12/3 = 4
4 cars per hour
4 x 5 = $20
20 x 8 = $160 for 8 hrs
The arc length is given by
.. s = rθ . . . . . . θ is the central angle in radians
.. = (8 in)*(35/180*π)
.. ≈ 4.9 in
_____
A disk 16 inches in diameter has a radius of 8 inches.
Answer:
4
Step-by-step explanation:
36 = 9*h
9*h = 36
h = 36/9
h = 4
The unknown b is stuck in the exponent position.
We can can fix that by using logarithms.
Log is the inverse operation of the exponential.
We'll take log of each side.
Log of what base tho?
Well, the base of our exponential is e,
so we'll take log base e of each side.
We'll apply one of our log rules next:
This allows us to take the exponent out of the log,
Another thing to remember about logs:
When the base of the log matches the inside of the log,
then the whole thing is simply 1,
So our equation simplifies to this,
As a final step, divide both sides by 3,
k, hope that helps!
Answer:
19.44 hours, about 19 hours 26 minutes
Step-by-step explanation:
The exponential equation that describes your caffeine level can be written as ...
c(t) = 120·(1 -0.12)^t . . . . where t is in hours and c(t) is in mg
We want to find t for c(t) = 10, so ...
10 = 120(0.88^t)
10/120 = 0.88^t . . . . . . . divide by 120
log(1/12) = t·log(0.88) . . . take logarithms
t = log(1/12)/log(0.88) ≈ 19.4386
It will take about 19.44 hours, or 19 hours 26 minutes, for the caffeine level in your system to decrease to 10 mg.
