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Lapatulllka [165]
3 years ago
6

Newton’s law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the o

bject and its surroundings. So the rate of cooling for a bottle of lemonade at a room temperature of 75°F which is placed into a refrigerator with temperature of 38°F can be modeled by dT/dt=k(T-38) where T(t) is the temperature of the lemonade after t minutes and T(0) = 75. After 30 minutes the lemonade has cooled to 60°F, so T(30) = 60.
To the nearest degree, what is the temperature of the lemonade after an additional 30 minutes?
Mathematics
1 answer:
Lapatulllka [165]3 years ago
4 0
DT/dt=k(T-38)
ln(T-38) = kt+C
T=38 + Ce^(-kt)
Since T(0)=75, 75 = 38+C, so C=37
Since T(30)=60, 60 = 38+37e^(-30k), so k = -ln(22/37)/30 ~= -0.017329
T(60) = 38+37e^(-0.017329*60) = 51.1°F
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HELPPP Provide the missing statements and reasons for the following proof:
agasfer [191]

The missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:

S2: ∠2 ≅ ∠3

R2: corresponding angles

S3: m∠2 ≅ m∠3

R3: Definition of congruent angles

R5: Definition of supplementary angles

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S8: ∠1 is supplementary to ∠2

Given the proof to show that ∠1 is supplementary to ∠2, thus:

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In summary, the missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:

S2: ∠2 ≅ ∠3

R2: corresponding angles

S3: m∠2 ≅ m∠3

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5 0
2 years ago
In which area of the diagram does the number −11 belong?
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8 0
3 years ago
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Brrunno [24]
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4 0
3 years ago
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