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3 years ago

Change this equation to standard form Y= (5x - 2) (x - 5)

Mathematics

1 answer:

Nutka1998 [239]3 years ago

4 0

Y= (5x - 2) (x - 5) in standard form should be Y= 5x^2 -27x +10

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Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per g

AysviL [449]

Answer:

The quantity of salt at time t is $m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$ , where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

$\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}$

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

$(0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}$

Where:

$c$ - The salt concentration in the tank, as well at the exit of the tank, measured in $\frac{pd}{gal}$ .

$\frac{dc}{dt}$ - Concentration rate of change in the tank, measured in $\frac{pd}{min}$ .

$V$ - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

$V \cdot \frac{dc}{dt} + 6\cdot c = 3$

$60\cdot \frac{dc}{dt} + 6\cdot c = 3$

$\frac{dc}{dt} + \frac{1}{10}\cdot c = 3$

This equation is solved as follows:

$e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }$

$\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }$

$e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt$

$e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C$

$c = 30 + C\cdot e^{-\frac{t}{10} }$

The initial concentration in the tank is:

$c_{o} = \frac{10\,pd}{60\,gal}$

$c_{o} = 0.167\,\frac{pd}{gal}$

Now, the integration constant is:

$0.167 = 30 + C$

$C = -29.833$

The solution of the differential equation is:

$c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }$

Now, the quantity of salt at time t is:

$m_{salt} = V_{tank}\cdot c(t)$

$m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$

Where t is measured in minutes.

7 0

3 years ago

Solve the system by substitution.

Iteru [2.4K]

Answer:

I gave you most of the answer. I'll let you check my work and find the point using the solution.

Step-by-step explanation:

The first thing we do is we divide by negative one in the first equation to get

y = -x.

-3x + 3y = -36

Plug in y = -x and get

-3x + 3(-x) = -36

= -3x - 3x = -36

This equals -6x = -36

divide both sides by -6 and you get 6. 6 is your x value

Plug 6 back in to the second equation.

-3x + 3y = -36

-3(6) + 3y = -36

-18 + 3y = -36

3y = -18

y = -6

3 0

2 years ago

NEED ANWERS ASAP 100 POINTS FOR CORRECT select the correct answer. x y 0 3 3 15 7 31 10 43 Which of the following linear equatio

creativ13 [48]

Answer:

theres is not table shown

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Problem Page

djyliett [7]

Because there are 2 pints in a quart, 712 quarts would equal 1,424 pints.

3 0

3 years ago

a camera is capable of snapping .75 of a picture per second how long will it take the camera to snap 6 pictures?

pashok25 [27]

Answer:

4.5 seconds.

Step-by-step explanation:

0.75 of a picture will be taken within a second. 6 times 0.75 is 4.5 seconds.

Hope this helps!

8 0

2 years ago