I need help with this problems
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The top of a 15-foot ladder leans against a wall, and the bottom of the ladder slides away from the wall at a rate of 4 ft/sec. Find the velocity of the top of the ladder at time t = 1 sec if the bottom of the ladder is 5 feet away from the wall at time t = 0. ft/sec Use the Pythagorean Theorem and implicit differentiation. Suppose that both the radius r and height h of a circular cone are increasing at a rate of 6 cm/s. How fast is the volume of the cone increasing when r = 7 cm and h = 5 cm? (Round your answer to three decimal places.) cm3/s A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 2.0 m/s. Find the rate at which his shadow is increasing in length. (Round your answer to three decimal places.) m/s At a given moment, a plane passes directly above a radar station at an altitude of 6 km. The plane's speed is 200 km/h. How fast is the distance between the plane and the station changing half an hour later? (Assume the plane maintains this speed and altitude over the half hour. Rund you answer to three decimal places.) km/h