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>
The probability according to the given scenario will be "
".
According to the question:
- The odds against winning the lottery are 48,000,000 to 1.
- Favorable outcome = 1
→ The total outcome will be:
= 
= 
As we know,
→ 
By putting the values, we get
→ 
Thus the above response is right.
Learn more about Probability here:
brainly.com/question/15739211
Answer:
SA = <em>41.</em>
Step-by-step explanation:
Add up everything and you get <em>41 </em>as the SA.
