Please help me solve a problem, who can help me solve this problem?

This is the 1997 Shanghai high school examination question, the original question is as follows:

It is known that there is a straight line and a curve in the Cartesian coordinate system, and the straight line intersects with the x-axis and y-axis at the point A and the point B respectively, and OA=ob=1, this curve is a branch of the image of the function y= in the first quadrant, the point p is any point on this curve, its coordinates are (a, b), and the perpendicular lines PM and Pn made by the point P to the x-axis and y-axis (the points M and N are perpendicular feet) intersect with the line AB at the points E and F respectively.

1) Set the points E and F on the ** section AB (as shown in the figure), and find the coordinates of the points E and F respectively (the coordinates of the points E and F are represented by the algebraic formula of A and B respectively, and only the answer needs to be written, and the calculation process is not required);

2) find the area of OEF (the result is expressed in the algebraic formula of A and B);

3) Whether AOF and BOE are necessarily similar, and if so, please prove it; If they are not necessarily similar or must not be similar, please briefly explain the reasons;

4) When the point p moves on the curve, the OEF changes accordingly, point out the angle and its magnitude that of the three inner angles of the OEF always remain the same, and prove your conclusion.

Legend analysis: (1) The coordinates of the point E are (a,1-a) from em ob=am oa; In the same way, the coordinates of point f are (1-b,b).

2）s△oef=s△aob-s△aoe-s△bof=（a+b-1）/2

3) AOF must be similar to BOE. Here's why:

From oa=ob=1, oaf= ebo

From the Pythagorean theorem, we get be= 2a, af= 2b

p is on the image of y=1 2x, b=1 2a, i.e., 2ab=1. Thus we get 2a· 2b=1 1. So af bo=ao be

aof∽△beo

4) When the point p moves on the curve, eof in eof must be equal to 45°. Here's why:

apr∽△beo

aof=∠beo

And beo= aoe+ oae, which in turn aof= eof+ aoe

eof=∠oae=45°

The reaction produces water and carbon dioxide (x+ o2 = h2o+ CO2) According to the law of conservation of mass, there must be two elements in the chemical formula, hydrogen and carbon (there may be oxygen elements, so here is a verification of this.

Verification method: see if the mass of hydrogen and the mass of carbon add up to the same, if it is less, it means that there is an aerobic element, and you can find the elemental composition and chemical formula).

Mass of hydrogen = (2*1 2*1+16*1)*100%*mass of carbon = (12*1 12*1+16*2)*100%*

Aerobic element, mass is.

The following requires the ratio of the number of atoms between them, using the formula Number of atoms = mass of the element relative to the atomic mass).

The ratio of atoms of carbon, hydrogen and oxygen is : =2:6:1 and the chemical formula is C2H6O

Wrong question, right? It should be the description agd= acb, right?

The proof is as follows: because EF AB, CD AB, so CD is parallel to EF, so 1= DCB, so DCB= 2, so GD is parallel to CB, so AGD= ACB

Suppose x sheets of aluminum sheets (150-x) make the bottom of the bottle.

Then there are 16x bottle bodies, 43* (150-x) bottle bottoms to make up a complete set.

So: 43*(150-x)=2*16x75x=150*43 so x=86 150-x=64

With 86 sheets of bottle body and 64 sheets of bottle base, exactly 1376 sets of beverage bottles can be made.

Angular AOC + angular AOB = 108°

Angle MOC = Angle Moa - Angle NOA = Angle AOC 2 - Angle AOB 2 = 40°, i.e. Angle AOC + Angle AOB = 108° Angle AOC - Angle AOB = 80° So Angle AOC = 94° Angle AOB = 14°