Can any of you guys help me?
2 answers:
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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
Answer:
(D) 30pi inches
Step-by-step explanation:
First, we use the given volume, the given height, and the formula of the volume of a cylinder to find the radius of the base. Then we use the radius of the base to find the circumference of the base.
We set the formula equal to the volume and replace h with 30 in.
Divide both sides by 30pi in.
Take the square root of each side.
The radius of the base is 15 in.
Now we use the radius of the base and the formula of the circumference of a circle to find the answer.
Step-by-step explanation: