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.
Answer:
25/30 and 28/30
Step-by-step explanation:
1. To find the least common denominator, you need to find the least common multiple of the two denominators which are 6 and 15. Prime factorization of these numbers gives:
6 = 2 x 3
15 = 5 x 3
A number that would evenly divide both 6 and 15 must contain 2 x 3 x 5 which is 30.
Thus 30 is the least common denominator.
2. Now we need to somehow change both fractions to make them have a denominator of 30. To do this we can multiply by fractions with same numerator and denominator since that would be like multiplying by 1.
So, 5/6 x 5/5 = 25/30
And 14/15 x 2/2 = 28/30
1/9 = 1.11
29/8 = 3.63
-------
3.73 = 269/72
or....
1/9 >>> 8/72 (72 is the common denominator) (Multiply the N and D by 8)
29/8 >>> 261/72 (72 is the common denominator) (Multiply the N and D by 9)
-------------
269/72
Answer: uhh
Step-by-step explanation:
I really don’t know how to do it.
5 People can be chosen in 1287 ways if the order in which they are chosen is not important.
Step-by-step explanation:
Given:
Total number of students= 13
Number of Students to be selected= 5
To Find :
The number of ways in which the 5 people can be selected=?
Solution:
Let us use the permutation and combination to solve this problem
So here , n =13 and r=5 ,
So after putting the value of n and r , the equation will be
