Thomas, a very talented builder, was putting a fence in the play area in his yard for his dogs. If he wants it to be square, and
have an area of at least 150 square feet, what is the smallest amount of fence he will need?
1 answer:
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ANSWER
672cm²
EXPLANATION
The area of a regular hexagon is given by the formula,
where a=14cm is the apothem and p=96cm is the perimeter of the regular hexagon.
We substitute the values into the formula,
Therefore the approximate area of the hexagon is 672cm²
Answer:
The differential equation for the amount of salt A(t) in the tank at a time t > 0 is .
Step-by-step explanation:
We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.
The concentration of the solution entering is 4 lb/gal.
Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;
where, = concentration of salt in the inflow
input rate of brine solution
and = concentration of salt in the outflow
outflow rate of brine solution
So, = 4 lb/gal
3 gal/min = 12 lb/gal
Now, the rate of accumulation = Rate of input of solution - Rate of output of solution
= 3 gal/min - 2 gal/min
= 1 gal/min.
It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.
So, = concentration of salt in the outflow
outflow rate of brine solution
= =
Now, the differential equation for the amount of salt A(t) in the tank at a time t > 0 is given by;
=
or .