A math problem in the United States ,,, which prawns to solve

This is a high school math problem, I just came to do it in the college entrance examination, and I have done this similar problem several times.

1).Solution: Set the nth year to start making a profit.

The cost of the nth year of the fisherman an=12+(n-1)*4=4n+8 (* is a multiplier sign).

It's just a series of equal differences with 12 as the first term and 4 as the tolerance, understand? )

So the fisherman's cost in the first n years: sn=12*n+1 2*n*(n-1)*4=2n 2+10n

The formula for summing the series of equal differences, n 2 is the square of n).

Then, the fisherman's profit bn=50n-98-(2n2+10n)=40n-2n2-98>=0 (a).

is greater than or equal to).

Solution (a) yields: n>=3

So, the 3rd year starts to make a profit.

Option 1: (The average annual profit is the total profit divided by the number of years) The average annual profit is g

g=bn/n =(40n-2n^2-98)/n ("/"is divided by).

When the basic inequality is solved by n=7, g is 120,000 yuan at a maximum, and the total profit is 1.1 million yuan.

Scenario 2: The total profit is BN

When the method of solving the unary 2nd order equation is solved, bn=102 is obtained when n=10, and the total profit is 1.1 million yuan.

In summary, option 1 and 2 are equally profitable, however, option 1 only takes 7 years, while option 2 takes 10 years, so option 1 is more reasonable.

It's so tricky here, don't say that the two plans are equally good)

Whew, tired to death. Probably yes, the landlord himself has to do it

The last sentence: I want to divide it

It's a bit difficult, but it can be calculated using a series of equal differences, which is sn=a1*n+(a1+an)*d 2

where A1 is 12, D is 40,000, and when Sn is greater than 0, it starts to make a profit.

Count yourself in the back, the process is too difficult to fight.

You can't just thank you but also offer a reward.

It took x months to build.

From the question: 1000-100=(70+80)x150x=900

x=6 that is: 100 meters left after 6 months of repair.

I don't know how to ask...

Solution: Design: Repaired for x months.

80x+70x=1000-100

150x=900

x=6A: I took it for 6 months.

Solution: 1 km = 1000 m.

Design: Repaired for x months.

80x+70x=1000-10

150x=900

x=6 Answer: After 6 months of repair, there are still 100 meters that have not been repaired.

It took x months to build.

From the title: 1000-100 = (70 + 80) x 150 = 900x = 6

1 km = 1000 m 1000-100 = 900 m 900 (80 + 70) = 900 150 = 6 (pcs).

A: After 6 months of repair, there are still 100 meters left to repair.

A: Because|y1|+|y2|=|y1+y2|You can get: y1 y2 with the same sign or y1 y2, one or both of which are 0, so y1 y2 0

B: Because |y1|+|y2|=|y1-y2|You can get: y1 y2 different sign or y1 y2, one or both of which are 0, so y1 y2 0

If y1>0; y2>0, then |y1|+|y2|=y1+y2=|y1+y2|

If y1>0; y2>0, then |y1|+|y2|=-y1-y2=-(y1+y2)=|y1+y2|

It can be seen that when y1 and y2 have the same sign, equation (1) holds, and there is y1 y2 0 at the same time

If y1>0; y2>0, then |y1|+|y2|=y1-y2=|y1-y2|

If y1>0; y2>0, then |y1|+|y2|=-y1+y2=-(y1-y2)=|y1-y2|

It can be seen that when y1 and y2 are different signs, equation (2) holds, and there are y1 y2 0 at the same time

The output value of the first phase of the project is x (10,000 yuan).

The number of employees in the first phase of the project is x 40, the number of people lifted out of poverty in the first phase is 10 x 40 (x 4), the total annual indirect income of the number of people lifted out of poverty is 5 million yuan, after the completion of the project, the number of employed people is x 4 + 2500, and the total number of people lifted out of poverty becomes 10 (1+2)*(x 40+ 2500)=10 3*(x 40+2500), the per capita income of the people lifted out of poverty is 4* (500 (x 4))=8000 x, and the total annual indirect income is (1+7)*500=4000

The per capita annual indirect income of those lifted out of poverty = 4000 (10 3 * (x 40 + 2500)) = 8000 x

Solution x = 20000000 yuan.

Then the annual comprehensive economic benefit = (1 + 2) * 20000 + 4000 = 640000 yuan.

(1).Dy dx = x 2 + 5 => dy = (x 2 + 5)dx simultaneous integration on both sides = >

y = 1 3 * x 3 + 5x + c, where c is an arbitrary constant.

2).Dy dx = 2xy = > 1 y Dy = 2x dx simultaneous integration on both sides = >

ln y = x 2 + c1 => y = c * e (x 2), c > 0 is any constant. (c=e^c1)

3).ydy = xdx simultaneous integration on both sides = > 1 2y 2 = 1 2x 2 + c1 = >

y 2 = x 2 + c, where c is an arbitrary constant.

4). dy/dx + y = e^(-x) => e^x * y ' + e^x * y = 1 =>

e^x * y) '= 1 simultaneous integration on both sides = > e x * y = x + c = >

y = x * e (-x) + c * e (-x), where c is an arbitrary constant.

x-b-c=1 x-c-a=1 x-a-b=1x=1+b+c x=1+c+a x=1+b+a, so a=b=c, so (x-b-c) a=(x-c-a) b=(x-a-b) c=1 so x=3 are all 1 I don't know, right.

Look.. Remember to give points if you are satisfied.。。。 I can't help it if I'm not satisfied. Genus.

Is it winter vacation homework? There is the answer later.

Let's say there are x rooms, 1From the fact that there are five people living in each room, then there are no less than 12 people arranged, and the total number of people is 5x+12

2.If each room has eight people, then there are some empty beds, assuming that the empty beds are y(0 because x,y are whole numbers and 04.).The school may have 6 rooms that can arrange student accommodation, and the students in the accommodation have 5*6+12=42, or the school may have 5 rooms that can arrange student accommodation, and the students in the accommodation have 5*5+12=37

The school may have x rooms that can be arranged for student accommodation.

According to the five people living in each room, then there are 12 people who can't be arranged, it can be seen that there are students 5x+12 people, each room lives eight people, then there is a room with some empty beds, set the vacant beds as a, there are students 8x-a people, where a, column equation.

5x+12=8x-a, solution.

x=（12+a)÷3

Because the number of rooms and students in the dormitory is an integer, a = 3 or 6

x = 5 or 6, 5 x + 12 for 37 students after 42 people.

That is, if there are more than 3 people in each room, there is one room that is not full, because 12 3 = 4, so there should be 4 + 1 = 5 rooms, and the number of people is 5 * 5 + 12 = 37 people.

There are 5 rooms that can be arranged for student accommodation, and there are 37 students living in the dormitory.

As the title knows.

The last room has some empty beds, because there is no specific number, so it can only be divided into the following cases: the last room is completely empty.

The school has x rooms and Y students are accommodating.

This results in 5x+12=y

8（x-1）=y

Solve the system of equations x=4 3 y=56 3;Not realistic Hypothesis 1 is not true 2: the last room is seven empty.

5x+12=y

8x-7=y

Solving the system of equations x=19 3 y=131 3 is also not realistic Hypothesis 2 is not true.

Three: The last room is empty six.

5x+12=y

8x-6=y

The solution x=6 y=42 fits the question.

Four: The last room is empty five.

5x+12=y

8x-5=y

The solution is x=17 3 y=121 3 does not hold five: the last room is empty four.

5x+12=y

8x-4=y doesn't hold up in the end.

From this we derive the pattern.

The number of beds vacant in the last room plus 12 is a multiple of 3 that holds, and from this we deduce that the last room is empty: zero, empty, six, empty, three, satisfies the question, i.e., if there are 0 empty.

x=4 y=32

Empty 3 x = 5 y = 37

Empty 6 x = 6 y = 42

Let's say the school has x rooms and Y students.

5x+12=y

8x>y>8(x-1)

Solve the above equations.

The following solution can be obtained:

4 So there are x=5 y=37 or x=6 y=42, so there may be 5 rooms and 37 boarders.

Or there are 6 rooms and 42 boarders.

There are x rooms with empty m beds. The equation is 5x+12=8x-mSolve m=3x-12. Depending on 0, there may be 5 or 6 rooms. The boarding students were 37 and 42 respectively

If there are x dormitories, then there are 5x+12 students.

8 > 5x+12 - 8*(x-1) >0 gives 4 < x < 6 so x=5

Accommodation: (12+8) (7-5)=10 (rooms).

People: 10 * 5 + 12 = 62 (people) maybe.

Binary Linear Equation Problem Solving.

There are x rooms, Y people.

5x+12=y

1≤8x-y≤7

solve, then x may be 5 or 6, and the corresponding y is 37 or 42

If you don't understand, you can ask me.

8 times 1 equals 8 people (12 plus 8) divided by (8 minus 5) equals 20/3

Solution: It's a question of profit and loss.

8 1 8 people.

12 8 8 5 20 3 is not an integer!!

Therefore, the data provided in the question is incorrect. Please proofread and I'll be at your service.

The age difference between the two is: 30-6 = 24 years.

When the mother's age is 3 times that of Xiao Ming, Xiao Ming is: 24 (3-1)=12

So, 12-6=6 years later.

The age difference is the same.

30-6 = 24 years old.

24 (3-1) = 12 years old.

12-6 = 6 years.

Solution: After X years, my mother's age is 3 times that of Xiao Ming.

30+x=3（6+x）

30+x=18+3x

12=2xx=6Answer: Six years later, my mother is three times older than Xiao Ming.

After X years, he is three times older than Xiao Ming.

Solution: 30+x=3(6+x).

The solution is x=6, so after 6 years, the mother's age is 3 times that of Xiao Ming.