reletad Rates and linear Approximation and differentiation 6 questions

A 53 feet long ladder is leaning against a vertical wall of a building. The base of the ladder is being pulled away from the wall at a rate of 8 feet per second. Determine the rate of change of the *angle* (in radians) formed by the top of the ladder and the wall when the base of the ladder is 28 feet away from the wall. Building Ladder Ground radians per second Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 22 feet high? Round to two decimal places. Recall that the volume of a right circular cone with height h and radius of the base r is given by V = ,Trz h min 1 pt An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per second. The pyramid, at the top, has the shape of a square b1 with sides of length 4 cm, and the height is 10 cm. Find the rate at which the water level is rising when the water level is 6 cm. Use similar triangles, and the fact that the volume of a pyramid is h V = 162 h The exact answer is cm/sec The decimal approximation (to one decimal place) is cm/sec Question Help: Vids shadow A street light is at the top of a 17 ft tall pole. A woman 5.5 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole? Round to two decimal places. ft sec Use linear approximation, i.e. the tangent line, to approximate 1.002 as follows: Let f(z) = and find the equation of the tangent line to f(a) at a "nice" point near 1.002. Then use this to 1 approximate 1002 Given the function below f(z) = V32x3 + 32 Find the equation of the tangent line to the graph of the function at a = 1. Answer in max + b form. L(x) = Use the tangent line to approximate f (1.1). L(1.1) = Compute the calculator's value of f(1.1). What is the error between the function value and the linear approximation? (Approximate to 5 decimal places.) Answer as a positive value only, |error | ~