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stealth61 [152]
3 years ago
6

a. For each of the Five Platonic Solids, count the number V of vertices, the number F of faces, and the number E of edges. Check

that in each case V - E + F = 2
Mathematics
1 answer:
natita [175]3 years ago
8 0

Answer:

1. The tetrahedron has 4 vertices, 6 edges and 4 faces. Then V-E+F=4-6+4=2

2. The cube has 8 vertices, 12 edges and 6 faces. Then V-E+F=8-12+6=2

3. The octahedron has 6 vertices, 12 edges and 8 faces. Then V-E+F=6-12+8=2

4. The icosahedron has 12 vertices, 30 edges and 20 faces. Then V-E+F=12-30+20=2

5. The dodecahedron has 20 vertices, 30 edges and 12 faces. Then V-E+F=20-30+12=2.

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To solve this we are going to use the average rate of change formula: A(x)= \frac{f(b)-f(a)}{b-a}
where
A(x) is the average rate of change of the function
f(a) is the position function evaluated at a
f(b) is the position function evaluated at b
a is the first point in the interval
b is the second point in the interval

We can infer for our problem that the first point is 3 and the second point is 6, so a=3 and b=6. Lets replace those values in our formula:
A(x)= \frac{f(b)-f(a)}{b-a}
A(x)= \frac{f(6)-f(3)}{6-3}
A(x)= \frac{6-6^2-2-(3-3^2-2)}{3}
A(x)= \frac{-32-(-8)}{3}
A(x)= \frac{-32+8}{3}
A(x)= \frac{-24}{3}
A(x)=-8

We can conclude that the average rate of change of the function f(x) = 1 x - x2 - 2 for <span>3 ≤ x ≤ 6 is -8</span>
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