A math problem, an afternoon exam, in a hurry!

I think this question can be seen as yes.

a+b+c≤-6

If we assume that a=b=c is equal to -2

Options A and B are too absolute.

Option c means "at least one -2".

That is, there may be 1 less than or equal to -2, there may be 2, there may be 3.

No matter how many of them fit the topic.

We can look at the exact opposite description of this option:

All three numbers must be greater than -2".

It is clearly not in accordance with a+b+c -6.

So option c is correct.

d option "at least one -2".

Not necessarily, because I can have all three numbers less than -2 so it's not comprehensive.

Assuming that a+(1 b), b+(1 c), and c+(1 a) are all greater than -2, then there is.

a+(1/b)>=-2

b+(1/c)>=-2

c+(1/a)>=-2

Three inequalities can be added to obtain: a+(1 b)+b+(1 c)+c+(1 a)>=-6

It contradicts that a+(1 b)+b+(1 c)+c+(1 a) is less than or equal to -6 in the question.

Therefore, a+(1 b), b+(1 c), and c+(1 a) cannot all be greater than -2, i.e., at least.

One is not greater than -2.

1 All (1) piecewise functions.

Let s be the cost.

When m<30, s=m

When m>30, s=30+

2) m=45>30, substituted.

The cost is f

f=m……(m less than or equal to 30).

f=30+greater than 30).

When m=45f=

1) When m is 30, the cost of checked m kg baggage = 1 * m = m

When m 30, the cost of checked m kg baggage = 1 * 30+

2) When m=45, freight=

According to physics it should be t= (h 5). where t is the time h is the height, so the total time is t = (plus the unit s (seconds)).

Substitute the four numbers into the relation and add them together to get the sum.

As shown in the figure below, it is analyzed

A, B, and C take turns to work in three sequences, the blue line in the figure represents the part where the three people take turns to work for the same time (the same job, so the three sequential working hours and workload are the same), and the red part represents the part that is not enough for the three people to take turns to work for the same time (the workload is the same, if enough for the three people to take turns to work for the same time, then no matter which order, the time should be the same).

Since the order of A, B and C is finally completed in whole hours, it can be divided into two situations: first, the remaining workload (red part) is completed by A alone, and the working time is 1 hour; Second, the remaining workload (red part) is completed by two people, and the working time is 1 hour each, a total of 2 hours.

Answer from this. Let B work alone for a few hours, and the work efficiency is 1 a; C needs b hours to work alone, and the work efficiency is 1 b; It is also known that A needs 6 hours to work alone, and the work efficiency is 1 6.

Situation 1: In the order of A, B and C, the remaining workload is completed by A alone, the working time is 1 hour, and the workload is 1 6;

According to the order of B C A than A B C C time more hours, so the remaining workload is completed by B and C, B works for 1 hour, C works for hours, the workload is 1 6, B work efficiency is 1 a, C work efficiency is 1 b, so 1 a + 1 2b = 1 6;

According to the order of C, A and B, it takes more hours than A, B and C, so the remaining workload is completed by C and A, C works for 1 hour, A works for hours, the workload is 1 6, C works 1 b, and A works 1 6, so 1 b + 1 6 * 4 = 1 6;

Solve the system of equations {1 a+1 2b=1 6,1 b+1 6*4=1 6}

Get a=48 5, b=8

Therefore, it takes time for three people to type a manuscript together.

1 (1 6 + 5 48 + 1 8) = 48 19 (hours).

Situation 2: In the order of A, B and C, the remaining workload is completed by A and B, with a working time of 1 hour each, a total of 2 hours, the work efficiency of A is 1 6, the work efficiency of B is 1 a, and the workload is 1 6 + 1 a;

According to the order of B, C and A, it takes more hours than A, B and C, so the remaining workload is completed by B, C and A, B works for 1 hour, C works for 1 hour, A works for hours, B works 1 a, C works 1 b, A works 1 6, and the workload is 1 a+1 b+1 6*2;

According to the order of C, A and B, it takes more hours than A, B and C, so the remaining workload is completed by C, A and B, C works for 1 hour, A works for 1 hour, B works for hours, C works 1 b, A works 1 6, B works 1 a, and the workload is 1 b + 1 6 + 1 4a;

The system of equations {1 a+1 b+1 6*2=1 6+1 a,1 b+1 6+1 4a=1 6+1 a}

The solution yields a=9, b=12

Therefore, it takes time for three people to type a manuscript together.

1 (1 6 + 1 9 + 1 12) = 13 36 (hours).

As can be seen from the title, A is completed in 6 hours alone, and A's ergonomics is 1 6

Start Analysis:

If the last person is C in the order of A, B and C, the three people take turns equally and the number of hours is a multiple of 3.

Regardless of the other order, the number of rotations of the three people is exactly the same as in the first case, and the same number of times will end when it is the same as in the first case.

So, the last person in the first case cannot be C, only A or B.

Next, let's assume that the last person is A.

Compare 3 cases:

1, A, B, C... CArmor.

2, B C A... Armor. Ethyl propylene (

3, C A B... B|C (

The first 3 cases to the vertical line have completed the round of integers, and the workload is the same. After comparing the vertical lines.

From 1,3, it can be seen that the workload of A for one hour = one hour for C + 4 hours for A1.

C is 3 4 of A, A is known to be 1 6, C is 1 6 3 4 = 3 24

From 1,2, we can see that A = B + C 1 2, B = A-1 2C = 1 6-1 2 3 24 = 5 48

A, B and C work at the same time, and the ergonomic efficiency is 1 6 + 3 24 + 5 48 = 19 48

It takes 48 19 = hours to complete the work.

Also assume that the last person is B.

Compare 3 cases:

4, A, B, C... CA and B.

5, B C A... Armor. B C A (

6, C A B... B|C A B (

The first 3 cases to the vertical line have completed the round of integers, and the workload is the same. After comparing the vertical lines.

From 4,5, it can be seen that A + B = B + C + 1 2A.

C = 1 2 A.

C is 1 2 of A, A is known to be 1 6, C is 1 6 1 2 = 1 12

From 5,6, we can see that B + C + 1 2 A = C + A + B 1 4, and both sides eliminate B + 1 2 A = A + 1 4 B.

3 4B = 1 2 A.

B = 2 3 A = 2 3 1 6 = 1 9

A, B and C work at the same time and the ergonomics is 1 6 + 1 12 + 1 9 = 13 36

It takes 36 13 = hours to complete the work.

So the result is 48 19 (hours) or 36 13 (hours.

The one sent last night has already been given.

One minus one half plus one half minus one third plus one third minus a quarter plus a quarter minus a fifth... minus one thousand and one-fifth plus two thousand and fifth minus one thousand and sixth.

Equals: one minus one thousand and sixth.

Equals: two thousand and five thousand/sixths.

It can be split into 1/1 2/1, and then the same split.