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LUCKY_DIMON [66]
3 years ago
5

Solve for b a=b-4/c

Mathematics
1 answer:
Agata [3.3K]3 years ago
6 0

Answer:

Rewrite the equation as

3

b

+

4

c

=

a

.

3

b

+

4

c

=

a

Subtract

4

c

from both sides of the equation.

3

b

=

a

−

4

c

Divide each term by

3

and simplify.

Tap for more steps...

b

=

a

3

−

4

c

3

Step-by-step explanation:

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A cold drink is poured out at 52°F. After 2 minutes of sitting in a 72°F room, its temperature has risen to 55°F. Find an equati
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Answer:

The model for the temperature of the drink can be written as

T=72-20e^{-0.08t}

Step-by-step explanation:

For a cold drink in a hotter room, we can say that the rate of change of temperature of the drink is proportional to the difference of temperature between the drink and the room.

We can model that in this way

\frac{dT}{dt}=k*(T_r-T)

If we rearrange and integrate

\int\frac{dT}{(T-Tr)} =-k*\int dt\\\\ln(T-T_r)=-kt+C1\\\\T-T_r=Ce^{-kt}\\\\T=T_r+Ce^{-kt}

We know that at time 0, the temperature of the drink was 52°F. Then we have:

T=T_r+Ce^{-kt}\\\\52=72+Ce^0=72+C\\\\C=-20

We also know that at t=2, T=55°F

T=T_r+Ce^{-kt}\\\\55=72-20e^{-k*2}\\\\e^{-k*2}=(72-55)/20=0.85\\\\-2k=ln(0.85)=-0.1625\\\\k=0.08

The model for the temperature of the drink can be written as

T=72-20e^{-0.08t}

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3 years ago
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