Question

Arrange the machines so that when 15 is dropped into the first machine, the last machine's output is-6.

Options:1: Machine order: y = -|3x|, y = -x/3 - 10, y = (x - 2)^2, y = -2x + 34
Options:2: Machine order: y = -2x + 34, y = -x/3 - 10, y = -|3x|, y = (x - 2)^2
Options:3: Machine order: y = (x - 2)^2, y = -x/3 - 10, y = -2x + 34, y = -|3x|
Options:4: Machine order: y = -x/3 - 10, y = -2x + 34, y = -|3x|, y = (x - 2)^2

Answer 1

After testing all given machine orders with the input of 15, none of the provided sequences resulted in the desired output of -6. Therefore, there's no correct arrangement within the given options that satisfies the condition.

Step-by-step explanation:

To arrange the machines in a sequence that produces an output of -6 when the input is 15, we must test each machine order with the input to determine which order yields the correct output. We'll test each of the four given machine orders until we find the correct one.

Option 1: Let's start with an input of 15 for the first machine in the sequence:

1. Machine 1: y = -|3x| → y = -|3×15| = -|45| = -45
   
2. Machine 2: y = -x/3 - 10 → y = -(-45)/3 - 10 = 15 - 10 = 5
   
3. Machine 3: y = (x - 2)^2 → y = (5 - 2)^2 = 3^2 = 9
   
4. Machine 4: y = -2x + 34 → y = -2×9 + 34 = -18 + 34 = 16
   

The output of the last machine is not -6, so option 1 is not correct.

Option 2: Testing the second option:

1. Machine 1: y = -2x + 34 → y = -2×15 + 34 = -30 + 34 = 4
   
2. Machine 2: y = -x/3 - 10 → y = -(4)/3 - 10 = -4/3 - 10 ≈ -13.33
   
3. Machine 3: y = -|3x| → y = -|3×(-13.33)| = -|-40| = -40
   
4. Machine 4: y = (x - 2)^2 → y = (-40 - 2)^2 = 42^2 = 1764
   

Again, the output is not -6. Option 2 is incorrect.

Following the same steps to calculate for Options 3 and 4, we find that neither of these options gives the correct output of -6 either. Therefore, based on the calculations using the given machine orders, none of the options provided correctly transform the input of 15 to an output of -6.