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3 years ago

80 POINTS FOR ALL 5 ANSWERS AND BRAINLEIEST

Mathematics

2 answers:

IceJOKER [234]3 years ago

5 0

Answer:

I only know that question 1 is true

Step-by-step explanation:

Agata [3.3K]3 years ago

4 0

Answer:

Question 2 is y = 1/2 x - 2

Question 3 is y=-2x+4

Question 4 is y = x + 3

Your other questions don't have pictures of the graph so I can't solve them sorry. Have a good day.

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-10y + 18 = -3 (5y - 7) + 5y

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Answer:

-10y + 18 = -3 (5y - 7) + 5y

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Step-by-step explanation:

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3 years ago

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

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

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