7 questions related rates and linear approximation

A 41 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 7 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 9 feet away from the wall. Building Ladder Ground radians per second shadow A street light is at the top of a 19 ft tall pole. A woman 4.75 ft tall walks away from the pole with a speed of 7 fu/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole? Round to two decimal places. sec Let y = tan(4x + 6). Find, to 4 decimal places, the differential dy when x = 5 and dx = 0.2 Find, to 4 decimal places, the differential dy when a = 5 and dx = 0.4 Let y = sin(5x). If Ax = 0.4 at x = 0, use linear approximation to estimate Ay to one decimal place Ay ~ = Find the percentage error to one decimal place. error = Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.09 cm thick to a hemispherical dome with a diameter of 30 meters. Round to the nearest whole cm". Things to watch out for: a hemisphere is *half* of a sphere the radius is *half* of the diameter units, cm versus m cm3 Lety = 5x2. The circumference of a sphere was measured to be 71 cm with a possible error of 0.5 cm. Find the change in y, i.e., Ay , when a = 1 and Ax = 0.3 The surface area of a sphere is 4mr2 Use linear approximation to estimate the maximum error in the calculated surface area, to 5 decimal places. Find the differential dy when a = 1 and dx = 0.3 Estimate the relative error in the calculated surface area, to 5 decimal places