The cafeteria contributed for pies to the sale. Each pie was then cut into five pieces and sold. There were a total of 60 pieces
2 answers:
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Answer:
Step-by-step explanation:
Use Newton's Law of Cooling for this one. It involves natural logs and being able to solve equations that require natural logs. The formula is as follows:
where
T(t) is the temp at time t
T₁ is the enviornmental temp
T₀ is the initial temp
k is the cooling constant which is different for everything, and
t is the time (here, it's in minutes)
If we are looking first for the temp after 20 minutes, we have to solve for the k value. That's what we will do first, given the info that we have:
T(t) = 80
T₁ = 30
T₀ = 100
t = 5
k = ?
Filling in to solve for k:
which simplifies to
Divide both sides by 70 to get
and take the natural log of both sides:
Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared). That gives us:
Divide both sides by 5 to get that
k = -.0672944473
Now that we have a value for k, we can sub that in to solve for T(20):
which simplifies to
On your calculator, raise e to that power and multiply that number by 70:
T(20)= 30 + 70(.260308205) and
T(20) = 30 + 18.22157435 so
T(20) = 48.2°
Now we can use that k value to find out when (time) the temp of the object cools to 35°:
T(t) = 35
T₁ = 30
T₀ = 100
k = -.0672944473
t = ?
which simplifies to
Now divide both sides by 70 and take the natural log of both sides:
which simplifies to
-2.63905733 = -.0672944473t
Divide to get
t = 39.2 minutes
(side note: your formula C = 2πr^2 is incorrect, it should be C = 2πr)
Answer:
r = 9
Step-by-step explanation:
First let's find the circumference of Circle A. To use the formula we need radius. Since we have a diameter just divide by 2 to get radius. 27 / 2 = 13.5
Now plug that into C = 2πr: 2π*(13.5) = 27π
The question says that the area of circle B is 3x this value, so Circle B's area must be: 27π * 3 = 81π
Now plug that into A = πr^2 and solve for r:
(edited to correct a brain fart)