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antoniya [11.8K]

3 years ago

12

Rational Exponents (See attachments)

1 answer:

Contact [7]3 years ago

6 0

Answer:

I cant read the handwriting sorry

Step-by-step explanation:

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Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te

Aleonysh [2.5K]

Answer:

t=5.18 minute

Step-by-step explanation:

Using Newton's law of cooling

$\frac{dT}{dt}=-k(T-T_{s})$

T is temperature of a cup of coffee at any time t $T_{s}$ , is the temperature of the surrounding and k is a constant of proportionality in this negative because temperature is decreasing.

$T(0)=190\\T(1)=170\\T_{s}=66$

$\frac{dT}{dt}=-k(T-T_{s})\\\frac{dT}{(T-T_{s})}=-k*dt\\\int\limits {\frac{1}{T-T_{s} } } \, dT=-\int\limits {k} \, dt\\ln(T-T_{s})=k*t+C\\e*ln(T-T_{s})=e^{k*t+C} \\T-T_{s}=e^{k*t}*e^{C}\\e^{C}=C\\T-T_{s}=e^{k*t}*C\\T=T_{s}+e^{k*t}*C$

To find constant knowing the time and the temperature the first step of the change of energy in cup of coffee

$T=T_{s} +e^{-k*t}*C\\ C=190-66=124\\170=66+124*e^{-k*2}\\ 170-66=124*e^{-k*2}\\ln(\frac{104}{124})=ln*e^{-k*2}\\-0.175=-k*2\\k=0.08794$

Now using the constant of decreasing can find the time to be a 145 temperature the cup of coffee

$145=66+124*e^{-k*t} \\145-66=124*^{-0.087*t}$

$ln(0.637)=ln*e(-0.087*t)\\-0.45=-0.087*t\\t=5.18minutes$

4 0

3 years ago

What is the equation of this graph? It is a cosine needing something along the lines of y=acos(b(x-c))+d

Sholpan [36]

Jesus Christ is the only true source of joy

6 0

3 years ago

Which answer best describes (n k)

trasher [3.6K]

The answer is A

Have to add characters to get to 20

8 0

3 years ago

Read 2 more answers

Zara walked 3/4 mile in 30 minutes. How long will it take her to walk 2 miles?

Talja [164]

Answer:

80 minutes

Step-by-step explanation:

(3/4)/30=2/x

cross product

30*2=(3/4)x

60=3/4x

x=60/(3/4)

x=(60/1)(4/3)

x=240/3

x=80

5 0

4 years ago

8 (p + 8 7 + 2q)<br><br> help me pleas!!!

77julia77 [94]

Answer:

8p +56 +16q

Step-by-step explanation:

8 (p+7+2q)

If we distribute the 8 into everything in the parenthesis, we get:

8p +56 +16q

5 0

3 years ago