For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
Answer:
There are 39 seats I think.
Step-by-step explanation:
548 divided by 14 is a decimal but rounded it to the nearest full number.
The three points A,B,C are all points on this circle.
Each point is then equal distance from the center, that distance being the radius of the circle.
Using the distance formula, we can find the center of the circle (x,y):

Plugging in points A and B into distance formula, then setting them equal to each other gives:

Right away we can cancel out the x terms leaving:

Expand Left side and Solve for y:


Plug in points B and C as before:

Here we can cancel the y-terms.
Expand and solve for x:



Therefore the center of the circle is the point (6,3)
Answer:
4x to the power of 2
Step-by-step explanation: