The answer is C) 11/20<4/7
Answer:
AB = 18
Step-by-step explanation:
tan 45° = 18/AB
1 = 18/AB
AB = 18
If the wheel has a diameter of 15 inches, its radius is half that, or 7.5 inches then.
a full turn, or a full cycle around the wheel, namely around the circle is 360° or 2π radians.
now, in one turn or cycle, it covered an angle of 2π, in 2 cycles it covered 2(2π), in 3 it did 3(2π) and in 4 of course 4(2π).
so, what is the arc's length, whose radius is 7.5 and its central angle is 8π?
well.... you already know that s = rθ, therefore then, s = (7.5) (8π).
Newton's Law of Cooling
Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.
200=68+(210-68)e^(-10k)
132=142e^(-10k)
132/142=e^(-10k)
ln(132/142)=-10k
k=-ln(132/142)/10
k≈0.0073 so
T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?
180=68+142e^(-0.0073t)
112=142e^(-0.0073t)
112/142=e^(-0.0073t)
ln(112/142)=-0.0073t
t= -ln(112/142)/(0.0073)
t≈32.51 minutes