If the area of a circle measures 25 pi cm², what is the circumference of the circle in terms of pi?
1 answer:
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Answer:
a) , b)
, c)
, d)
Step-by-step explanation:
a) Let assume an initial mass m decaying at a constant rate k throughout time, the differential equation is:
b) The general solution is found after separating variables and integrating each sides:
Where is the time constant and
c) The time constant is:
The particular solution of the differential equation is:
d) The amount of radium after 300 years is:
The graph of y=ax+b, where a≠0, is always a line:
i) increasing if a>0
ii) decreasing if a<0
Consider the decreasing case.
The line is above the x-axis, that is positive but decreasing. At 1 single point it cuts the x-axis, so x=0, and then it continues decreasing below the x-axis.
Back to our problem:
The graph of y=-1/2 x +2 is a decreasing line.,
so it CANNOT be
"positive over the interval (4, infinity) and negative over the interval (-infinity, 4)"
it is
"<span>negative over the interval (4, infinity) and positive over the interval (-infinity, 4)</span>"
the graph is "<span>positive over the interval (-infinity, 4)</span>", it means that the line is decreasing but above the x-axis until 4, (4 not included).
then, "negative over the interval (4, infinity)", which means that the line is now decreasing below the x-axis.
when x=4, the line cuts the x-axis.
check the graph of the line generated using desmos.com
