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:
View graph
Step-by-step explanation:
The closest by default to 1100 cubic inches is taking two side and two front covers and that would give you 1080.12 cubic inches since two of the covers you must subtract 3 cm per side and side which would add 6 cm in total so outside would be 35 cm and indoor 29 cm
. According the graph
29*50*3= 4350 * 2 lid = 8700 cm3
30*50*3= 4500*2 lid = 9000 cm3
So 8700+9000 = 17700 cm3 to inches 3 = 1080.12 cm3
Answer:
, it is the amount of money earned per number of hours of work, x
Step-by-step explanation:
Here we have two functions:

This function represents the amount of money (the earning) per unit x
Then we have the function

which represents the number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works.
Here we want to find the composite function
which means that we use the output of
as input for
. In this context, this means that the function
represents the amount of money earned per number of hours of work, x.
Substituting g(x) into the x of f(x), we find:

Answer: Amy = domestic stock
Rick = Employer stock
Nisha = International stock
Step-by-step explanation:
Amy invests in shares that won't be affected by exchange rate fluctuations. This shows that the stock that Amy invested in is a domestic stock. These are the stocks that are usually sold by companies in the home country.
As a part of Rick's full-time benefits package, he can invest in compally stock. This shows that Rick invested in the employer stock.
Nisha needs to research the political situation in a specific country before she purchases stock. Nisha invested in an international stock.