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rewona [7]
2 years ago
14

Write the equation of a line in slope-intercept form with the given slope that passes through the given point:

Mathematics
1 answer:
dimaraw [331]2 years ago
7 0
Y=3x+12 (its the first option)
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A tank with a capacity of 1600 L is full of a mixture of water and chlorine with a concentration of 0.0125 g of chlorine per lit
Veronika [31]

Answer:

y(t) = 20 [1600^(-5/3)] x (1600-24t)^ (5/3)

Step-by-step explanation:

1) Identify the problem

This is a differential equation problem

On this case the amount of liquid in the tank at time t is 1600−24t. (When the process begin, t=0 ) The reason of this is because the liquid is entering at 16 litres per second and leaving at 40 litres per second.

2) Define notation

y = amount of chlorine in the tank at time t,

Based on this definition, the concentration of chlorine at time t is y/(1600−24t) g/ L.

Since liquid is leaving the tank at 40L/s, the rate at which chlorine is leaving at time t is 40y/(1600−24t) (g/s).

For this we can find the differential equation

dy/dt = - (40 y)/ (1600 -24 t)

The equation above is a separable Differential equation. For this case the initial condition is y(0)=(1600L )(0.0125 gr/L) = 20 gr

3) Solve the differential equation

We can rewrite the differential equation like this:

dy/40y = -  (dt)/ (1600-24t)

And integrating on both sides we have:

(1/40) ln |y| = (1/24) ln (|1600-24t|) + C

Multiplying both sides by 40

ln |y| = (40/24) ln (|1600 -24t|) + C

And simplifying

ln |y| = (5/3) ln (|1600 -24t|) + C

Then exponentiating both sides:

e^ [ln |y|]= e^ [(5/3) ln (|1600-24t|) + C]

with e^c = C , we have this:

y(t) = C (1600-24t)^ (5/3)

4) Use the initial condition to find C

Since y(0) = 20 gr

20 = C (1600 -24x0)^ (5/3)

Solving for C we got

C = 20 / [1600^(5/3)] =  20 [1600^(-5/3)]

Finally the amount of chlorine in the tank as a function of time, would be given by this formula:

y(t) = 20 [1600^(-5/3)] x (1600-24t)^ (5/3)

7 0
3 years ago
What is equivalent to 35d-25
baherus [9]

Answer:

5(7d-5)

Step-by-step explanation:

taking 5 common from  35d-25

= 5(7d- 5)

7 0
3 years ago
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carly and rob combined their dvd collections. now they have 42 dvds in all carly had 4 more dvds than rob. how many dvds did car
mrs_skeptik [129]
So r+c=42 c=4+r subsitute c=4+r for r in r+c=42 r+4+r=42 add like terms 2r+4=42 subtract 4 from both sides 2r=38 divide both sides by 2 r=19 rob=19 subsitute r=19 for r in c=4+r c=19+4 carly=23
5 0
3 years ago
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Skcncjnds<br>kjsndjcjknskjckjzxc
timama [110]

skskhfkakakan what is this haha

6 0
2 years ago
Round 905154 to the nearest ten thousand
beks73 [17]
905,154 rounded to the nearest ten thousand is 910,000. This is because the 5 in the thousands place is equal to 5, and when the number is 5 or more, you round up. That’s why when you round that number to the nearest ten thousand, it is 910,000.
8 0
3 years ago
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