Nima uses 2/3 cup peanuts, 1/2 cup cashews , 3/4 cup pecans, and some raisins in a recipe that makes 2 1/4 cups of trail mix. Ho
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Answer:
Step-by-step explanation:
slope is the change in y over the change in x.
change in y is 14-18= -4
change in x is 30-(-20)= 50
so the answer is -4/50
we can factor out 2 from both equations to simplify the fraction. this gives us -2/25
The distance between a point 
on the given plane and the point (0, 2, 4) is
but since
and 
share critical points, we can instead consider the problem of optimizing subject to 
.
The Lagrangian is
with partial derivatives (set equal to 0)
Solve for
:
which gives the critical point
We can confirm that this is a minimum by checking the Hessian matrix of:
is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.
At this point, we get a distance from (0, 2, 4) of
but since
The Lagrangian is
with partial derivatives (set equal to 0)
Solve for
which gives the critical point
We can confirm that this is a minimum by checking the Hessian matrix of
At this point, we get a distance from (0, 2, 4) of