You come home one day during a spring rain shower to discover your roof is leaking in different places.
someone has already placed 50 gallon buckets under each of the leaks, and the buckets have already collected some water. the hole in the kitchen ceiling is leaking an average rate of 2 gallons per minute and the bucket already contains 19 gallons of water. the hole in the living room must be bigger because it is leaking at an average rate of 3 gallons per minute and the bucket already contains 7 gallons. (it must have been emptied once.)
how much longer before the buckets contain the same amount of water? how much eater will that be?
-choose the most appropriate algebraic method to solve this problem
-variables should be chosen and labeled.

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.

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130