In order to set up a linear equation of three variables, there must be a process There are three kinds of goods: A, B and C. If you buy 3 pieces of a, 7 pieces of B and 1 piece of C, the total cost is 580 yuan. If you buy 4 pieces of a, 10 pieces of B and 1 piece of C, the total cost is 630 yuan. If you buy one piece of a, B and C, how much is the total cost?

Let a be x yuan, B be y yuan, C be Z yuan
According to the meaning of the title, it has 3x + 7Y + Z = 580
4X+10Y+Z=630
Let x + y + Z = a
Then the first equation is reduced to 2x + 6y + (x + y + Z) = 580, that is, 2x + 6y + a = 580, and X + 3Y = (580-a) / 2
Similarly, the second equation is reduced to 3x + 9y + a = 630 to get x + 3Y = (630-a) / 3
x+3y=(580-a)/2 x+3y=(630-a)/3
A = 480, that is, to buy a, B, C each, a total of 480 yuan

In the three plots of land a, B and C, the grass grows as dense and as fast. The third and third hectare of land a can feed 12 cows for 4 weeks, the 10 hectare of land B can feed 21 cows for 9 weeks, and the 24 hectare can feed several cows for 18 weeks;

If a cow eats one portion of grass a day, and the amount of grass stored per hectare is x, and the amount of growth per hectare is y, then there are: 12 cows eat 12 * 28 = 336 parts of grass 10 / 3 (x + 28y) = 336 (a) 21 cows eat 9 weeks 21 * 63 = 1323 parts of grass 10 * (x + 63y) = 1323 (b)

If Liman → infinity does not exist and limbn → infinity does not exist, does LIM (anbn) → infinity exist

It may or may not exist

If A. B is opposite to each other and C. B is reciprocal to each other, what is the square root of AB + the open power of CB

a+b=0
cb=1
"Then AB's square root + CB's square root = how much" you will have the result

We know that 3sinb = sin (2a + b), and prove that Tan (a + b) = 2tana

The proof is as follows:
From 3sinb = sin (2a + b)
3sinb = sin2acosb + sinbcos2a
sinb(3-cos2a)=sin2acosb
SINB (2 + 2sina ^ 2) = 2sinacosb
sinb=sina(cosacosb-sinbsina)=sinacos(a+b)
And Tan (a + b) - 2tana = (sin (a + b) cosa-2sinacos (a + b)) / (COA (a + b) COSA)=
(SINB sinacos (a + b)) / (COA (a + b) COSA) from Tan (a + b) - 2tana = 0

Approximate value of positive real root of equation x & # 178; + 2x = 5 by dichotomy (accuracy 0.1)

F (x) = x & # 178; + 2x-5f (0) = - 5F (1) = - 2F (2) = 3f (3) = 10 take the midpoint of (1,2) 1.5: F (1.5) = 0.25 take the midpoint of (1,1.5) 1.25: F (1.5) = 0.3125 take the midpoint of (1,1.25) 1.125: F (1.5) = - 0.359375 take the midpoint of (1.125,1.25) 1.1875: F (1.5) = - 0.02734375x ≈ 1.2

Linear Algebra: given the adjoint matrix A * = diag (1,1,1,8) of matrix A, and ABA (- 1) = BA (- 1) + 3E (which means matrix a × matrix B × inverse matrix A = matrix B × inverse matrix A + 3e), find B

First, there are three equations (a is reversible)
A^(-1)=A*/|A|
A A*=diag(|A|,|A|,|A|,|A|)=|A| E
|A | a * | = | a | ^ n, that is | a * | = | a | ^ (n-1) n = 4
From the known ABA ^ (- 1) = Ba ^ (- 1) + 3e
On both sides of the equation, multiply a * on the left and a * on the right
|A|B = A*B+3|A|E
Because | a * | = 8 = | a | ^ (4-1)
So | a | = 2
2B = A*B+6E
That is, (2e-a *) B = 6e
So B = 6 (2e-a *) ^ (- 1) = 6diag (1,1,1, - 6) ^ (- 1) = 6diag (1,1,1, - 1 / 6)
= diag(6,6,6,-1).

What is the distance between the center of circle x ^ 2 + y ^ 2 = 0 and the line 3x + 4y-1 = 0?

How to find the distance between the center of circle x ^ 2 + y ^ 2 = 1 and the line 3x + 4y-1 = 0?
The center of the circle is (0,0)
Then the distance from the point to the straight line formula is d = 1 / 5

Given that x is an integer, and (x + 3) 2 + (3-x) 2 + (X & # 178; - 9) 2 + (2x + 18) is an integer, find the sum of all x values that meet the conditions

It can be reduced to 2 (x + 3) / (X & # 178; - 9) + 2 (x-3) / (X & # 178; - 9) + (2x + 18) / (X & # 178; - 9) = 6 / (x-3)
Hope to solve your problem

If the equation AX * 2 + 2x + 1 = 0 about X has at least one negative root, the value range of a is obtained

When a = 0, x = - 1 / 2 satisfies the meaning
When a ≠ 0, the equation AX * 2 + 2x + 1 = 0 has one positive and one negative root, then 1 / A