Dave bought jeans at a store. • The jeans had an original price of $45.50 • The jeans were discounted 30% from the original pric
1 answer:
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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 
.
You're minimizing
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
For this case we must resolve the following inequality:
Adding 7 to both sides of the inequality:
Different signs are subtracted and the major sign is placed.
Thus, the solution is given by all the values of "x" less than -5.
The solution set is: (-∞, - 5)
Answer:
See attached image
