2 Olympiad math problems, math masters to do it!

1.Since the length increases by 3cm, the volume increases by 180 cubic centimeters, and the side area can be seen to be 180 3 = 60 square centimeters;

In the same way, the frontal area is 150 2 = 75 square centimeters; The base area is 160 4 = 40 square centimeters;

A box has a total of six faces, where the two opposite faces are equal in area, and the surface area of the box is:

2 x （40+60+75）

350 square centimeters.

2。First, find the volume of this piece of plasticine as: 363x225x55=3x11x11x5x5x3x3x5x11

11^3x5^3x3^3

11x5x3)^3

From this, it can be seen that the edge length of the cube is 165

So the surface area of the cube is 165x165x6

163,350 square centimeters.

Let the sides be a, b, c

The area of each face.

180/3=60=ab

150/2=75=ac

160/4=40=bc

Volume = abc = abacbc under the root number = 60 * 75 * 40 = 15 * 4 * 15 * 5 * 5 * 4 * 2 = 600 times the root number 2 cubic centimeters.

Cube volume = cuboid volume = 363 * 225 * 55 = 11 * 11 * 3 * 15 * 15 * 5 * 11 = a * a * a = 11 * 15

Surface area = 6 * a * a = 6 * 11 * 15 = 990 square centimeters.

1. Set length, width and height x, y, z

There are 3yz=180, 2xz=150, 4xy=160, simplified yz=60, xz=75, xy=40, s=2xy+2yz+2xz=350 (cm2).

So the edge length of the cube = 11*15

The surface area is 11*15*11*15*6=163350 (cm2).

The area is (60 + 40 + 75) * 2 = 350

363*225*55=11*11*3*5*5*3*3*5*11=(11*5*3) to the third power.

So the side length is 165

The surface area is 165*165*6=163350

Question 1. 3bc=180,2ac=150,4ab=160bc=60,ac=75,ab=40

2 (bc + ac + ab) = 2 * (60 + 75 + 40) = 350, but it is not a primary school practice, and it may not pass.

Question 2. The principle of volume invariance.

v=363*225*55=(3*11*11)*(3*3*5*5)*(5*11)=(3^3)*(5^3)*(11^3)=(3*5*11)^3

Because v=a 3=(3*5*11) 3

So: a=3*5*11=55

s=6*a^2=6*55^2=18150

3 = 60 (square centimeters).

150 2 = 75 (square centimeters).

160 4 = 40 (square centimeters).

60 + 75 + 40) 2 = 350 (square centimeter) 225 55 = 4492125 (square centimeter) = 165 165 165 So, the surface area is 165 165 6 = 163350 (square centimeter).

2.Solution: 363 times 225 times 55 is equal to 4492125, and only the cube of 165 is equal to 4492125, then the surface area of this cube is 165 times 165 times 6 equals 326,700 square centimeters.

I hope the only answer to the question is right, of course 99% of the time, ok?

1.Add the two numbers together, and the sum of the numbers is 3, and the sum of the numbers is 3, in the order of the smallest, as follows:

2.The method of exclusion, which is excluded, cannot be distinguished; 102, can be divided: 49 and 53, the smallest difference is 4

54+48=102 The sum of digits is 3

5+4+4+8=21 is divisible by 7.

The difference is 1, the sum of the number A and the number B is 3, at least two digits, and there are three possible tens of corresponding single digits; i.e

and must meet a multiple of 7 i.e.

So the sum can only be 21,

The sum of the numbers is 5+6+5+5=21, the sum of the two numbers that meet the condition of dividing by 7: 56+55=111, and the sum of the numbers that meet the requirements of 3A-B: 56-55=1

The first question is that I don't understand what you are writing.

2: Original = 3 2x1 2x4 3x2 3x5 4x3 4x....x10 9x8 9x11 10x9 10=1 2x11 10=11 20 (can be removed).

3: Same as question 1.

4: Original = (1-1 3) + (1 3-1 5) + (1 5-1 7) +1/97-1/99）=1-1/99=98/99

5: Extract a 1 from each thing, and then split the item like question 4:

Original = 6 + (1 2-1 4) + (1 4-1 6) + (1 6-1 8) + (1 8-1 10) + (1 10-1 12) + (1 12-1 14).

6 + 1 2-1 14 = 6 and 3/7

2009 (2009 and 2009/2010) +1 2011

2010 (2010 and 2010/2011) +1 2012

5 questions, no ideas!

2012 in parts

11/11 and 1/2012

I don't understand the rest of it.

Believe in sister, absolutely right!!

Hey hey handed it over to me! When the number of students is the lowest, there are more students who have won three good students in a row, and there are three students who have won three good students in four, five or six years. By counting 35 people (can be asked).

When the number of students is the largest, there are no three good students for three consecutive years. Count 38 people.

You delay it, I'll do it for you now, and I'll adopt it later, okay?

You set the equation to xyz

Then: x+y+z=26

x/5+y/

0 is less than or equal to x y z and less than or equal to 11

The solution is x=15 y=5 z=6

I'm playing it with pure hands.,If the back plagiarism me.,You class will adopt it to me.,You just look at the time...

Solution: Let the three coins of 1 cent, 2 cent, and 5 cents be x, y, and z respectively and obtain the system of equations according to the meaning of the problem

x＋y＋z＝26

x/5＋2y/5＋z＝11

z＝（29－y）/4

Because x, y, z are positive integers.

So x, y, z can only be the following groups:

1 point 2 points 5 points.

Since 1 cent and 2 cents should be exchanged for 5 cents, only the set of x 15, y 5, z 6 is eligible, so the original 5 cent coins are 6 pieces.

If all 2 points are 2, there is 26*2=52

The total amount is: 11 * 5 = 55 points.

In this case, 5 points are: (55-52) (5-2) = 1 piece, then it is 1 point 0 pieces, 2 points 25 pieces, and 5 points 1 piece.

Since 1 point cannot be 0, and 4 2 points can be divided into 3 1 points and 1 5 points, there are:

1 point 2 points 5 points.

That is, the original number of 5 points may be

There are 1 cents, 2 cents, and 5 cents coins with x, y, and z coins, respectively, and there are equations:

x+y+z=26。。。There are 26 coins in total (x+2y) 5+z=11... After changing to 5 points, there are a total of 11 x+2y+5z=5*11...

All coins total 55 cents, three equations, three unknowns, solvable x, y, z, and time relations are not solved.

In the order of 1 point, 2 points, and 5 points, it is in order.

(2A-3)*6+10=11A+1, 12A-8=11A+1, A=9, and so on to get B=15, C=100, and the sum is 124