Which property of multiplication is shown by the equation ƒ • 8 = 8ƒ ?

At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
$42 = (80-20)e^{-3k} +20 \\ \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\ \\ k = -\frac{1}{3} ln (\frac{11}{30})$

Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

8 0

3 years ago

If the discriminant of an equation is zero, which of the following is true of the

miss Akunina [59]

Answer:

Step-by-step explanation:

if the discriminate is 0, it means that both roots are the same. Not only that, but it also means that the roots are real. I would pick D, but realize that that is the expected answer and the answer could be B, depending on how the person writing the problem thinks about it.

5 0

3 years ago

How do I write and simplify the expressions that are represented for the perimeter of each figure shown?

alexgriva [62]

Answer:

hope this helps you.......

4 0

3 years ago

There are 6 buses transporting students to a baseball game with 32 students on each bus. Each row at the baseball stadium seats

9966 [12]

6 buses with 32 students per bus.....6 x 32 = 192 students

each row seats 8 students...192/8 = 24 rows will be needed for all students

8 0

3 years ago

1. Carly bought some tickets and some snacks and paid $34 from the Redhawk Rangers selling raffle tickets for $2 each

GaryK [48]

Answer:

$2(T) + $1.5(S) = $34

Step-by-step explanation:

Let:

tickets be represented by T

Snacks be represented by S

As total amount she paid is $34

The expression would be:

$2(T) + $1.5(S) = $34

i hope it will help you!

4 0

3 years ago

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