A 26 foot ladder is lowered down a vertical wall at a rate of 3 feet per minute. The base of the ladder is sliding away from the wall. A. At what rate is the ladder sliding away from the wall when the base of the ladder is 10 feet from the wall

Step-by-step explanation:

We can apply the Pythagorean theorem here:

where x is the distance of the ladder base from the wall and y is the distance of the ladder top from the ground. Taking the time derivative of the expression above, we get

Solving for we get

We can replace y by rearranging Eqn(1) such that

Therefore,

Since y is decreasing as the ladder is being lowered, we will assign a negative sign to . Hence,

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c