Which Fraction in this place is less than 1/2?
1 answer:
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Answer: Choice D
15(cos85° + i sin85°)
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Explanation:
Let's say we had these two general complex numbers, which are in polar form.
We can abbreviate them into the shorthand form
The notation "cis" stands for "cosine i sine".
Now that we have those complex numbers set up, multiplying them is as simple as saying this:
We do two basic things:
- Multiply the r values out front
- Add the theta values inside the the cis function
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With all that in mind, let's tackle the problem your teacher gave you.
The given complex numbers
abbreviate into
then those multiply to
which is why choice D is the final answer.
Given:
The function is:
Where p(t) represents the number of milligrams of the substance and t represents the time.
To find:
The correct explanation for the number 0.25 and 500 in the given function.
Solution:
The general exponential function is:
...(i)
Where, a is the initial value and b is the growth/decay factor. If , then decay factor and if
, then growth factor.
We have,
...(ii)
On comparing (i) and (ii), we get
, it means initial there are 500 milligrams of the substance.
, this value is less than 1, it means the substance is decreasing by a factor of 0.25.
Therefore, 0.25 means the substance is decreasing by a factor of 0.25 and 500 means the initial value of substance is 500 milligram.