Question

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

Answer 1

When the initial input is equal to 15 and the final output is -6, the machines should be stacked in this order:

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

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

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

How to determine the arrangement?

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:

1. Fourth machine (y₄ = -2x + 34)
2. Second machine (y₂ = (x - 2)²)
3. First machine (y₁ = -|3x|)
4. 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:

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

Read more on final outputs here: 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?