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3 years ago

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What does the inequality x + 3 ≤ 2 say? A number and three is at most two. A number and three is less than two. A number and thr

ee is at least two. A number and three is no less than two.

2 answers:

sesenic [268]3 years ago

4 0

$x+3\leq2$

Answer: A number and three is at most two.

Jobisdone [24]3 years ago

3 0

Answer:

A number and three is at most two

Step-by-step explanation:

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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

7.1 as a fraction or mixed number in simplest form?

Andreas93 [3]

The simpliest form is 71/10, the fraction

Step-by-step explanation:

Since this isn't a really small (1/1000000000) or really big (like the radius of the earth) number you don't need the standard notation, so the fraction 71/10 is the simpliest because there is only a decimal, so it can be a fraction of ten.

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2 years ago

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The diagram shows a scale drawing of a lacrosse field. The diagram is 5

maks197457 [2]

Need more details than that

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3 years ago

Can you please help me please

r-ruslan [8.4K]

Answer:

Scale factor of 2

Hope that helps!

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3 years ago

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Nic paid a total of +25.68 for a game, including 7, tax. What was the

Inga [223]

Answer:

x=24

Step-by-step explanation:

x + 0.07x = 25.68

1.07 x = 25.68

x = 24

3 0

2 years ago