A math problem. Fast forward urgently needs to be 5 tonight

Suppose that the commemorative book to be produced is x volumes.

Then Company A needs to pay (5x+1500) yuan, and Company B needs to pay 8x yuan.

1) When (5x+1500) < 8x, it is cost-effective to choose company A.

5x+1500<8x

3x>1500

x>500

That is, it is more cost-effective when the total number of commemorative books to be produced is greater than 500 volumes.

2) When (5x+1500) >8x, it is cost-effective to choose company B.

5x+1500>8x

3x<1500

x<500

3) When 5x+1500=8x, both companies are equally cost-effective.

5x+1500=8x

3x=1500

x=500 satisfied, thank you

1) It is necessary to make x volumes.

Then there are 1500 + 5x < 8x

x>500

That is, when more than 500 commemorative albums are produced, it is more cost-effective to select a company.

2) by (1) solution, when less than 500, company B.

3) When it is equal to 500, the two companies are equally cost-effective.

Solution: Set the commemorative album that needs to be made as x volumes, and get the following by the title

1) The material cost of company A: y1 = (5x + 1500) yuan.

Company B's material cost: y2 = 8x yuan.

Reaming y1500

Therefore, when the total number of commemorative albums to be produced is greater than 500 volumes, it is more cost-effective to select company A.

2) Reel y18x

solution, get x<500

Therefore, when the total number of commemorative books to be produced is less than 500 volumes, it is more cost-effective to choose Company B.

3) Let y1=y2, then 5x+1500=8x solution, get x=500

Therefore, when the total number of commemorative books to be produced is equal to 500 copies, it is equally cost-effective to choose two companies.

Look

Solution: (1) From the meaning of the question: y1=5x+1500;(2 points) 2) from the meaning of the question: y2=8x;(4 points).

3) When y1=y2, y1=5x+1500=8x, x=500 When y1 y2, 5x+1500 8x, x 500;

When y1 y2, 5x+1500 8x, x 500 (7 points) so when the number of copies of the customized commemorative book is 500, you can choose both companies A and B;(8 points) When the number of copies of the commemorative book is less than 500, select Company B;(9 points) When the number of copies of the customized commemorative album is more than 500, choose Company A (10 points) Satisfied, thank you

There are three different surfaces, with an area of 25 20 = 500 square centimeters.

25 4 = 100 square centimeters, 20 4 = 80 square centimeters.

Stacking the largest surfaces on top of each other saves the wrapping paper.

So stacked together, the length is 25cm, the width is 20cm, and the height is 4 4 = 16cm, so the minimum wrapping paper to be used is 2 (25 20 + 25 16 + 20 16) 2440 square centimeters.

Because there is also a joint, it is necessary to add 20 8 = 160 square centimeters.

A: A minimum of (2600) square centimeters of wrapping paper should be used.

If you have any questions, you can hi、

Each book is stacked on top of each other 25 cm long and 20 cm wide, with the smallest amount of wrapping paper.

25*20*2+25*4*8+20*4*8=2440 square centimeters.

6 sides must be wrapped, a total of 8 joints.

2440 + 20 * 8 = 2600 square centimeters.

a>-1

a+1>0

a³-a²-a+1=a^2(a-1)-(a-1)=(a-1)(a^2-1)=(a-1)(a-1)(a+1)=(a-1)^2(a+1)

a-1)^2≥0

a -a -a+1=(a-1) 2(a+1) 0 If a>-1, then the value of the polynomial a -a -a+1 is (c.).Non-negative number).

a3-a2-a+1

a3-a2)-(a-1)

a^2(a-1)-(a-1)

a-1)(a^2-1)

a-1)(a-1)(a+1)

a-1)^2(a+1)

Because a>-1

So (a-1) 2>0 a+1>0

So (a-1) 2(a+1) >0

So a3-a2-a+1 is positive.

a³-a²-a+1

a²（a-1）-（a-1）

a²-1）（a-1）

a+1）（a-1）²

Because a>-1 so a+1>0 and (a-1) >=0 (when a=1 is equal to 0).

So the value of a -a -a+1 is greater than or equal to 0

That is, it is a non-negative number.

c is non-negative, a3-a2-a+1=(a3-a)-(a2-1)=a(a2-1)-(a2-1)=(a-1)(a2-1)=(a-1)(a-1)(a+1)=(a-1)2(a+1).

a-1)2>=0.a>-1,a+1>0, so it is not negative.

=(a³-a)-(a²-1)

a(a²-1)-(a²-1)

a²-1)(a-1)

a+1)(a-1)(a-1)

a+1)(a-1) 2 ( 2 squared meaning) a>-1 then (a+1)>0 (a-1) 2 is greater than or equal to zero, so the result is c non-negative.

There are three cases, a is a positive number, the value is positive, a is 1, the value is 0, a is 1 -1, the value is positive, choose c

Since we have found the analytic formula, we can simply find the coordinates d(-1,0) of point d. Points on the parabola can be marked as (x,-x 2+2x+3).

The following is considered in two cases: one is when x belongs to (-1,3), when point e is above the x axis, and the distance between point e and the y axis is positive, that is, the y coordinate of point e (-x 2+2x+3); Second, when x>3 or x is less than -1, then point e is above the x-axis, and the distance between point e and y-axis is negative, which is (x2-2x-3).

The first case: there are two kinds of solutions, but the solution method is basically the same.

When x belongs to (-1,1), s = left triangle area + middle trapezoidal area + right triangle area = (x + 1) * (x 2 + 2x + 3) 2 + (-x 2 + 2x + 3 + 4) * (1-x) 2 + (3-1) * (4-0) 2, concretize and simplify it yourself.

When x belongs to (1,3), s = left triangle area + middle trapezoidal area + right triangle area = (1-(-1))*4-0) 2+(-x 2+2x+3+4)*(x-1) 2+(3-x)*(x 2+2x+3) 2

The second case: there are two more types, but the solution method is exactly the same. It's all a triangle at the top + a triangle at the bottom.

When x<-1 or x>3, s=(3-(-1))*4 2+(3-(-1))*x 2-2x-3) 2

Finally, you can get:

When x belongs to (-1,1), s=(x+1)*(x 2+2x+3) 2+(-x 2+2x+3+4)*(1-x) 2+(3-1)*(4-0) 2,when x belongs to (1,3), s=(1-(-1))*4-0) 2+(-x 2+2x+3+4)*(x-1) 2+(3-x)*(x 2+2x+3) 2

When x<-1 or x>3, s=(3-(-1))*4 2+(3-(-1))*x 2-2x-3) 2

Your question is indeed a bit difficult, let me give you a piece of advice first, you should add some money or no one will answer! I'm a little better at math, but I hate this kind of problem the most (remember my opinion!). Give someone some money).

The radius of a large circle is a multiple of the radius of a small circle.

then the area of the great circle is a multiple of the area of the small circle.

The area of the great circle is more than that of the small circle.

The area of the small circle is.

square decimeters. The area of the great circle is.

square decimeters. The largest square must have four vertices on the circle, that is to say, the circle is the circumscribed circle of the square, the diagonal length of the square is 10 cm in diameter, the side length is 10 (change sign)2, the area is 50, and the remaining area.

Think for yourself! The brothers know and are not interested in telling you.

1. Let the radius of the small circle be r and the radius of the big circle be r from the title

r square + squared

Two-formula simultaneous equation solving.

2. To intercept the largest square, the square diagonal is equal to the radius, and the square becomes longer than a

10 cm for rice.

According to the Pythagorean theorem, a square + a square = (squared.

Find a and then a square is the square area, and subtract a square from r square to get the remaining part of the area.

120 yuan.

The original price of the product is 360 (1 80%) = 200 yuan.

The lowest price is 200 (1 20%) 240 yuan.

The price was reduced by 360 240 120 yuan.

Set the purchase price x

360=(1+80%)x

x=200 and the lowest price is 200 (1+20%)=240

Price reduction 360-240=120

Solution: If the purchase price is regarded as 1, then the list price is 1+80 = the boss's lowest selling price is 1+20=

The list price is 360 yuan, and the purchase price is 360 yuan.

The minimum selling price is $200.

The minimum price that the boss can reduce is 360-240 = 120 yuan, and the purchase price is x yuan, then the lowest selling price is x (1 + 20) = yuan, and the price tag is x (1 + 80) = yuan, and the minimum price reduction is.

x=200 Answer: The boss can reduce the price by 120 yuan at the bottom.

Set the original price to x.

x(1+80%)=360 x=225 minimum**: 225x(1+20%)=270

The price will be reduced by up to 90 yuan.

Let the purchase price be x yuan (1 + 80%) x = 360 x = 200 yuan.

And the profit is not less than 20% of the purchase price, that is, the selling price" = 200 (1 + 20%), that is, the selling price" = 240 yuan.

360-240=120 yuan The store owner can reduce the price by up to (120) yuan.

Prove; Connect to be cf

It can be proved that OAB = OBA (by proving the congruence of triangles DBA and CAB).

AOB is 60 degrees.

You can know triangles, AOB equilateral triangles.

ae = oe, so be is perpendicular to ao

g is the midpoint of the hypotenuse bc, so eg = bc 2 is the same way, and fg = bc 2

FE is the triangular AOD median, EF=AD2

And bc=ad

So ef=fg=eg

5a—4>=0

a>=1

9—2a>=0

a<=4

At the same time, 9-2a<=5a-4

a>=2

So the value of a may be 2, 3, 4

That is, there were 6 or 11 or 16 passengers on the bus.

2.Solve inequality 1.

x<21

Solve inequality 2.

x>2-3a

Combine the two solutions.

2-3a and x have four integer solutions, and observing the above equation, we can see that these four integer solutions are , so 16<=2-3a<17

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The first question is **.

Question 2: Select C

1,(5a-4) 0,(9-2a) 0,(5a-4) (9-2a), the solution is 13 7 a 9 2, therefore.

The value of a can be 2, 3, or 4

That is, there were 6 or 11 or 16 passengers on the bus.

2，｛(x+15)/2＞x-3

2x+2)/3＜x+a ｝

That is, x<21,x>2-3a, and there are only 4 integer solutions, then x=20,19,18,17, then the value range of a is 17>2-3a 16, that is.

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