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omeli [17]
3 years ago
5

Helppppppppppppppppp​

Mathematics
1 answer:
viktelen [127]3 years ago
4 0

Answer:

i dont get it

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
I am Lyosha [343]

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}

7 0
4 years ago
The Gaineys and the Arnolds are saving money for a trip to Utah to go snowboarding. The Arnolds are going to save a nickel on th
natali 33 [55]

Answer: see Explanation

Step-by-step explanation:

THE GAINEY'S:

Recursive Formula :

A1 = $10

An = An-1 + $10

A2 = $10 + $10 = $20

Where n = day of the month

Explicit formula :

y = a + b(c - 1)

WHERE:

y = final amount

initial amount = a

Increment on initial amount = b

Day of the month = c

THE ARNOLD'S :

Recursive formula:

First day of the month (A1) = $10

An = 2(An-1)

A2 = 2(A1) = 2(10) = $20

A3 = 2(A2) = 2(20) =$40

Explicit formula:

y = a(b)^c

Where :

y = final amount

initial amount = a

Increment on initial amount = b

Day of the month = c

5 0
3 years ago
⚠️10 points⚠️
Lostsunrise [7]

Answer:

8.9

Step-by-step explanation:

The distance between each point is 8.9, hope this helps!

7 0
3 years ago
A store normally sells a floor lamp for $83.99. The store is having a sale that reduces the lamp's price by 15%. How much does t
-Dominant- [34]
The answer should be $71.39
4 0
3 years ago
$200 at 15.5% for 2 years
Inessa05 [86]
15.5 I believe but don’t hold me to it!
8 0
3 years ago
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