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:
15 goals out of 50 penalty kicks was scored by brock
Step-by-step explanation:
If Brock shoots 50 penalty kicks and the probability that he scores a penalty kick is 3/10, the number of goal brock is expected to make can be expressed as:
Number of goals scored = probability value * total penalty kicks taken
Number of goals scored = 
Number of goals scored = 
Answer:
E and F= 54 Degrees D is 90 degrees
Step-by-step explanation:
Answer:
All angles in a rectangle are congruent, because in a rectangle, all angles are 90 degrees.
