Answer:

Step-by-step explanation:
Let L be the length of the ladder,
Given,
x = the distance from the base of the ladder to the wall, and t be time.
y = distance from the base of the ladder to the wall,
So, by the Pythagoras theorem,

,
Differentiating with respect to time (t),




Here,

Also,
( Ladder length = constant ),




Which is the required notation.
Answer:
The GCF of 36 and 90 is 18
Answer:

Step-by-step explanation:
GIVEN: A farmer has
of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is
.
TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.
SOLUTION:
Let the length of rectangle be
and
perimeter of rectangular pen 


area of rectangular pen 

putting value of 


to maximize 



but the dimensions must be lesser or equal to than that of barn.
therefore maximum length rectangular pen 
width of rectangular pen 
Maximum area of rectangular pen 
Hence maximum area of rectangular pen is
and dimensions are 
Answer:
x = (5/3 , 7)
Step-by-step explanation: