Four less than half of a number is 17. find the number
1 answer:
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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.
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
Check the Hessian for
Answer:
2.4 pints
Step-by-step explanation:
Araceli uses 9.6 pints of blue paint and white paints, that means the total volume of paint is 9.6 pints
If Three fourths of this amount is blue paint ,
Then
7.2 pints of blue paint was used.
We want to find out how much white paint was used by Araceli
Volume of Blue Paint+Volume of White Paint=Total Volume of Paint
7.2+Volume of White Paint=9.6
Volume of White Paint=9.6-7.2=2.4 pints