Help answer 4 junior high school math Olympiad questions, thank you

1. Pass P as AD and DC perpendiculars respectively, and intersect H and I

Let hp=x, pi=y

then there is x (1-x) = (2-y) y

2x+y=2

and s=(4-x)(4-y)=(4-x)(2+2x)=2(-x 2+3x+4) (0So, when x=1 is maximum, s=12

2、de=

1.Let am be x and area y, then mb is 4-x and bn is 2+2xy=(4-x)(2+2x).

When x=, the maximum value of y is .

But 0=< x<=1, so when x=1, y has a maximum value of 12< p>

Plan 1: After the expiration of 5 years, the income is 50% + 20% = 70% of the original shop price, and the actual investment amount is the original shop price.

Return on investment = 70%.

Plan 2: After the expiration of 5 years, the income is 30% * (1-10%) + 20% = 47% of the original shop price

The actual investment amount is 85% of the original shop price, and the investment rate of return = 47 85 * 100% is approximately equal.

2) If the price of the shop is X million yuan, the income of A is 70%X, and the income of B is 47%X, a difference of 23%X

23%x=5 x=5/

A's investment is 10,000 yuan, and B's investment is 85%x= 10,000 yuan.

1.The ratio of circumference is 5:2, and the difference in circumference is 60, so the circumference is 40cm and 100cm respectively

2.The ratio of the area is 25:4, and the difference in area is 588, so the area is 112 cm2 and 700 cm2 respectively

Walking 5 kilometers per hour means that it takes 1 5 hours to walk 1 kilometer, which means that it takes 12 minutes.

Cycling takes 8 minutes per kilometer less than walking, that is, it takes 12 8 4 minutes, i.e. 1 kilometer is 1 kilometer in 4 minutes of cycling, then the speed of cycling or bending is 12 4 3 times that of walking.

According to the symmetry of the circle, it can be seen that "every 10 minutes, they can meet an oncoming tram, and every 15 minutes another tram catches up with them from behind." ". Xiao Hua and Xiao Ming must start from the opposite side of the tram starting point.

It is a place where the distance between the two people and the starting station is equal.

When they first encountered the tram, the sum of the distance between the two was: 1-1 24 (10+10)=1 6

Therefore, the total time for an individual to complete the journey is: (10+10) 1 6=120 minutes Because the speed of the two people is equal, the meeting time is: 120 2=60 minutes Description:

Every 15 minutes, another tram catches up with them from behind" is redundant and can be used for inspection.

Set the speed of the tram to be xkm minutes and the speed of people to be y

The total distance is 24x km.

By the title: 15x+10x-5y=24x

After 10 minutes from the starting point, I met a tram, and after 5 minutes, I met another train, and the second tram walked for 15 minutes, and it was in the opposite direction, so the distance of the first car + the distance of the second car - the distance traveled by people = the total distance).

The solution is x=5y

y=1/5x

It takes 24 minutes to complete the train.

It takes 24 5 = 120 minutes for a person to walk through.

It takes 60 minutes for the two to meet each other.

Suppose the speed of the car is v0 and the speed of the person is vi, and the car drives out every other TO, and the total distance is ss=v0*24

15v0-15v1=v0*to

10v0+10v1=v0*to

v0=5v1

Therefore, the time for a person to complete the course is 24*5=120

So the time required is 120 2=60

Solution: A person should not shake hands with himself, so everyone is shaking hands with others, if the serial number, after the first person shakes hands, the second person will have one less time, because the first person has already shaken hands with him, and so on: so there are 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28, and the handshake 7 times should be 8 people, not 7 people, because any handshake is two people.

Hehe. A: There were 8 people in attendance.

A total of 7 people.

The solution is: This question is the inverse of the variation of the number graph problem, and the solution to the number graph problem is; (side-1) + (side-2) + (side-3) + (side-n), from this question, 28 = 7 + 6 + 5 + 4 + 3 + 2 + 1, the largest number is 7, so use 7 + 1 = 8 (people).

A: There were 8 people in attendance.

Solution: Suppose there are x people in total.

1/2x(x-1)=28

Solution: x=8

A: There were 8 people in attendance.

Analysis: If there are three people, the number of handshakes is 1+2

There are four people, and the number of handshakes is 1+2+3

That x person is 1+2+3+......x-2+x-1

1+2+3+……x-2+x-1=28

x-1）/2*（1+x-1）=28

x-1）x/2=28

x+7）（x-8）=28

x=-7，x=8

People are not negative, so x=8

From one to seven is twenty-eight, and the answer is seven people, and it's more interesting to think about it yourself.