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2 years ago

Find the equation of the line that passes through the points A (2, 3) and B (5, -7)

Mathematics

1 answer:

aliina [53]2 years ago

3 0

Answer:

10x+3y=29

Step-by-step explanation:

Given points:(x1,y1)=(2,3)

(x2,y2)=(5,-7)

We know, the equation of line passing through two points is given by,

y-y1={(y2-y1)/(x2-x1)}*(x-x1)

Hence,y-3={(-7-3)/(5-2)}*(x-2)

or,y-3=(-10/3)*(x-2)

or,3y-9= -10x+20

or,3y+10x=20+9

or,10x+3y=29 is the required equation.

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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

Find the common difference of the sequence shown 1/6, 1/4, 1/3

Damm [24]

1/4 - 1/6 = (6-4)/24 = 2/24 = 1/12
1/3 - 1/4 = (4-3)/12 = 1/12

7 0

3 years ago

Read 2 more answers

Joe has eaten 3/5 of pizza. Jane has eaten 1/7 of pizza. how many times more pizza has Joe eaten than Jane

Lana71 [14]

The answer would be 14/5.

First of all, get the denominators to be the same. The LCM is 5 × 7 = 3/5

So 1 /7 × 5/ 5 = 5 /3/5

And 2/ 5 × 7 /7 = 14 /35

Now we have 5 /35 and 14 /35

Then all you have to do is divide Joe's by Jane's to get the answer.

14 /35 ÷ 5 35 =14 /35 × 35/ 5 = 14 /5

Meaning the answer is 14/5.

Hope I could help! :)

4 0

3 years ago

Read 2 more answers

What is the product? 4⋅(−9)⋅(−3)⋅(−1) 1# −108 2# −81 3# 81 4# 108

alexdok [17]

The product of this equation is #1

6 0

3 years ago

Read 2 more answers

Four people each invested $450 in an account that earns simple interest assuming no other deposit or withdrawal were made witch

lina2011 [118]

Answer: $250

Step-by-step explanation: Step 1: Multiply $50 by 4 Step 2: Subtract $450 by $250 Step 3: Then you get $200 leftover

8 0

3 years ago