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Dafna11 [192]
2 years ago
13

Y+1=x :write the equation in slope intercept form to find the slope and the y-intercept

Mathematics
2 answers:
Ilya [14]2 years ago
8 0
You have the equation:

Y + 1  =  X

You need it in "slope and intercept" form.
Slope and intercept form is:

Y = (slope) X + (intercept)

The equation you have ALMOST looks like the form you need,
but there's something wrong.   

What you have is:  Y + 1 = X .
What you need is ' Y ' on one side all by itself.

How can you get rid of that " + 1 " that's on the left side with Y ?

Well, you can subtract ' 1 ' from the left side of the equation.
But whatever you do to one side, you must do the same thing
to the other side.
No problem !  Take the original equation:

Y + 1  =  X

Subtract ' 1 ' from each side:

Y = X - 1

And there you have what you need.

Remember, "slope and intercept form" is

Y = (slope) X + (intercept) .

and you have 

Y = (1) X + (-1)

The slope is 1 .
The intercept is -1 .

You're letting something easy scare you and
grab you by the throat.  Don't let it do that. 
Nat2105 [25]2 years ago
5 0
We know that y=MX+c
here m=1 and c=-1
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Answer:

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3 years ago
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} })

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