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: 9 i think, i don't know hope i helped :)
Answer:
It's B :)
Step-by-step explanation:
Total cost = a + (13a/100)
<u>Step-by-step explanation:</u>
Let the price of the monster truck be 'a'
He should pay 13% tax
Total cost = price of the truck + tax
Total cost = a + (13a/100)
The equation to represent the total cost is
Total cost= a + (13a/100)
YES, this is correct. All quadrilaterals whether is a trapezoid, parallelogram, rhombus and others, they are all polygons and all they have 4 sides and 4 angles. We know that a polygon is a figure with at least three sides and three angles.
Not all polygons are quadrilateral, this is also correct since some polygons have five or more sides and angles.
