<span>D=20+50t
120=20+50t
50t=100
t=2 hours
Domain of t from t=-(2/5)hr to t=2hr. Since they already drove 20 miles.
[-2/5,2]</span>
We have been given a system of inequalities and an objective function.
The inequalities are given as:

And the objective function is given as:

In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.
The graph of the region is shown below:
From the graph, we can see that corner points of the feasible region are:
(x,y) = (15,30),(30,15) and (30,60).
Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.

Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30
Answer:
The larger cross section is 24 meters away from the apex.
Step-by-step explanation:
The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.
The length of the side of the hexagon is equal to the radius of the circle that inscribes it.
The area is

Where
is the radius of the inscribing circle (or the length of side of the hexagon).
Now we are given the areas of the two cross sections of the right hexagonal pyramid:
From these areas we find the radius of the hexagons:
Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that
form similar triangles with length
Therefore we have:

We put in the numerical values of
,
and solve for
:
