The linear relationship is y = 20x, 0 ≤ x ≤ 17.5 and the quadratic relationship is y = -16x² + 288, 0 ≤ x ≤ 3√2
<h3>The equations that represent the relationships</h3>
<u>The linear relationship</u>
When making the trip up, we have:
Rate = 20 feet per seconds
This means that the relationship is:
Distance = Rate * Time
So, we have:
y = 20x
The height of the tower is 350.
So, we have:
20x = 350
Divide by 20
x = 17.5
Hence, the linear relationship is y = 20x, 0 ≤ x ≤ 17.5
<u>The quadratic relationship</u>
The quadratic equation can be represented as:
y = -0.5ax² + vx + h
Where:
- a = acceleration due to gravity = 32
- v = velocity = 0
- h = height = 288
So, we have:
y = -0.5 * 32x² + 0 * x + 288
Evaluate
y = -16x² + 288
When you get to the ground level, we have:
-16x² + 288 = 0
Subtract 288 from both sides
-16x² = -288
Divide by -16
x² = 18
Take the square root of both sides
x = ±3√2
Remove negative domain
x = 3√2
Hence, the quadratic relationship is y = -16x² + 288, 0 ≤ x ≤ 3√2
Read more about linear and quadratic equations at:
brainly.com/question/72196
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