When the initial input is 8 in what order should the machines be arranged so that the final output is 2?

From the information provided, we know that the initial input is equal to 15 and the final output is -6. Thus, we would solve the puzzle as follows:

For the fourth machine, we have;

y₄ = -2x + 34

y₄ = -2(15) + 34

y₄ = -30 + 34

y₄ = 4.

Therefore, the output is equal to 4.

For the second machine, we have:

y₂ = (x - 2)²

y₂ = (4 - 2)²

y₂ = 2²

y₂ = 4

Therefore, the output is equal to 4.

For the first machine, we have:

y₁ = -|3x|

y₁ = -|3 × 4|

y₁ = -12.

Therefore, the output is equal to -12.

For the third machine, we have:

y₃ = -x/3 - 10

y₃ = -(-12)/3 - 10

y₃ = 12/3 -10

y₃ = 4 - 10

y₃ = -6

Therefore, the output is equal to -6.

In conclusion, we can logically deduce that the machines should be stacked in this order:

Fourth machine (y₄ = -2x + 34)
Second machine (y₂ = (x - 2)²)
First machine (y₁ = -|3x|)
Third machine (y₃ = -x/3 - 10)

Part 2.

When the initial input is equal to 8 and the final output is 2. Thus, we would solve the puzzle as follows:

y₁ = -|3x|

y₁ = -|3 × 8|

y₁ = -24.

For the third machine, we have:

y₃ = -x/3 - 10

y₃ = -(-24)/3 - 10

y₃ = 24/3 -10

y₃ = 8 - 10

y₃ = -2.

For the second machine, we have:

y₂ = (x - 2)²

y₂ = (-2 - 2)²

y₂ = 4²

y₂ = 16

For the fourth machine, we have;

y₄ = -2x + 34

y₄ = -2(16) + 34

y₄ = -32 + 34

y₄ = 2.

When the initial input is equal to 8 and the final output is 2, the machines should be stacked in this order:

First machine (y₁ = -|3x|)
Third machine (y₃ = -x/3 - 10)
Second machine (y₂ = (x - 2)²)
Fourth machine (y₄ = -2x + 34)

Read more on final outputs here: https://brainly.com/question/17670171

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Complete Question:

1. In what order should you stack the machines so that when 15 is dropped into the first machine, and all four machines have had their effect, the last machine’s output is -6?

2. When the initial input is 8 in what order should the machines be arranged so that the final output is 2?