The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

“The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”

The word that best fills the blank in the above sentence is

The value of the expression

$${1 \over {1 + \log _u^{vw}}} + {1 \over {1 + \log _v^{wu}}} + {1 \over {1 + \log _w^{uv}}}$$ is

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?