Question

A jump rope held stationary by two children, one at each end, hangs in a shape that can be modeled by the equation h = 0.01x² - 26x, where h is the height (in inches) above the ground and x is the distance (in inches) along the ground measured from the horizontal position of one end. How close to the ground is the lowest part of the rope?

1) 0.5 in.
2) 1 in.
3) 1.25 in.
4) 2 in.

Answer 1

The lowest part of the rope is approximately 1416.67 inches above the ground.

Step-by-step explanation:

The equation provided, h = 0.01x² - 26x, represents the shape of a jump rope held stationary by two children. To find the lowest part of the rope, we need to determine the minimum value of h. This can be found by using the vertex formula, which gives us the x-coordinate of the vertex of a parabola in the form y = ax² + bx + c as x = -b / 2a. Plugging in the values from the equation, we get x = -(-26) / (2 * 0.01) = 1300 inches. Substituting this value into the equation, we find h = 0.01(1300)² - 26(1300) = -16900 inches. However, since we are looking for the distance above the ground, we take the absolute value, which is 16900 inches or 1416.67 feet. Therefore, the lowest part of the rope is approximately 1416.67 inches above the ground.