The xianren bridge is located in guangxi province, china. this arch is the world’s longest natural arch, with a length of 400 feet. write and graph an inequality that represents the lengths l (in inches) of all other natural arches.

Step-by-step explanation:

Given : The Xianren Bridge is located in Guangxi Province, China.

This arch is the world’s longest natural arch, with a length of 400 feet.

if the length of all other natural arches ( in inches) is represented by 'l'.

Then, the required inequality will be :-

Hence, the inequality that represents the lengths l (in inches) of all other natural arches :

The graph for this inequality is given below:

For strictly less than or more than we use circle to exclude that value from the interval.

Also, the length cannot be negative so the line(orange in color) is stopped at 0 .

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.