles = 2(12) : 4(12) : 9(12) = 24 : 48 : 108

In short, Your Angles would be: 24, 48 & 108

Hope this helps!
3 0
3 years ago
Greatest to least - 1/2, 3/5, 3/7
Natalka [10]
3/7, 3/5, 1/2 is the answer it starts from the lowest to the lagest
4 0
2 years ago
Solve for x: 2x + 13 = 8x - 41
kherson [118]

Answer:

9 is your answer for x.

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x. Do the opposite of PEMDAS.

PEMDAS is the order of operations, & =

Parenthesis

Exponent (& Roots)

Multiplication

Division

Addition

Subtraction

First, subtract 13 & 8x from both sides:

2x (-8x) + 13 (-13) = 8x (-8x) - 41 (-13)

2x - 8x = -41 - 13

Simplify. Combine like terms:

-6x = -54

Isolate the variable, x. Divide -6 from both sides:

(-6x)/-6 = (-54)/-6

x = (-54)/(-6)

x = 9

x = 9 is your answer.

~

8 0
3 years ago
Read 2 more answers
Pls help parents will ground me from everything if I don’t get me my homework done PLEASE
Nikitich [7]

Answer:

x=13 and y=sqrt338

Step-by-step explanation:

so basically the opposite of one of the 45 degrees is 13 so the other 45 degrees is 13 too and you find pythagorean theorem of the other one

7 0
3 years ago
Read 2 more answers
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