Aladder 25 feet long is leaning against the wall of a house. the base of the ladder is pulled away from the wall at a rate of 2 feet per second. (do not use mixed numbers. round your answers to three decimal places.)

(a) how fast is the top of the ladder moving down the wall when the base is given below?
15 feet away from the wall
ft/sec

20 feet away from the wall
ft/sec

24 feet away from the wall
ft/sec

last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez

calculus says

and you are told that

so you know

or

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: