A junior high school math problem, do yourself a favor, help do a junior high school math problem

This teacher belongs to the geometry value in junior high school mathematics, and uses knowledge: between two points, the line segment is the shortest.

Because the two points of ab are located in the fourth quadrant, the first quadrant, and are not in the same quadrant; The point M is on the X-axis, so when AMB is collinear, the value of MA+MB is the smallest, which is equal to the length of the line segment AB, so the coordinates of the point M are the intersection of the line AB and the X-axis. The analytic formula of the straight line ab is: y=-6x+8, the coordinates of the intersection point with the x-axis are (4 3,0), and the minimum value is:

Root No. 37. (ENDS).

Connecting AB, the intersection point with the x-axis is the minimum point m, and the rest needs to be proved that, except for this point, m+mb is larger than the value of this place elsewhere in the x-axis (the reason is that the sum of the two sides of the triangle is greater than the third side).

The straight line between two points is the shortest, connect the two points A and B, find the straight line equation through the two points A and B, and bring x=0 into the straight line equation to obtain the Y value. (0,y) is the coordinate of m.

The shortest straight line between two points.

The equation for the straight line ab is y=8-6x

Therefore, when ma+mb is taken as the minimum value, y=0

then x = 4 3, so the coordinates of point m are (4 3, 0).

Idea: Find the symmetry point C of A, and find the intersection point of BC and X axis.

If you don't know, ask again; Satisfied! May you open and good luck!! 】

It's very easy, the answer has been given by others, and the hardest thing I've ever done is a quadratic function problem in Xiangtan.

From the symmetry, it can be seen that (0,-3) and (2,-3a) are symmetrical with respect to x=1, from which the value of a is 1,, and the value of b from the axis of symmetry is x=1 is -2,;

Then the coordinates of point m are (1,-4) c(0,-3).

1. If team B alone needs x months to complete, then team A needs 3x months to complete, then there is 1 x+1 (3x)=1 3 to solve x=4

Team B alone needs to complete in April, and team A needs to complete in December.

2. From the conclusion of 1 to B 4

If b = 4 a = 0 is completed in April, the project cost of 15 * 4 = 600,000 meets the requirements.

If b = 3 then a = 3 will be completed in June, and the project will be 15 * 3 + 12 * 3 = 810,000 yuan to meet the requirements.

If b = 2, then a = 6 will be completed in August, and the project cost is 15 * 2 + 12 * 6 = 1.02 million to meet the requirements.

If b = 1, then a = 9 will be completed in October, and the project cost is 15 * 1 + 12 * 10 = 1.35 million yuan that does not meet the requirements.

If b = 0, then a = 12 will be completed in December, and the project cost is 15 * 0 + 12 * 12 = 1.44 million that does not meet the requirements.

So there are only 3 construction options.

Solution: If it takes 3x months and x months for teams A and B to complete this project separately, then 1 3x 1 x 1 3

It will take December and April for the two teams to complete the project separately;

According to the title, yes.

a 12 b 4 1 12a 15b 102 i.e. a 12 3b 0 4a 5b 34

4 12 3b 5b 34 solution b 2

2≦b≦4b＝ 2，3，4

a＝12－3b＝6，3，0

3﹙48－7b﹚＝102，81，60

The construction plan is as follows:

A construction in June, B construction in February, the total construction period in June, the total project cost of 1.02 million yuan;

A construction in March, B construction in March, the total construction period in March, the total project cost of 810,000 yuan;

A construction in 0 months, B construction in April, the total construction period in April, the total project cost of 600,000 yuan;

(1) Team A takes 3 times as much time as B and the work efficiency is different: B completes 3 copies at ---the same time, and A completes 1 copy.

In the 3-month cooperation completed, A completed 1 4 ,-- A alone for 12 months.

B completed 3 4 --- B alone for 4 months.

2）∵b≤4

1）b=4 a=0 15x4=60＜102

2）b=3 a=3 15x3+12x3=81＜102

3）b=2 a=6 15x2+12x6=102

1. Let the velocity of A be x and the velocity of B be y, then 3(x+y)=1 and 3x=y. The solution is x=1 6, y=1 2A: 6 days B: 2 days.

Let A be completed separately to x, and B should be y from the meaning of the problem: the column equation x=3y3(1 y+1 x)=1 is solved to obtain x=12 y=4

A 12w 12a + 15b 102 a + b 12 per month (a b belongs to n).

b≤4 a≤12

b=4 a=0 The two inequalities hold.

b=3 a=3 The two inequalities hold.

b=2 a=6 The two inequalities hold.

b = 1 a = 9 Exceeds appropriation.

b = 0 a = 12 Excess of appropriation.

To sum up, in order to ensure the cost and construction period, there are three construction plans.

(1) Solution: It takes X months to set up Team B to complete, and Team A needs 3X months to complete.

From the meaning of the title: 1 x + 3x = 1 3

Solution: x=3 4, 3x=4

A: It takes 4 days for Team A to complete this project alone, and it takes 3 to 4 days for Team B to complete this project alone.

The comprehensive treatment project of Yueyang Wangjia River Basin has been officially launched, and one of the projects can be completed in 6 months if the construction teams A and B work together, and if they are done by the two teams A and B alone, team A will take 5 months less than team B to complete

1) How many months will it take for teams A and B to complete the project alone?

2) It is known that the monthly construction cost of team A is 150,000 yuan, which is 60,000 yuan more than team B, and the total cost of the project does not exceed 1.41 million yuan according to the requirements, and the project must be completed within one year (including 12 months) In order to ensure the cost and construction period, team A does a month, and team B does a month (a and b are integers) division of labor and cooperation.

Solution: (1) It takes x months to set up team B.

then Team A will need (x-5) months to complete.

According to the title:

1/(x-5)]+1/x)=1/6

Solution: x=15

It is verified that x=15 is the root of the original equation.

2) Set up a team for a month.

Then Team B does (12-a) months.

According to the title:

15a+9b≤141，a/10+b/15=1

Solution: a 4

b 9 a, b are both integers.

a=4，b=9

or a = 2, b = 12

A: Team A needs 10 months to complete, and Team B needs 15 months to complete. The construction scheme is a=4, b=9 or a=2, b=12.

It takes X months for Team A to complete the project alone, and Team B takes y months to complete the project alone: x+y=3 3y=x The solution is y=3 4 x=9 2