A kite glides horizontally at an altitude of 30 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 50 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 11 m/s. To solve this problem, let be the angle in radians made between the string and the horizontal, x is the kite's horizontal position in meters since being attached to the ground, and t is the time in seconds. We further suppose that the string is straight and taut.

a) sketch a diagram of this to use to express in rad as a function of x

b) what is the value of x at the moment in the equation (exact value)

c) what is the value of dtdat the same moment? (exact value)