Question 1 (Essay Worth 10 points)

A 500500-gallon tank initially contains 200200 gallons of brine containing 100100 pounds of dissolved salt. brine containing 11

mixer [17]

Let $A(t)$ denote the amount of salt in the tank at time $t$ . We're given that the tank initially holds $A(0)=100$ lbs of salt.

The rate at which salt flows in and out of the tank is given by the relation

$\dfrac{\mathrm dA}{\mathrm dt}=\underbrace{\dfrac{11\text{ lb}}{1\text{ gal}}\times\dfrac{44\text{ gal}}{1\text{ min}}}_{\text{rate in}}-\underbrace{\dfrac{A(t)}{200+(44-11)t}\times\dfrac{11\text{ gal}}{1\text{ min}}}_{\text{rate out}}$
$\implies A'(t)+\dfrac{11}{200+33t}A(t)=484$

Find the integrating factor:

$\mu(t)=\exp\left(\displaystyle\int\frac{11}{200+33t}\,\mathrm dt\right)=(200+33t)^{1/3}$

Distribute $\mu(t)$ along both sides of the ODE:

$(200+33t)^{1/3}A'(t)+11(200+33t)^{-2/3}A(t)=484(200+33t)^{-1/3}$
$\bigg((200+33t)^{1/3}A(t)\bigg)'=484(200+33t)^{-1/3}$
$A(t)=484\displaystyle\int(200+33t)^{-1/3}\,\mathrm dt$
$A(t)=22(200+33t)^{2/3}+C$

Since $A(0)=100$ , we get

$100=22(200)^{2/3}+C\implies C\approx-652.39$

so that the particular solution for $A(t)$ is

$A(t)=22(200+33t)^{2/3}-652.39$

The tank becomes full when the volume of solution in the tank at time $t$ is the same as the total volume of the tank:

$200+(44-11)t=500\implies 33t=300\implies t\approx9.09$

at which point the amount of salt in the solution would be

$A(9.09)\approx733.47\text{ lb}$

4 0

3 years ago

Susan is hiking at an elevation of 20 feet above sea level. Who is located the same distance from sea level but in the opposite

Brrunno [24]

Answer:

If its in the opposite direction but the same distance from sea level then its located at -20 feet or 20 feet below sea level.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Given a dilation with the origin O (0, 0), by observation determine the scale factor "K." DO, K = (5, 0) (10, 0) The dilation an

Eddi Din [679]

False because the scale factor is twice as much as it is in the equation so its false

6 0

4 years ago

A cell phone service provider charges customers a fixed rental charge and a call charge based on the number of call minutes. The

ycow [4]

We are given the following data in tabulated form:

Call minutes, y Bill Amount ($), x

125 75

150 85

175 95

200 105

We can see that for every 25 increase in call minutes, there is a constant 10 increase in bill amount. Therefore the equation relating the two variables is linear. The call minutes is y while the bill amount is x, therefore:

y = m x + b

where m is the slope and b is the y-intercept

Calculating for the slope m:

m = (y2 – y1) / (x2 – x1)

m = (150 -125) / (85 – 75)

m = 2.5

So, y = 2.5 x + b

Calculating for b using the 1st pair:

125 = 2.5 (75) + b

b = - 62.5

So the final equation is:

y = 2.5 x – 62.5

To match, simply plug in the value of the bill amount ($) as x in the equation and the answer will be y which is the call minutes.

6 0

4 years ago

Read 2 more answers

12x2 +2 x - 24<br> Factor it

GenaCL600 [577]

Answer:

The answer is 2x

Step-by-step explanation:

6 0

3 years ago