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3 years ago

7.

Mathematics

1 answer:

aivan3 [116]3 years ago

6 0

Answer:

non-linear: C, E, F

Step-by-step explanation:

Choices A, B, D are linear functions, so the rest are non-linear: C, E, F

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Show the work on 6 divided by 5,406

fenix001 [56]

I think it's the 0.0011098779

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3 years ago

HELP PLEASE <br> (Look at the picture)

aksik [14]

Answer:

D is correct (I think).

Step-by-step explanation:

A and C are completely invalid, as A is a linear function and C does not go up in intervals of 25.

Answer C is a linear function and is represented by y=x+1, but there are potential other reasons that it could be considered a linear function.

Answer D cannot be solved by y=mx+b because it is an exponential function.

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2 years ago

A 500500-gallon tank initially contains 200200 gallons of brine containing 100100 pounds of dissolved salt. brine containing 11

mixer [17]

Let $A(t)$ denote the amount of salt in the tank at time $t$ . We're given that the tank initially holds $A(0)=100$ lbs of salt.

The rate at which salt flows in and out of the tank is given by the relation

$\dfrac{\mathrm dA}{\mathrm dt}=\underbrace{\dfrac{11\text{ lb}}{1\text{ gal}}\times\dfrac{44\text{ gal}}{1\text{ min}}}_{\text{rate in}}-\underbrace{\dfrac{A(t)}{200+(44-11)t}\times\dfrac{11\text{ gal}}{1\text{ min}}}_{\text{rate out}}$
$\implies A'(t)+\dfrac{11}{200+33t}A(t)=484$

Find the integrating factor:

$\mu(t)=\exp\left(\displaystyle\int\frac{11}{200+33t}\,\mathrm dt\right)=(200+33t)^{1/3}$

Distribute $\mu(t)$ along both sides of the ODE:

$(200+33t)^{1/3}A'(t)+11(200+33t)^{-2/3}A(t)=484(200+33t)^{-1/3}$
$\bigg((200+33t)^{1/3}A(t)\bigg)'=484(200+33t)^{-1/3}$
$A(t)=484\displaystyle\int(200+33t)^{-1/3}\,\mathrm dt$
$A(t)=22(200+33t)^{2/3}+C$

Since $A(0)=100$ , we get

$100=22(200)^{2/3}+C\implies C\approx-652.39$

so that the particular solution for $A(t)$ is

$A(t)=22(200+33t)^{2/3}-652.39$

The tank becomes full when the volume of solution in the tank at time $t$ is the same as the total volume of the tank:

$200+(44-11)t=500\implies 33t=300\implies t\approx9.09$

at which point the amount of salt in the solution would be

$A(9.09)\approx733.47\text{ lb}$

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3 years ago

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Nataliya [291]

Answer:

Step-by-step explanation:

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mel-nik [20]

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3 years ago