Use Euler’s Formula to find the number of edges in a polyhedron with seven faces: two pentagons and five rectangles.

1 answer:

6 0

We know that

Euler's formula states that Number of Faces plus the Number of Vertices (corner points) minus the Number of Edges is always equals 2

F+V-E=2
in this problem
F=7
V=2*5+5*4---> 30-----> (two pentagons and five rectangles)
E=?
E=F+V-2
E=7+30-2
E=35

the answer is
the number of edges is 35

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Write the equation of a piecewise function with a jump discontinuity at x =3. Then, determine which step of the 3-step test for

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Answer:

Here's a possible example:

Step-by-step explanation:

$f(x) =\begin{cases} x & \quad x < 3\\x+3 & \quad x \geq 3\\\end{cases}$

Each piece is linear, so the pieces are continuous by themselves.

We need consider only the point at which the pieces meet (x = 3).

$\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) = \lim_{x \longrightarrow 3^{-}} x = 3\\\\\displaystyle \lim_{x \longrightarrow 3^{+}} f(x) = \lim_{x \longrightarrow 3^{+}} x+3 = 6\\\\f(3) = x + 3 = 6\\\\\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) \neq f(3)$