Which option correctly shows how this formula can be rearranged to isolate x^2?
1 answer:
Answer:
A
Step-by-step explanation:
We have:
And we want to isolate x₂.
So, let’s first remove the denominator by multiplying both sides by it:
The right side will cancel. This will leave:
Now, we can subtract x₁ from both sides. So:
Finally, we will multiply both sides by -1. So:
Hence, our answer is A.
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Answer:
1.5
Step-by-step explanation:
Note there is a common ratio between consecutive terms, that is
768 ÷ 1536 = 0.5
384 ÷ 768 = 0.5
192 ÷ 384 = 0.5
96 ÷ 192 = 0.5
This indicates that the terms form a geometric sequence with
= a
where a is the first term and r the common ratio
Here a = 1536 and r = 0.5, thus
= 1536 ×
= 1.5
You're using Rolle's theorem. This theorem states that, if a function is continous in and differentiable in
, and
, then there exists a middle point
such that
In other words, if a continous and differentiable function starts and ends at the same height, then it has a maximum or minimum.
In your case, since the function is differentiable in the closed interval, it is also continuous in the closed interval (differentiability implies continuity), and also being differentiable in the closed interval obviously implies that the function is differentiable in the open interval. Also, you're given that the function evaluates to 4 at both extreme points, so the hypothesis of the theorem are granted.