Answer:
Step-by-step explanation:
The formula for determining the sum of the first n terms of an arithmetic sequence is expressed as
Sn = n/2[2a + (n - 1)d]
Where
n represents the number of terms in the arithmetic sequence.
d represents the common difference of the terms in the arithmetic sequence.
a represents the first term of the arithmetic sequence.
If a = 5, the expression for the sum of the first 12 terms is
S12 = 12/2[2 × 5 + (12 - 1)d]
S12 = 6[10 + 11d]
S12 = 60 + 66d
Also, the expression for the sum of the first 3 terms is
S3 = 3/2[2 × 5 + (3 - 1)d]
S3 = 1.5[10 + 2d]
S3 = 15 + 3d
The sum of the first 12 terms is equal to ten times the sum of the first 3 terms. Therefore,
60 + 66d = 10(15 + 3d)
60 + 66d = 150 + 30d
66d + 30d = 150 - 60
36d = 90
d = 90/36
d = 2.5
For S20,
S20 = 20/2[2 × 5 + (20 - 1)2.5]
S20 = 10[10 + 47.5)
S20 = 10 × 57.5 = 575
The volume of cone shaped popcorn cup is 75.36 cubic inches.
According to the given question.
The height of the popcorn cup = 8inches
And the diameter of the cup = 6 inches
⇒ Radius of the popcorn cup = 6/2 = 3 inches
As we know that, the volume of cone is calculated by the formula
volume of cone = (πr^2h)/3
Therefore, the volume of cone shaped popcorn cup
= 3.14((3)^2)(8)/3
= 3.14(3)(8)
= 75.36 cubic inches
Hence, the volume of cone shaped popcorn cup is 75.36 cubic inches.
Find out more information about volume of cone here:
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Answer:
(7/2, 0)
Step-by-step explanation:
A= π r2 and v=3.14d
---Volume(v=3.14d):
3.14(15) equals 47.1
47.1 rounds to 47
nearest hundreth would be 0 that rounds to .1 or .10,which rounds to 47
v=47
---Area(π r2)
3.14(7.5)^2 is 3.14(56.25)
176.625
176.625 rounded to the nearest hundreth is 176.630.
Answer:
The area of a circle with the diameter of 15 is 176.630.
Answer:
1?
Step-by-step explanation:
