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2 answers:
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Answer:
Step-by-step explanation:
For any circle point with coordinate of center (a,b) and radius r
equation of circle is given by
_______________________________________
Given
coordinate of center = (-5,2)
radius = 6
thus, equation of circle can be written by substituting a and b with (-5 ,2) and r =6 as shown below
Thus, equation of circle is
<h2>Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:
where n is a positive integer.
- Let us take n=1
then we have:
Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.
- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u>
Let us take n=k+1
Hence, we have:
( Since, the result was true for n=k )
Hence, we have:
Also, we know that:
(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,
Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.