Using partial derivative to find the extremum of function z = 1-x2-y2 Such as the title

Using partial derivative to find the extremum of function z = 1-x2-y2 Such as the title

∂z/∂x=-2x
∂z/∂y=-2y
Let &; Z /; X = 0 &; Z /; y = 0: x = 0, y = 0
∂2z/∂x2=-2 ∂2z/∂x∂y=0 ∂2z/∂y2=-2
At (0,0) a = - 20
(0,0) is the maximum point, and the maximum is Z (0,0) = 1

Find the partial derivative of Z = x2 + 3xy + Y2,

z'x=2x+3y
z'y=6x+2y

The distance between a and B is 750 km. The passenger cars and freight cars leave from the two places at the same time. Three hours later, the two cars are 450 km apart. How many hours can the two cars travel together

(750-450) / 3 = 100 km
A + B = 100 km / h
450 / 100 = 4.5 hours
Four and a half hours

A question about the division of dedkin
When dedkin defined irrational numbers, he proposed three kinds of sets. One is that rational numbers less than 2 are the upper set, and rational numbers greater than or equal to 2 are the lower set (the other two types are omitted). He also pointed out that rational numbers less than 2 have no supremum. But according to the definition of limit, rational numbers less than 2 are infinitely close to 2, and the difference is less than any positive number, Then they must be equal in the end. That is to say, the lower set will coincide with the upper set
There is something wrong in the narration. But you should be able to understand. On the second floor, infinite approach can not be equal in the end? Isn't that how Hillary chases turtles? The distance between the two is infinitely reduced and eventually equal. Another example is 0.999... = 1.0000. Isn't that a good proof? I don't agree with your understanding of limit. where are you?

It is infinitely close, not equal or nearly equal

The two trains of a and B depart from ab at the same time and meet at the distance of 60 km from the midpoint 4 hours later. It is known that the speed of car a is 4 / 5 of that of car B, and there is a gap between AB and B
How many kilometers is the distance between you and me?

Distance = 60 × 2 × (4 + 5) / (5-4) = 1080 km;
If you don't understand this question, you can ask. If you are satisfied, remember to adopt it
If you have any other questions, please take this question and send it to me. Please understand
I wish you progress in your study

The average number of a, B and C is 50, and the ratio of a, B and C is 1:2

Let a be x, then B be 2x and C be 3x
(x+2x+3x)/3=50
6x=150
x=25
So the C number is 3x = 3 * 25 = 75

The sum of five consecutive even numbers is 130, and the five consecutive even numbers are 130

Let five numbers be A-4, A-2, a, a + 2, a + 4
The sum is 5A = 130
So a = 26
So these five consecutive even numbers are 22, 24, 26, 30, 32

A number is composed of 1 10, 8 1, 7 0.1 and 6 0.01. This number is () and it is ()

18.76
one thousand eight hundred and seventy-six

On a map with a scale of 1:5000000, the distance between the two places is 6cm
When a and B vehicles run from two places at the same time for 3 hours, the speed ratio between a and B vehicles is known to be 3:2. How many kilometers per hour does a and B vehicles travel?

1: The scale of 5000000 means the length of 1 unit on the graph = the actual length of 5000000 units
First, calculate the actual distance between the two places
6×5000000=30000000cm=300km
If the speed of car a is 3K (km / h), then the speed of car B is 2K (km / h)
As the two vehicles leave each other and meet in three hours, the total distance of vehicle a and vehicle B is equal to the total distance
3k×3+2k×3=300
That is, 3 × (2k + 3K) = 300
The solution of the equation is: k = 20
So the speed of car a is: 3 × 20 = 60 (km / h)
Speed of vehicle B: 2 × 20 = 40 (km / h)
A: the speed of car a is 60km / h, and that of car B is 40km / h

Given that the determinant of the third-order matrix A = (a, B, c) is equal to D, find the determinant of the matrix C = (A-B, B + 2c, a + B-C). What is the meaning of "the determinant of the third-order matrix A = (a, B, c) is equal to D"?

If the determinant of the third order matrix A is equal to D, it means that the value of the matrix is d
For the matrix from C there are:
C=(a,b,c)(1,0,1)
----------(-1,1,1)
----------(0,2, - 1) then C = - 5D