Which of the following statements would be supported by both a communist and a utopian socialist? A. A classless society can be brought about in Europe without a violent revolution.
B. The gains of the industrial revolution should be shared by all members of society. C. Governments have no right to restrict the actions of businesses or customers.
D. A government should restrict the number of imports and exports to protect its gold reserves.

A

Step-by-step explanation:

B. The gains of the industrial revolution should be shared by all members of society.

Step-by-step explanation:

Communists were opposed to the power that the wealthy bourgeoisie had, who controlled the means of production.

Instead, Communists wanted the proletariat (working class) to control the means of production, in order to create a more even distribution of wealth and power in society.

So, they supported making the Industrial Revolution's benefits shared by society.

Utopian socialists also would support this, as they also supported public ownership of the means of production.

The correct answer is B.

9514 1404 393

  a) see attached for the drawings

  b) p = 8n -4

  c) a(n) = 4n(n -3) +13  for n > 1; a(1) = 1

  d) none

Step-by-step explanation:

a) The overall dimensions of the next two stages of the pattern will be 7×7 and 9×9. Excluding the 4 "ears", the central squares are 5×5 and 7×7. The drawings are shown in the attachment.

__

b) The sequence of perimeter values is ...

  4, 12, 20, 28, 36, ...

This is an arithmetic sequence with a common difference of 8. A suitable formula for the perimeter p of stage n is ...

  p = 8n -4

__

c) The sequence of area values is ...

  1, 5, 13, 29, 53, ...

The first differences are ...

  4, 8, 16, 24, ...

and the second differences are ...

  4, 8, 8, ...

At no level are the differences "common", so this sequence cannot be described by a polynomial function. After the first one, the second differences are common, so the sequence after the first term can be described by a quadratic function.

The function describing the sequence must be defined in two parts:

__

d) Because the function must be piecewise defined, the area sequence is not any of the types of sequences listed. After the first term, it is a quadratic sequence.

_____

Additional comment

The leading coefficient of the quadratic formula for the area sequence is half the second difference. When 4n² is subtracted from the sequence of areas, the remaining arithmetic sequence has a common difference of -12. In order to bring the total of these quadratic and arithmetic sequences up to the correct area value, 13 must be added. This formula would give a(1) = a(2) = 5, which is not the correct value for a(1). Hence, that must be defined separately.