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frez [133]
3 years ago
13

Plz help!

Mathematics
2 answers:
Virty [35]3 years ago
6 0
Dy/dx=25, 35, 45, 55

d2y/dx2=10,10,10  (this constant just proves that it is a quadratic relation)

Now we can set up a system of equations for ax^2+bx+c

16a+4b+c=80, 9a+3b+c=45, 4a+2b+c=20  getting differences

7a+b=35, 5a+b=25  and again

2a=10, a=5, making 7a+b=35 become:

7(5)+b-35, b=0, making 4a+2b+c=20 become:

4(5)+2(0)+c=20, c=0 so

y=5x^2

So the constant of variation for this quadratic is 5.
Elan Coil [88]3 years ago
6 0
The correct answer to the problem is A or 5
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Juli2301 [7.4K]

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3 years ago
A tank contains 300 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu
bonufazy [111]

Answer:

A(t) = 300 -260e^(-t/50)

Step-by-step explanation:

The rate of change of A(t) is ...

A'(t) = 6 -6/300·A(t)

Rewriting, we have ...

A'(t) +(1/50)A(t) = 6

This has solution ...

A(t) = p + qe^-(t/50)

We need to find the values of p and q. Using the differential equation, we ahve ...

A'(t) = -q/50e^-(t/50) = 6 - (p +qe^-(t/50))/50

0 = 6 -p/50

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From the initial condition, ...

A(0) = 300 +q = 40

q = -260

So, the complete solution is ...

A(t) = 300 -260e^(-t/50)

___

The salt in the tank increases in exponentially decaying fashion from 40 grams to 300 grams with a time constant of 50 minutes.

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