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2 years ago

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The temperature outside of Brandon's house is −5°F, while the temperature outside of Nick's house is 3°F. How many degrees warme

r is the temperature outside of Nick's house?

1 answer:

STatiana [176]2 years ago

3 0

Answer:

9F

Step-by-step explanation:

-5...-4...-3...-2...-1...0...1...2...3

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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

Mark and raquel were playing a word game.Raquel played the word math on a game board on a space marked’’triple points’.If her wo

Reika [66]

Answer:

111 points

Step-by-step explanation:

First, thing I like to do is to convert word problems into an eqaution or write down the important information. So, Math = 37 points and now the points are tripled because of where she placed the word. Also, tripled is implying that her base score for the word is 3 times the original value.

So, $37*3$

= 111 points.

5 0

3 years ago

Read 2 more answers

What is the height of the tree show all work

poizon [28]

Answer:

x=32.91

Step-by-step explanation:

Given: Triangle

Find: x

_______

Tan(35°)=x/47

x=tan(35)×47

x=0.7×47

x=32.91

Hope it helps!

3 0

2 years ago

Read 2 more answers

Determine the measure of <br> will give brainliest

Xelga [282]

Step-by-step explanation:

Tha angle b is 57 degree !!

5 0

2 years ago

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Why is the adjusted average used in math?

Tatiana [17]

It’s used to correct statistical averages that include obvious imbalances because of outliers in the data set.

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3 years ago