Upper AA 66-ft-tall fence runs parallel to a wall of a house at a distance of 3030 ft. Find the length of the shortest ladder that extends from the ground, over the fence, to the house. Assume the vertical wall of the house and the horizontal ground have infinite extent.

0.33 ft

Step-by-step explanation:

From the diagram, triangle ACE is similar to triangle BCD.

Therefore,

Let the Length of the Ladder, L

Using Pythagoras theorem

To find the least value, we have to equate the derivative of L to 0.

Therefore:

b³-1080=0

b³=1080

b=10.26

The minimum length of the ladder is:

=0.33 ft

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation:

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.