The distance between an arbitrary point on the surface and the origin is
Recall that for differentiable functions
and
, the composition
attains extrema at the same points that
does, so we can consider an augmented distance function
The Lagrangian would then be
We have partial derivatives
Set each partial derivative to 0 and solve the system to find the critical points.
From the second equation it follows that either
or
. In the first case we arrive at a contradiction (I'll leave establishing that to you). If
, then we have
This means
so that the points on the surface closest to the origin are
.
Answer:
1 1/3
Step-by-step explanation:
you have to take away 2/3 and 1/4 and add the one and your answer is 1 1/3 and the bottom of the fraction stay the same
Part A)
Total stores = 362 + 66 = 428
362 / 428 = 0.845 = 84.5% = 85%
66 / 428 = 0.154 = 15.4% = 15%
Yes this is consistent with the percentages shown in the first table.
Part B)
Total stores : 197 +115 = 312
197 / 312 = 0.631 = 63.1% = 63%
115 / 312 = 0.368 = 36.8% = 37%
The percentage for current stores is less than what is shown in the first table, so this would not be consistent.
Part C )
Percentage of new stores for the Northeast = 60 / 310 = 19%
The percentage of new stores for The Midwest and Northeast are below 25%, but the percentage of new stores in the South is above 25%, so the additional training wouldn't be required for the South, but should be required for the other two areas.
Answer:
1. he eats 5 per day (5 less every day)
2. he starts with 83 pieces of candy
3. 53
4. on day 11
Step-by-step explanation:
1. self explanatory
2. self explanatory
3. 6*-5=-30 -30+83=53
4. put y as 28
28=-5x + 83 now solve for x
subtract 83 both sides
-55=-5x
divide -5 from both sides
11=x
Answer:Perry and Lorna take the maximum time and Maria and Lorna take the minimum time when they work together.
Explanation: Since, according to the question- Perry takes time when he works alone = 3 hours
Similarly, Maria takes = 2 hours, While Lorna takes= 2 hours 30 minutes or 2.5 hours.
since, there are three people thus their are three possibility to choose any two of them.
1- when Perry and Maria work together then time taken by them is 
=
= 6/5= 1 hour 12 minutes.
2- when Maria and Lorna work together then time taken by them is 
= 10/9= 1 hours 1/9 minutes ≈ 1 hours 7 min
3- when Perry and Lorna work together then time taken= 
= 15/11= 1 hour 4/11 minutes≈ 1 hours 21 minutes
From the above explanation, it has been proved that when we talk about 2 members team then Perry and Lorna take the maximum time. While Maria and Lorna take the minimum time when they work together.
