Asquare has an area of 289 sq cm. what is the length of one side

For this problem you can do it one of two ways. The first way would be simply take the square root because the area of a square is one side squared. The other way using the same rule would be to go up from a reasonable number and square it, if that is not the number you are looking for add 1 to the original number and square it again. if you cannot square and square root in your head, you should be allowed to use a calculator to get the answer or 17 as the length of a side.

Iwould say rat and vsu but i’m not 100% sure

Answer

1 number

explanation

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.