We are given witha1 = 2r = 4These are components of a geometric series. The first term is 2 and the prevalent proportion is 4. To obtain the initially six terms, we usage the formula:an = a1 r^(n-1)a1 = 2 (4)^(1-1) = 2a2 = 2 (4)^(2-1) = 8a3 = 2 (4)^(3-1) = 32a4 = 2 (4)^(4-1) = 128a5 = 2 (4)^(5-1) = 512a6 = 2 (4)^(6-1) = 2048

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Notice that for 3 out of the 4 numbers, there is a partnership in between the x and also the y coordinate of the number; for 3+i, -2i, -2-4i we have that the actual part is larger by 2 from the imaginary part. Therefore, the points are on the same line in the imaginary plane; they accomplish x=y+2 or Rez=Imz+2. However before, 2-4i does not meet this equation considering that 2 is not equal to -4+2. Hence, this point does not belong to the line that the various other 3 points define.

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4.5(8 - x) + 36 - 2.5(3x + 24) = 102

Use distributive law.

36 - 4.5x + 36 - 7.5x - 60 = 102

Combine favor terms.

- 4.5x - 7.5x + 36 + 36 - 60 = 102

Simplify.

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-12x + 12 = 102

Subtract 12 from both sides.

-12x = 90  A spbelow is just enclosed inside a ideal circular cylinder. If the volume of the spbelow is 140 cm3, uncover the volume of the gap b      -----------------------------------------------------------Find volume of the cylinder :-----------------------------------------------------------   -----------------------------------------------------------Find volume of the gap :-----------------------------------------------------------  ----------------------------------------------------------- -----------------------------------------------------------