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3 years ago

Use Euler's Theorem to calculate how many vertices a polyhedron has if it has 6 faces and 12 edges.

Mathematics

2 answers:

Sav [38]3 years ago

7 0

$v+f-e=2\\
v=2-f+e\\
v=2-6+12\\
v=8$

Alex Ar [27]3 years ago

6 0

Hello,

E=V+F-2 with
E number of edges
F number of faces
V number of vertices;

So V=E-F+2=12-6+2=8

Your polyhedron is a cube. (or a "parrallélipipède ")

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A linear function contains the following points.

nydimaria [60]

Find the slope first using m=y2-y1/x2-x1
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4 0

3 years ago

One vertex of a triangle is located at (0, 5) on a coordinate grid. After a transformation, the vertex is located at (5, 0). Whi

madreJ [45]

Answer:

The Transformations are R(O , -90°) & R(O , 270)

Step-by-step explanation:

* Lets revise the rotation of a point

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

(270° anti-clockwise or -90°)

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise (-180°) or

anti-clockwise (180°) around the origin

* Lets solve the problem

∵ One vertex of a triangle is located at (0, 5) on a coordinate grid

∵ The image of the point after the transformation is (5 , 0)

- The coordinates are switched with each other

∴ There is no rotation with 180° or -180° because in the rotation with

180° and -180° around the origin we change only the signs of the

coordinates without switch them

∴ There is a rotation with 90° are 270° or -90°

- The zero has no sign

- When we rotate the point (0 , 5) by -90° or 270° around the origin

we will change the sign of x-coordinate and switch the two

coordinates

∴ The image of the point is (y , -x)

∵ x = 0 and y = 5

- There is no sign for zero, so we switch the coordinates only

∴ The vertex is located at (5, 0)

∴ The Transformations are R(O , -90°) & R(O , 270)

3 0

3 years ago

Read 2 more answers

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Sholpan [36]

Answer and explanation:

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$P(X$