(Solved): A ladder 13ft long rests against a vertical wall. Let x be distance base of ladder is from wall. Le ...

A ladder $13\mathrm{ft}$ long rests against a vertical wall. Let $\mathbf{x}$ be distance base of ladder is from wall. Let $y$ be distance top of ladder is from floor. a) What is the expression $x^2+y^2$ always equal to? b) If the base of ladder is 12 feet from the wall, how far (feet) is the top of the ladder from the floor? c) What is the cosine of the angle formed from the base of ladder and the floor when the base of ladder is $12\mathrm{ft}$ from wall? d) Determine the missing expression in the equation for how fast the ladder would be sliding down the wall toward the floor if the base of ladder was pulled away from wall at a constant rate $\frac{dy}{dt}=($ expression $)\frac{dx}{dt}$ e) Suppose the base of ladder is being pulled away from wall at a rate $5\mathrm{ft}/\sec$ when base is $12\mathrm{ft}$ from wall. At what rate is the top of ladder moving(ft/sec). You are finding $y^{?}$. f) How fast would the area between ladder, wall, and floor be changing when the base is $12\mathrm{ft}$ from wall and ladder is being pulled away from wall at a rate of $5\mathrm{ft}/\sec$. Round to nearest whole number.