Answer:
y'(t) = k(700,000-y(t)) k>0 is the constant of proportionality
y(0) =0
Step-by-step explanation:
(a.) Formulate a differential equation and initial condition for y(t) = the number of people who have heard the news t days after it has happened.
If we suppose that news spreads through a city of fixed size of 700,000 people at a time rate proportional to the number of people who have not heard the news that means
<em>dy/dt = k(700,000-y(t)) </em>where k is some constant of proportionality.
Since no one has heard the news at first, we have
<em>y(0) = 0 (initial condition)
</em>
We can then state the initial value problem as
y'(t) = k(700,000-y(t))
y(0) =0
So each 1 revolution it travels the distance around the rim of the wheele aka circumference
circumference=pi times diameter
diameter=21
circunference=pi times 21 or 21pi
so distance=number of revolutions times circunference
number of revolutions=3
subsitute
distance=3 times 21pi
distance=63pi
answer is 63pi
or aprox pi to 3.14 and do 63 times 3.14=197.82
aprox 197.82 inches
Your answer should be:
(10-6)x(2+8)=40
