The Lagrangian for this function and the given constraints is

which has partial derivatives (set equal to 0) satisfying

This is a fairly standard linear system. Solving yields Lagrange multipliers of

and

, and at the same time we find only one critical point at

.
Check the Hessian for

, given by


is positive definite, since

for any vector

, which means

attains a minimum value of

at

. There is no maximum over the given constraints.
The original number to the nearest tenth is 23.8
Answer:
= - 3n
Step-by-step explanation:
There is a common difference between consecutive terms, that is
- 6 - (- 3) = - 9 - (- 6) = - 12 - (- 9) = - 3
This indicate the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 3 and d = - 3 , thus
= - 3 - 3(n - 1) = - 3 - 3n + 3 = - 3n
The n th term is - 3n
You didn't ask a question but its called a period
Answer:
93.5 square units
Step-by-step explanation:
Diameter of the Circle = 12 Units
Therefore:
Radius of the Circle = 12/2 =6 Units
Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.
Area of the Hexagon = 6 X Area of one equilateral triangle
Area of an equilateral triangle of side length s = 
Side Length, s=6 Units

Area of the Hexagon
