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klio [65]
3 years ago
12

A gem cutter cuts a polyhedral crystal from a garnet gemstone. The crystal has 10 fewer vertices than edges and twice as many ed

ges as faces. How many faces, vertices, and edges does the crystal have?
Mathematics
1 answer:
Vikki [24]3 years ago
3 0

Answer:

vertices (V) = 6, faces (F) = 12 and edges (E) = 16

Step-by-step explanation:

A polyhedron is a three-dimensional shape with straight edges and flat faces and sharp corners.The point where the faces of a polyhedron meet each other is known as the edge while the corners of the polyhedron is known as the vertices.

Euler formula gives the relationship between the number of vertices (V), faces (F) and edges (E) of a polyhedron. This formula is given as:

F + V - E = 2.

Given that:

E - V = 10, Therefore E = V + 10

F = 2 × V = 2V

Substituting into the Euler formula:

2V + V - (V + 10) = 2

2V + V - 10 - V = 2

2V = 12

V = 12/2 = 6

Therefore, E = V + 10 = 6 + 10 = 16

F = 2V = 2 × 6 = 12

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b) The <em>piecewise</em> function is continuous.

<h3>How to understand a piecewise function</h3>

A <em>piecewise</em> function is a <em>conditional</em> combination of two or more functions, whose expression depends on which value of the domain is the function evaluated at.

a) The <em>piecewise</em> function described in the question is plotted on a graphing tool (i.e. <em>Desmos</em>), whose result is presented in the image attached below.

b) A function is <em>continuous</em> if and only if there is one value from range for every value of domain. The <em>piecewise</em> function is continuous as <em>linear</em> functions are continuous and the two functions of the <em>conditional</em> combination have the same value for x = 30.

To learn more on piecewise functions: brainly.com/question/12561612

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2 years ago
In the diagram AB=AD and
hammer [34]

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS congruence theorem, if two triangles have 2 corresponding sides that are equal, and also have one included corresponding angle that are equal to each other in both triangles, both triangles are regarded as congruent.

Given ∆ABC and ∆ADC in the question above, we are told that segment AB ≅ AD, and also <BAC ≅ <DAC, the additional information that is necessary to prove that ∆ABC and ∆ADC are congruent, according to the SAS theorem, is segment AC ≅ segment AE.

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3 years ago
What is the quotient of 4.68 x 106 and 2.6 x 102 expressed in scientific notation?
zaharov [31]

Answer:

1.8x {10}^{4}

Step-by-step explanation:

4.68x {10}^{6}  \div 2.6x {10}^{2} \\ = (4.68 \div 2.6)x {10}^{6 - 2} \\ answer \: is \: 1.8x {10}^{4}

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2 years ago
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5 0
3 years ago
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GenaCL600 [577]
The first step here would be to write out an equation.

$32 ÷ 8 = ?

The reason we are doing thirty-two divided by eight is because this equation will give us the cost of one pound of Cashew Nuts.

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