you're pretty close. Using the law of cosines, we know that c^2 = a^2 + b^2 - 2*a*b*cos(O). If you differentiate this equation with respect to time, you should get a relation dc/dt with a, b, O, da/dt, db/dt, and dO/dt. Plug and chug from there
The minute hand on a watch is 4 mm long and the hour hand is 3 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)
minute hand = a
hour hand = b
distance between a and b = c
I know that I am looking for dc/dt
I know that the angle between the hands, O, at 1:00 is 30 degrees
I know that by using the law of cosines c = sqrt(25-12sqrt(3))
I know da/dt = 2pi radians/hr and db/dt = pi/6 radians/hr
so dO/dt = -11pi/6 radians/hr
I have this much figured out but I don't know how to relate dO/dt to dc/dt, the instantaneous rate of change of c, which is what the question asks for. Could someone give me a hint as to how I should relate the information I have and what I need?
you're pretty close. Using the law of cosines, we know that c^2 = a^2 + b^2 - 2*a*b*cos(O). If you differentiate this equation with respect to time, you should get a relation dc/dt with a, b, O, da/dt, db/dt, and dO/dt. Plug and chug from there