When creating a histogram, the first recorded scale is 0 to 10. What should the second scale indicate?
1 answer:
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Answer:
The side length of of the base of the tank is 15 inches.
Step-by-step explanation:
We are given the following in the question:
Cost of the tank and filter system = $280
Perimeter of tank base = 60 inches
The perimeter of tank is in the shape of square.
We have to find the side length of the base of the tank.
Perimeter of tank base = Perimeter of square =
Thus, the side length of of the base of the tank is 15 inches.
The distance between a point 
on the given plane and the point (0, 2, 4) is
but since
and 
share critical points, we can instead consider the problem of optimizing subject to 
.
The Lagrangian is
with partial derivatives (set equal to 0)
Solve for
:
which gives the critical point
We can confirm that this is a minimum by checking the Hessian matrix of:
is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.
At this point, we get a distance from (0, 2, 4) of
but since
The Lagrangian is
with partial derivatives (set equal to 0)
Solve for
which gives the critical point
We can confirm that this is a minimum by checking the Hessian matrix of
At this point, we get a distance from (0, 2, 4) of