There s a math problem that s really annoying, so let s help me solve it.

Now I do 5 units a day, four days in advance.

It's in front, do more, 3*4=12 units.

This is the result of the accumulation of two more units per day. 12 2 = 6 is the actual number of days worked.

Then the original plan was 4 + 6 = 10 days of work.

And the original plan was to make 3 units per day, so the total number of machines is: 10*3=30

Solution: If this batch of machine tools is a total of x sets, then 3 sets per day will be manufactured according to the original plan, so that the planned task is completed in x 3 days. Now 2 more units are manufactured per day than originally planned, that is, 3 units are manufactured per day, so that the task is completed in x 5 days, and the equation is arranged according to the problem, there is.

x 3-4=x 5, and the solution is x=30

A: There are 30 machines in this batch.

Set up this batch of machine tools x sets.

x/3-4=x/5

The solution is x=30 and the answer ......

Solution 1: Set this batch of machine tools as x sets.

x/3 -4=x/(3+2)

x/3 -x/5=4

2x/15=4

Solution x=30

Solution 2: 4 days in advance, the 3 * 4 = 12 units that should have been completed in the next 4 days are distributed to the machines that are done more every day, that is, 3 * 4 12 = 6 days.

So 6*(3+2)=30 units.

(1) Since is a linear transformation, let its characteristic polynomial be:

f( ) According to the Cayley-Hamilton theorem, the characteristic polynomial must be a zero-neutral polynomial.

f(σ)=0

It is also a linear transformation in a three-dimensional real space.

then the number of eigenpolynomials does not exceed 3

So there must be a polynomial f(x) with a degree less than 9 such that f( )=0. (I don't know if it's right here in the end, why is the title 9?) ）

2)=》Let be an invertible matrix, then its eigenvalues are not zero, so that its eigenvalues are 1, 2, 3, then its eigenpolynomial is:

f( )=( -1)( 2)( 3), the constant term of this polynomial is - 1 2 3≠0

There is a polynomial f(x) where the constant term is not zero such that f( )=0

Let there be a polynomial f(x) with a non-zero constant term such that f( )=0

Since the minimum polynomial of is a zeroed polynomial divisible by .

Then the root of the minimum polynomial must be the root of f(x)=0.

The root of the minimal polynomial must be the eigenvalue of .

The constant term f(x)=0 is not zero.

0 is not the root of f(x)=0.

i.e. 0 is not a eigenvalue of .

The eigenvalues are not zero, so it is proved that the invertible matrix is obtained.

Based on the knowledge learned in non-mathematics majors with a bachelor's degree, such problems cannot be solved.

I can't help it...

The arc length formula l=2 r * n 360[n is the angle of the circle of the central angle].

So here it is.

50=2πr *100/360

r=50x360/200π≈ m)=(cm)

Don't know what grade the landlord has? If it is a lower grade, the answer on the first floor should be correct. If it is high school or above, I provide a solution, which requires the formula of summing the proportional series, and the answer is bottle.

1. Buy 100 bottles for the first time, and keep exchanging them after winning the lottery, and finally get 200 bottles, that is: 100+100*

2. The second time the 200 bottles are exchanged for wine bottles, and every six bottles are exchanged for one bottle of wine, and 40 bottles of wine are obtained (the same as the calculation method in the first step). Use these 40 bottles to win the lottery continuously, and finally get 80 bottles of wine, which is 200 * (2 5).

3. In the same way, each subsequent item is a proportional series with 200 as the first term and 2 5 as the proportion.

4. Final sum:

A bottle of beer costs 3 yuan, and there is a 50% chance of getting a bottle, so it is equivalent to 3 yuan to buy a bottle of beer, and there is also a bottle, so the price of the liquid in each bottle of beer itself is equivalent to:

Therefore, for the cost of 100 bottles of beer, you can actually buy 3*100 bottles.

Fill 800ml first, then pour 500ml of it into the 500ml bottle, so that there are 300ml in the 800ml bottle, pour out... Fill up another 800ml and pour it out.

300 + 800 = 1100 ml...

That's how it should be...

Step 1: Fill an 800ml bottle with water.

Step 2: Pour the water received in the first step into the 500ml bottle, and the remaining water in the 800ml bottle is 800ml-500ml=300ml.

Step 3: Pour 300ml of water from the 800ml bottle into the 500ml bottle Step 4: Fill the 800ml bottle with water, at this time 800ml + (in step 3) 300ml = 1100ml.

800 ml is filled and poured into the 500 ml bottle, the water in the 500 ml bottle is emptied, the remaining 300 ml of water in the 800 ml bottle is poured into the 500 ml bottle, and then the 800 ml bottle is filled, a total of 1100 ml.

Fill 800ml and pour the water into the 500ml bottle, leaving 300ml. Pour all into a separate container, then fill it with 800ml and pour it into another container.

One. Fill 800, 500 is empty, and then pour 800 into 500, leaving a 300ml, two. Empty the 500, pour the remaining 300ml in the 800ml bottle into the 500ml bottle, fill the 800ml bottle, add the water in the 500ml bottle, it is exactly 1100ml

(1)ad=8;Then find CE: ABC area = 1 2 * ab * CE = 1 2 * BC * AD (AD is the angular bisector, that is, the height of the isosceles).

>ce=12*8/10=48/5;

CHD is similar CBE==>CH CB=CD CECH 12=6 (48 5)==>CH=15 2(2) CHF is similar CEB==>ch CE=CF CB can be obtained CF=CH*CB CE=(15 2)*6 (48 5)=75 16

The volume ratio of a cylinder to a cone of contour is 3:1

So the volume of the cone is 64 (3-1)=32 m 3

The volume of a cylinder is 32*3=96 m3

sh-1/3sh=64

sh = 96 i.e. volume of the cylinder = 96

The volume of the cone1 3sh = 32

You don't know this, you can ask the teacher more, in fact, you have to do a few more of these questions after you encounter it, one question, one hundred questions.