4/9 of apples in a bag are green if there are 36 green apples in the bag how many all together
2 answers:
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Answer:
Step-by-step explanation:
Given:
Solve for:
Solution:
Step 1: Select the formula to solve for
There are some ways to solve quadratic equations.
One of the simple way (if possible) is performing the factorization.
Another way is using the quadratic formula.
Here, we are going to use factorization.
Step 2: Perform factorization
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Hope this helps!
:)
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