Urgent! Kneeling for math problems is easy

First of all, your second condition is very strange, 9 yuan per person, someone will not get 9 yuan, which means that the last person may get 0 yuan, 1 yuan. 8 pieces, assuming that the person is called a fool, and assuming that everyone else has 9 pieces of candy when he doesn't have a single one.

Let's look at the first condition first, 8 yuan per person is more than 10 yuan, then the fool also has 8 yuan in his hand, but just now I assumed that the fool didn't get the sugar the second time, so I confiscated the fool's sugar first, plus the remaining 10 yuan before, then I have 18 more pieces of sugar.

Hehe, I gave 18 pieces of sugar to other children, they used to have 8 pieces of sugar each (fools have no sugar), I gave them one piece is 9 pieces of candy per person, of course, I can only send 18 children at most So how many children are there? 18 + fool = 19.

Another way to use the equation is to assume that there are x children: there are 8x+10 pieces of sugar in total, and (8x+10) 9 is easy to solve. That's too little!

Solution: Set the number of students to x.

Then there are: 9(x-1)<8x+10< 9x-10 can be decomposed into two inequalities:

9x-19<8x

and 8x<9x-10

Solve the first inequality to get: x<19

Solve the second inequality to yield: x>10

So 10 is: x can take any number between 10 and 19.

Analyze from the topic; In the second allocation, the last person can only get 1 piece, so there is a lack of 8 pieces.

The first allocation of 8 blocks and 10 pieces remained, and the second allocation of 9 blocks and 8 pieces were missing, the difference was 18 pieces.

10+8) (9-8) = 18 people.

More than 11 people are OK, thank you

There are polygons with different sides of A, B, and C types, and the polygons of each type are equal to each side and equal to each angle; If you take one polygon of each type and put it together at point A, which just happens to cover point A and the small area around it, please write a conjecture about the relationship between a, b, and c, can you prove the conjecture you gave?

From the Pythagorean theorem, it can be obtained: hypotenuse ac*ac=ab*ab+bc*bc substituting data to solve ac=13

It is then solved according to the area of the triangle.

The height can be set to x:

Substituting the data to solve x=13 60 (cm).

It is known that RT abc right-angled edge ab=5 bc=12 is obtained by using the Pythagorean theorem to obtain ac=13

The area of the triangle is ab*bc 2=5*12 2=30

The height on the hypotenuse of the triangle is 30*2 13=60 13

A 1 is 5 to 17 hours.

B 1 is 6 to 23 hours.

5 17 = 5 * 6 (17 * 6) = 30 1026 23 = 6 * 5 (23 * 5) = 30 115 The numerator is the same, and the fractional value with a small denominator is large.

So 30 115 is smaller.

So B fast.

A does 17 pieces in 5 hours, so it takes 5 to 17 hours for A to make a part;

B makes 23 pieces in 6 hours, so it takes 6 23 hours for B to make a part;

And because 5 17 6 23, B does it quickly.

A5-17

B 6 23 then than size 5 17 6 23

So B fast.

A does 17 pieces in 5 hours, so it takes (5 17) hours for A to make one piece alone, about a minute.

B does 23 pieces in 6 hours, so it takes (6 23) hours for B to make one piece alone, about minutes.

So A does it faster.

A 17 5 an hour.

B 23 6 hours a day.

17 5 = 102 30 23 6 = 115 30 so B is faster.

3 to 11

is 11-3=8

There are a total of 12 hours in the lap.

Then the minute hand has gone 1 revolution 8 12 = 2 3

The radius is 12 A: the arc of the tip of the needle is centimeters long.

The surface is a total of 360 degrees, 12 points, each is 360 12 = 30 degrees, the minute hand 3 points to 11 and has walked 8, 8 * 30 = 240 degrees, the minute hand is 12 cm long, in fact, it is equivalent to the radius, the central angle of the circle is 240 degrees, and the arc length formula is brought in

1. A day's work efficiency:

A + B = one-sixth.

C = 1/12.

1 (1/6 + 1/12) = 4 (days).

4. Radius 8 2=4(m).

4 Thirds

5.Solve the equation and let warehouse B be twice as large as warehouse A after x days.

2（32+4x）=57+9x

64+8x=57+9x

x = 73, and the grain stock of the first is x tons.

One-twelfth x + 24 = x + eight ninths (one-twelfth x + 24) 2, assuming that the distance is 1, the speed of the passenger car is more than the speed of the truck: 3 to 2240 two-thirds + 240 = 400 (km).

1. Let the speed of A be v A, the speed of B is v B, the speed of C is v C, and the engineering quantity is 1, V A + V B = 1 2 3 = 1 6

v C = 1 12

So v A + v B + v C = 1 6 + 1 12 = 1 4 So A, B C work together, it takes 1 (1 4) = 4 days to complete.

2. Let the distance between A and B be x

The speed of the passenger car is x 10 and the speed of the truck is x 15

At the time of the encounter, the passenger car travels 240 km, which is 240 (x 10) = 2400 x hours.

Then the truck also travels 2400 x hours, then the truck travels a distance of speed * time = x 15 * 2400 x = 2400 15 = 130 kilometers, and the distance between the two places is 240 + 160 = 400 kilometers.

3. Set up warehouse A to store 12x tons of grain, warehouse B 11x, and warehouse B to transport 24 tons, which becomes 11x+24

Warehouse A is 1 9 less than B, 12x=(1-1 9)(11x+24)12*9x=8*11x+8*24, resulting in x=

Therefore, warehouse B originally stored 11x = tons.

4. Cone circumference = , bottom circle radius =

Conic volume = 1 3 r h = 1 3 * 4

The radius of the cylindrical ground is 8 2 = 4 meters.

The volume of the cylinder is r h=

h=1 3* 4 m).

5.After X days, warehouse B is twice as large as warehouse A.

2（32+4x）=57+9x

64+8x=57+9xx=7

1. The speed of A and B is 1 6, and the speed of C is 1 12, so it takes a total of 1 (1 6 + 1 12) days.

2. Let the distance be x and the encounter time is t, then the equation can be listed: t times x 10 is equal to 240, t times (x 10 + x 15) is equal to x, and the solution is 400 meters apart.

3. If warehouse A has 12x tons of grain, then warehouse B has 11x tons, and the equation can be listed: 12x=8 9 times (11x+24), and the equation can be solved by yourself.

4. You can find the radius r of the bottom circle, and then find the area of the bottom circle, you can find the volume of the cone (the area of the bottom circle multiplied by one-third of the height), and then find the area of the bottom circle of the cylinder, the height is the volume divided by the area of the bottom circle.

5. Let x days, then there is 2 (32 + 4 x) = 57 + 9 x, and the solution is 7 days.

1) The domain is defined as 2 x-1<>0, i.e., x<>0f(-x)=-x[1 (2 (-x)-1)+1 2]=-x[2 x (1-2 x)+1 2]=-x[-1+1 (1-2 x)+1 2]=-x[1 (1-2 x)-1 2]=x[1 (2 x-1)+1 2]=f(x).

Therefore f(x) is an even function.

2) Since f(x) is an even function, you might as well make x>0

Then 2 x>1 obtains: 1 (2 x-1)+1 2>0, so f(x)>0 also has f(x)>0 when x<0 is known by the symmetry of the even function

Hence the proof.

f(-x)=-x(2 x (1-2 x)+1 2)=-x((2 x+1) 2(1-2 x))=x(1 2+1 (2 x-1))=f(x) i.e. the function is even.

x≠0 from the meaning of the title; If the function is even, i.e., x 0 or x 0, the result is the same, then x 0 is taken to get f(x) 0;In fact, if the problem is difficult, it is to find the minimum limit.