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djyliett [7]
3 years ago
5

Determine the number of ways the faces of a regular tetrahedron can be colored with three colors

Physics
1 answer:
GREYUIT [131]3 years ago
5 0
Tetrahedron is a geometrical figure or solid that is formed in similar manner as a pyramid. The faces of the formed pyramid are triangles. Also is the base. 

By the statement above, it can be deduced that the figure has four sides. The number of ways in which the sides can be colored by any of the three (3) colors is,
             3 x 3 x 3 x 3 = 81

Since the sides can still have the same colors, we deduct this value by 3 in order to eliminate the uniform colors of the four sides.
             = 81 - 3 = 78

Also, we can eliminate the concern on only two colors can mix,
              = 3 x 2 = 6
 Subtracting,
                      78 - 6 = 72

Hence, the answer is 72. 
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A 0.750 kg block is attached to a spring with spring constant 17.5 N/m. While the block is sitting at rest, a student hits it wi
Dmitriy789 [7]

Answer:

a

 A =  0.081 \  m

b

The value is  u =  0.2569 \  m/s

Explanation:

From the question we are told that

   The mass is  m  =  0.750 \ kg

   The spring constant is  k  =  17.5 \  N/m

    The instantaneous speed is  v  =  39.0 \  cm/s= 0.39 \  m/s

    The position consider is  x =  0.750A  meters from equilibrium point

   

Generally from the law of  energy conservation we have that

        The kinetic energy induced by the hammer  =  The energy stored in the spring

So

          \frac{1}{2} *  m * v^2  =  \frac{1}{2}  *  k  *  A^2

Here a is the amplitude of the subsequent oscillations

=>      A =  \sqrt{\frac{m *  v^ 2 }{ k} }

=>      A =  \sqrt{\frac{0.750 *  0.39 ^ 2 }{17.5} }

=>       A =  0.081 \  m

Generally from the law of  energy conservation we have that

The kinetic energy  by the hammer  =  The energy stored in the spring at the point considered   +   The kinetic energy at the considered point

             \frac{1}{2}  * m *  v^2 = \frac{1}{2}  * k x^2 + \frac{1}{2}  * m *  u^2

=>          \frac{1}{2}  * 0.750 *  0.39^2 = \frac{1}{2}  * 17.5* 0.750(0.081 )^2 + \frac{1}{2}  * 0.750 *  u^2

=>          u =  0.2569 \  m/s

3 0
3 years ago
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Nadusha1986 [10]

Answer:

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3 0
3 years ago
The exhaust fan on a typical kitchen stove pulls 600 CFM (cubic feet per minute) through the filter. Given that 1.00 in. = 2.54
zysi [14]

Answer:

0.283\ m^3/s

Explanation:

Given that,

1.00 in = 2.54 cm

We know that,

1 feet = 12 inches

1\ feet =12\times0.0254

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We calculate the number

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The number required is

600ft^3/min = \dfrac{600\times(0.3048)^3}{60}

600ft^3/min=0.283\ m^3/s

Hence, This is the required solution.

4 0
3 years ago
Why was Mars orbiter sent to mars?​
Dafna11 [192]

Explanation:

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6 0
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What is the independent variable?<br><br> Diameter<br> Circumference
spin [16.1K]

Answer:

Diameter

Explanation:

I know that circumference is dependent, so diameter has to be independent

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