To represent the situation described in the egg-drop project, we want to establish equations that show how the height \( y \) of the egg decreases over time \( x \) as the egg falls.
The initial height of the egg is 10 feet, and the egg falls at different rates for the two designs.
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For the first design, the egg falls at a rate of 5 feet per second:
- The height \( y \) decreases from 10 feet at a rate of 5 feet per second, so the equation is \[ y = 10 - 5x. \]
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For the second design, the egg falls at a rate of 3 feet per second:
- Similarly, the height \( y \) also decreases from 10 feet at a rate of 3 feet per second, resulting in the equation \[ y = 10 - 3x. \]
The correct system of equations that represents this situation is:
3. \( y = 10 - 5x \)
\( y = 10 - 3x \)
So the answer is option 3.