1 junior high school math problem to process .

1) G is the center of gravity, the center of gravity is the intersection of the three middle lines and the ratio of the two parts of the middle line is 2:1, so the length of CG is 5/3

2) The distance from point G to hypotenuse AB is four-fifths.

Process; Assuming that AG crosses BC to P, BG crosses AC to Q, CG crosses AB to R, and GD is perpendicular to AC, GE is perpendicular to CB, and GF is perpendicular to AB, then the triangle ADG is similar to the triangle ACP, the triangle BEG is similar to the triangle BCQ, and the similarity ratio is 3:2, so Gq=4 3, Ge=1

According to the knowledge of the area of the triangle ABC, the length of gr can be found to be 4 5

1) According to the nature of the center of gravity: the center of gravity of the triangle is divided into two parts: 1:2, wherein the distance from the center of gravity to the vertex of the triangle is two-thirds of the whole center line, and the middle line on the hypotenuse of the right triangle is equal to half of the hypotenuse by the Pythagorean theorem and the right triangle, and GC 5 3 can be obtained

2) Let the distance from point G to hypotenuse AB be gh, make the perpendicular line of point C vertical hypotenuse AB, the vertical foot is m, and set the midpoint of hypotenuse as d, then the triangle DGH is similar to the triangle DCM, so that GH 1 3cm 1 3*12 5=4 5

Solution: The workload of B for one day is 6 divided by 6 days, so the 5 days that B adds in the middle are all done by A, and it takes 5 * days.

Therefore, the number of days for A to do it alone is 2 + 4 + 5 + 1 = 12 days, and the number of days for B to do it alone is 12 divided by the days.

If the ergonomics of A is 1 x, then the workload of 6 days is 6 x, so the ergonomics of A is (6 x).

4 (5x), the entire quantity is considered as the unit "1", then the quantity of work completed by A in two separate days is:

2 x A and B to do 5 days to complete the amount of work is:

5[1/x4/(5x)]

9 x So far, the remaining engineering quantity is: 1-

2/x-9/x= 1

11 x, according to the title.

1×(1/x)=1

11 x is 1 x

4/(5x)

Answer: This project will be completed by A and B alone, which will take 12 days and 15 days respectively.

1, Zhang Qiang: 11 hours, 40 km, v=40 11km wide branch grinding h, Wang Li: 5 hours, v=8km h

Set Wang Li to catch up with Zhang Qiang after T hours.

4+t) 40 11=8t t=10 3 3 hours 20 minutes.

So it was 1:20 p.m. to catch up with Zhang Qiang.

n(n+1) Shen Dou 2 ; n(n-1)/2

If they don't take a break halfway, then it will be the first time they meet in two hours, but in fact, because after two hours, Xiao Zhang Xiaowang really walked for 110 minutes and 100 minutes respectively, and the distance traveled was 11km and 10km, so there is still a gap of 24-11-10=3km.

Time also needed = 3 12 = 1 4 hours = 15 minutes.

Therefore, total time = 120 + 15 = 135 minutes.

If you don't stop halfway, the first encounter time is 24 (6+6)=2 (hours) after departure, but because there is a break, two hours, Xiao Zhang walks 6*(120-2*5) 60=11 kilometers.

Two hours, Xiao Wang walked 6*(120-2*10) 60=10 kilometers, and the difference between the two met was 24-11-10=3 kilometers, so he had to walk another 3 (6+6)=1 4 hours.

So the two set off 2+1 4=9 4 hours later and met.

(1) The second group is 450 x-450 per decimeter

x=5 is tested to be the solution of the original equation.

2) The second group is set to be per decimeter x meter, and the first group is per decimeter ax meter h x-h ax=t

x=(ha-h)/t

It is verified that x=(ha-h) t is the solution of the original equation.

ax=（ha-h）/t

Let x be the climbing speed of group 2, then it will be the climbing speed of group 1.

450/x-450/

x=(2) The second group is set as per decim x m, and the first group is per decim ax m h x-h ax=t

x=(ha-h)/t

ax=（ha-h）/t

Solution: (1) Let the speed of the second group be x meter minutes, then the speed of the first group is meter minutes, and the solution of 450 x = 450 meters according to the meaning of the question is x = meter minutes) Answer: The speed of the first group is 9 meters, and the speed of the second group is meters.

2) Let the speed of the second group be x meters minutes, then the speed of the first group is ax meters minutes, according to the meaning of the topic.

450/x=450/ax+t

3x+7=k, deformed as x=(k-7) 3, substituted by 2x+5y=20, after deformation, 15y=53-k, that is, 5*(3y)=53-k, that is to say, 53-k is a multiple of 5, in the above 4 groups of numbers, only b satisfies the condition, therefore, answer: b

Pick B answer. Substitute the answer to 3x+7 k to find out, so that B may be chosen.

Of the four answers, +7 must be divisible by 3 and choose C

Take the midpoint F of AB and connect CF.

It is known that ACB and ECD are both isosceles triangles, ACB = ECD = 90°, we can get: ACB and ECD are both isosceles right triangles;

So, af = bf = cf and de = 2cd.

ad²+db² = (af-df)²+bf+df)² = (cf-df)²+cf+df)²

2(cf²+df²) = 2cd² = de² 。

The numerator and denominator are divided by xy

3/y-4+3/x）/(1/x+2+1/y)

Divide the top and bottom by xy, and it will come out.

The known deformation x+y=3xy

Think of x+y as a whole (9xy-4xy) (3xy+2xy)=1

The numerator, denominator and denominator are divided by xy at the same time

It is known that both sides multiply xy: x+y=3xy

Substantiation: [3(x+y)-4xy] [(x+y)+2xy]=(9xy-4xy) (3xy+2xy)=(5xy) (5xy)=1

Original: x+y=3xy

Substituting (3x-4xy+3y) (x+2xy+y) can be found to be equal to 1