8) T
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Answer:
Step-by-step explanation:
We want to write the equation of a circle with a center at (3, -2) and a radius of 6 units.
Recall that the equation of a circle is given by:
Where (<em>h, k</em>) is the center and <em>r</em> is the radius.
Since our center is at (3, -2), <em>h</em> = 3 and <em>k</em> = -2. <em>r</em> = 6. Substitute:
Simplify:
In conclusion, the equation of the circle will be:
When the initial input is equal to 15 and the final output is -6, 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)
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)
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)
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: 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?
