Answer:
<h2>BELOW </h2>
Step-by-step explanation:
7.
8.
9.
10.
11.
12.
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15.
Answer:
a. 8
b. 12(n -2)
c. 6(n -2)^2
d. (n -2)^3
Step-by-step explanation:
A cube has 8 vertices (corners), 12 edges, and 6 faces.
a. Three faces will be painted on each of the 8 corner cubes.
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b. Two faces will be painted on the edge cubes that are not corner cubes. For an n-inch edge, n-2 inches of it are not part of the corner cubes. Two faces will be painted on 12(n -2) edge cubes.
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c. One face will be painted on each face cube that is not part of an edge or a corner. For a face of dimensions n inches square, the cubes of interest comprise a square that is n-2 inches on a side. There are 6 such faces of the larger cube. One face will be painted on 6(n -2)^2 face cubes.
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d. The cubes internal to the larger cube that are not part of any face, edge, or corner make up a cube that is (n -2)^3 smaller cubes. This is the number with no paint.
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e. Of course the total number of cubes with or without paint is n^3. This is the sum of the cubes in each category:
(((n -2) +6)(n -2) +12)(n -2) +8 = ((n +4)(n -2) +12)(n -2) +8
= (n^2 +2n +4)(n -2) +8
= n^3 +2n^2 -2n^2 +4n -4n -8 +8
= n^3
Answer:
b. 495
Step-by-step explanation:
Given
15, 21, 27, 33, 39, ...., 75
Number of terms = 11
Required
Evaluate
To evaluate means to add up all term of the series above;
The first step is to determine if the series is arithmetic or exponential;
If its arithmetic, then the difference between successive terms must be equal;
In other words;
21 - 15 = 27 - 21 = 33 - 27 = 39 - 33 = 6
<em>Since the result of the above expression gives 6, then it is an arithmetic series;</em>
<em></em>
The sum of n terms of an arithmetic series is calculated as this
Where n = 11
a = First term = 15
T_n = Last term = 75
The formula becomes
Hence, the series when evaluated is 495
Answer:
c
Step-by-step explanation:
i got it right
Answer:
i will try my best
Step-by-step explanation: