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2 years ago

Which of the following illustrates the truth value of the given conditional statement?

Mathematics

1 answer:

AleksandrR [38]2 years ago

5 0

Answer:

it looks like its c

Step-by-step explanation:

sorry if im wrong

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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

What single decimal multiplier would you use to increase by 18% followed by a 12% decrease?

ValentinkaMS [17]

Answer:

The single decimal multiplier used to increase by 18% followed by a 12% decrease is 0.21.

Step-by-step explanation:

Let 'x' be the number

As first the number has to be increased by 18%

Step 1: write the percentage '18%' in decimal form

18% = 0.18

Step 2: For percentage increases: add the decimal to 1

1 + 0.18 = 1.18

Step 3: Multiply the number x by the multiplier, found in Step 2

x × 1.18 = 1.18x

NEXT WE HAVE TO DECREASE 1.18x by 12%

Apply the same method but with a number 1.18x

Write the percentage '12%' in decimal form

12% = 0.12

For percentage decreases: subtract the decimal to 1

1 - 0.18 = 0.18

Multiply the number 1.18x by the multiplier, found in Previous step

1.18x × 0.18 = 0.21x

Therefore, the single decimal multiplier used to increase by 18% followed by a 12% decrease is 0.21.

7 0

2 years ago

It took you 6.5 h to drive 550 km. what was your average speed?

strojnjashka [21]

Average speed = Total distance/Time

A = 550km/6.5hr

A = 84.6 km per hr

5 0

3 years ago

Read 2 more answers

Is the following relation a function

sashaice [31]

Yes because each x only has one y output

5 0

2 years ago

12. Determine the slope of the line having the equation 2x + y = 12

Virty [35]

Answer:

b. -2

Step-by-step explanation:

Note the slope-intercept form: y = mx + b

Note that:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

First, isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Subtract 2x from both sides of the equation:

2x (-2x) + y = (-2x) + 12

y = -2x + 12

Remember, m is the variable for the term that stands for the slope (directly next to the x variable). In this case, your answer will be -2

b. -2 is your answer.

4 0

2 years ago

Read 2 more answers