Question

A jump rope held stationary by two children, one at each end, hangs in a shape that can be modeled by the equationh = h=0.01x² - x + 26, 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?

a. 0.5 in.
b. 1 in. d. 2 in.
c. 1.25 in.
please select the best answer from the choices provided a b c

Answer 1

To find the lowest part of the jump rope, the vertex of the parabola h = 0.01x² - x + 26 is calculated using the vertex formula, resulting in a minimum height of 1 inch from the ground.

Step-by-step explanation:

The lowest part of the jump rope would correspond to the vertex of the parabolic equation h = 0.01x² - x + 26. To find the minimum height h, which is how close the jump rope is to the ground at its lowest part, we need to complete the square or use the vertex formula. The vertex formula for a parabola given by y = ax² + bx + c is (-b/2a, c - b²/4a). In this case, a = 0.01, b = -1, and c = 26. The x-coordinate of the vertex is given by -(-1)/(2*0.01) which simplifies to 50. Substituting x = 50 back into the original equation gives the height above the ground at the vertex, which is the lowest point of the rope. Therefore, h at x = 50 is 0.01*50² - 50 + 26 = 1 in. So the correct answer is (b) 1 in.