Step-by-step explanation:
18.
4(c+5)-f⁴
4(-1+5)-4⁴
4(4)-4⁴
16-256
-240
19.
-3[(w-6)²+x]²
-3[(5-6)²+6]²
-3[-1²+6]²
-3[1+6]²
-3[7]²
-3(49)
-147
20.
3.5[h³-(3j/6)²]
3.5[3³-(3*-4/6)²]
3.5[27-(-12/6)²]
3.5[27-(-2)²]
3.5[27-4]
3.5[23]
80.5
21.
x[y²-(55-y^5)÷3]
-6[6²-(55-6^5)÷3]
-6[36-(55-7776)÷3]
-6[36+7721÷3]
-6[7757÷3]
-6[2585.66]
-15513.96
Answer:
The perimeter of the original octagon is:
The perimeter of the new octagon is:
Step-by-step explanation:
When it is mentioned that an octagon is regular, it means that all its sides are equal, therefore, each side of the original octagon has a length of 9 units, considering the formula of the octagon's perimeter:
- Perimeter of an octagon = 8 * length.
By replacing you get:
- Perimeter of the original octagon = 8 * 9 = 72 units.
For the new octagon, it is mentioned that each side increases by 27 units, therefore:
- New length = 27 + 9 = 36 units.
Applying the formula of perimeter of an octagon with the new values we obtain:
- <u>Perimeter of the new octagon = 8 * 36 = 288 units.</u>
You can prove the proofs by showing your work to prove the proofs.
An alternating series
converges if
is monotonic and
as
. Here
.
Let
. Then
, which is positive for all
, so
is monotonically increasing for
. This would mean
must be a monotonically decreasing sequence over the same interval, and so must
.
Because
is monotonically increasing, but will still always be positive, it follows that
as
.
So,
converges.
