Please help me with this its for math will give brainly for correct answer
2 answers:
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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
Answer: 11 is the required number that always divides such differences for the following types of numbers.
Step-by-step explanation:
Take any 3 - digit number, say, 325
On reversing its digit it becomes, 523
On subtracting the smaller of the two numbers from the larger,
we can see that 198 is an even number.
take another number say, 629
On reversing its digit, it becomes = 926
On subtracting , we get that
But 297 is not an even number.
But there is one common in both the cases is that both the differences are divisible by 11.
Hence, 11 is the required number that always divides such differences for the following types of numbers.