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:
6045000000000000000000000 kg.
Step-by-step explanation:
We have been given that the mass of Earth is
kg. The mass of the Moon is
kg.
To find the total mass we will add mass of Earth and Moon.
First of all let us convert the given masses in standard form.



Therefore, the mass of Earth and Moon is 6045000000000000000000000 kg.
Hmmm.....................
We can easily get the quarts per hour rate by dividing the number of quarts by the number of hours:

Now that we have the quarts per hour rate, we can easily address the question: the factory could make

quarts in 48 hours, with a daily rate of

quarts per day