Newton's law of cooling states that under forced convection (which is assumed to be true), then
dT(t)/dt = -k(T(t)-Ta)..............(1)
T(t)=temperature
Ta=ambient temperature=40F
k=cooling constant = 0.1947
T(0)=98.6F (assuming victim did not have fever)
Integrate (1)
T(t)-Ta=(T(t)-T(0))e^(-kt)
Solve for t
(T(t)-Ta)/(T(t)-T(0)) = e^(-kt)
take log:
-kt=log_e((T(t)-Ta)/(T(t)-T(0)))
substitute T(t)=80F, Ta=40F,T(0)=98.6F
-kt=log_e((80-40)/(98.6-40))=-0.38186
t=0.38186/0.1947
=1.96, or almost 2 hours (assuming k=0.1947 is in hours)
Answer:
The question is incorrect as it lacks the "x" component. Function f(x) cannot be stated without the x, elseways it couldn't be called "f(x)"
For direct variation:
y = kx
-12 = 9k
k = -12/9 = -4/3
Therefore, the required equation is y = -4/3 x
Y2-y1/x2-x1
5-(-3)/(-6-(-1))
8/-5
-8/5 is the slope
Answer:
16 is 2/5th's of the line between the point at 6 and the point at 31.
Step-by-step explanation:
First, to get the point on the number line that would be 2/5th's of point 31 and point 6, you need to get the absolute value / difference between both points.
31 - 6 = |25|
So then you need to get what a fifth (1/5) equals from 25.
25 / 5 = 5.
So 2/5th's of the difference between point 31 and point 5 would be two 1/5th's (5 + 5) which equals 10.
Add 6 to 10 (since 6 is the beginning of the line between both points) and you get 16, which is 2/5th's of the line from point 6 to point 31.