Question

Each cable joining the two towers on the Golden Gate Bridge can be modeled by the function

y= 1/9000 x² - 7/15 x+500

where x and y are measured in feet. What is the height h above the road of a cable at its lowest point?

Answer 1

The height above the road of a cable at its lowest point is 3559.43 feet.

Step-by-step explanation:

To find the height above the road of a cable at its lowest point, we need to determine the lowest point of the cable, which corresponds to the minimum value of the function y = (1/9000)x^2 - (7/15)x + 500.

The lowest point occurs at the x-coordinate of the vertex of the quadratic function. The x-coordinate of the vertex is given by the formula x = -b/(2a), where a, b, and c are the coefficients of the quadratic equation.

Using the formula, we find x = -(-7/15)/(2(1/9000)) = 7/15(9000/2) = 2100 feet.

Plugging this value of x into the equation y = (1/9000)x^2 - (7/15)x + 500, we can determine the height above the road at the lowest point.

y = (1/9000)(2100)^2 - (7/15)(2100) + 500 = -21 + 980 - 7/15(2100) + 500 = -21 + 980 + 2100 - (7/15)(2100) + 500 = 3559.43 feet.