PLZ HELP ANYONE NOW THIS ILL GIVE 50 POINTS
1 answer:
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Answer:
see explanation
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
=
[2a + (n - 1)d ]
where d is the common difference and a is the first term
here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence
=
[(2 × 5) + 2(n - 1) ]
= (10 + 2n - 2)
= (2n + 8)
= n² + 4n
When sum = 165, then
n² + 4n = 165 ← rearrange into standard form
n² + 4n - 165 = 0 ← in standard form
(n + 15)(n - 11) = 0 ← in factored form
equate each factor to zero and solve for n
n + 15 = 0 ⇒ n = - 15
n - 11 = 0 ⇒ n = 11
but n > 0 ⇒ n = 11
<u>Given</u>:
The equation of the circle is
We need to determine the center and radius of the circle.
<u>Center</u>:
The general form of the equation of the circle is
where (h,k) is the center of the circle and r is the radius.
Let us compare the general form of the equation of the circle with the given equation to determine the center.
The given equation can be written as,
Comparing the two equations, we get;
(h,k) = (0,-4)
Therefore, the center of the circle is (0,-4)
<u>Radius:</u>
Let us compare the general form of the equation of the circle with the given equation to determine the radius.
Hence, the given equation can be written as,
Comparing the two equation, we get;
Thus, the radius of the circle is 8