Answer:
It should be 92
Step-by-step explanation:
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be

.
You're minimizing

subject to the constraint

. Note that

and

attain their extrema at the same values of

, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is

Take your partial derivatives and set them equal to 0:

Adding the first three equations together yields

and plugging this into the first three equations, you find a critical point at

.
The squared distance is then

, which means the shortest distance must be

.
Answer:
21/10
Step-by-step explanation:
Trust Me
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Information Given:
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ON = 7x - 9
LM = 6x + 4
MN = x - 7
OL = 2y - 7
-----------------------------------------------
Since it is a parallelogram:
-----------------------------------------------
ON = LM and
MN = OL
-----------------------------------------------
ON = LM:
-----------------------------------------------
7x - 9 = 6x + 4
-----------------------------------------------
Subtract 6x from both sides:
-----------------------------------------------
x - 9 = 4
-----------------------------------------------
Add 9 to both sides:
-----------------------------------------------
x = 13
-----------------------------------------------
MN = OL:
-----------------------------------------------
x - 7 = 2y - 7
-----------------------------------------------
Sub x = 13:
-----------------------------------------------
13 - 7 = 2y - 7
-----------------------------------------------
Simplify:
-----------------------------------------------
6 = 2y - 7
-----------------------------------------------
Add 7 on both sides:
-----------------------------------------------
13 = 2y
-----------------------------------------------
Divide by 2:
-----------------------------------------------
y = 13/2
-----------------------------------------------
Answer: x = 13, y = 13/2 (Answer D)
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1. y<span> ≤ 4x/3+5
2. y</span><span>< 6x/4+3</span>