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
Answer:
23.5(to the nearest tenth)
Step-by-step explanation:
pythagoras theorem states
c^2= a^2+ b^2
a= 23
b=5
c^2= 529+25
c^2= 554
c= square root of 554
c = 23.5 (approximately)
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Answer:
6.5
Step-by-step explanation:
you take the sides all added up (which was 13in) and divided it by two
Answer:
A=3, B=4, C=-5
Step-by-step explanation:
So A represents the amplitude, which is the distance between the midline (C), the middle of the graph, and the maximum (or minimum). B is the distance of the period of the graph. In this case, we see that the midline is C=-5 because that is the halfway point of the sine function. We also see that the period distance is B=5-1=4, so our period would be 2π/4 or π/2. Our amplitude would be A=3 because |a|=|-5-(-2)|=|-5+2|=|-3|=3. Observe the graph to see this visually.