Math Puzzle to be fast!!! ）

1. Judgment. 1.The volume of a cylinder is generally larger than its surface area. (x, area and volume can't be compared, different units).

2.Two cylinders with equal base area have equal volumes. (x, also related to height) 3The height of a cylinder is doubled, the radius of the base surface is reduced to half of the original, and the volume remains the same.

x, calculated volumes, unequal).

2. Practical questions.

1.Saving water is the obligation of every primary school student, the diameter of the water pipe used in the school is decimeter, the flow rate of tap water is generally 5 decimeters per second, if you forget to turn off the tap for a minute, how many liters of water will you waste?

v = 5 * liters.

1 Wrong, 2 Wrong, 3 Wrong.

2. 1 minute = 60 seconds, so r2*2 h=

It's a question of extreme thinking.

At least – or in the best case of optimism – draw 12 cards of the same color.

At most, in the most pessimistic and unlucky scenario, 12 cards of the same color are drawn.

To have 12 cards of the same color, let's consider the most optimistic scenario.

I've drawn 11 red cards now, and none of the others have been drawn, so if I draw another red, then I'll be guaranteed that 12 of them will be the same color.

Then at least 12 cards must be drawn to ensure that 12 of them are of the same color.

To have 12 cards of the same color, let's consider the worst of the worst cases.

You've drawn a whole bunch of cards.

There are 11 red, 11 yellow, 11 green, and 10 blue.

A total of 43 cards.

Bad luck, isn't it? But then, no matter which color you draw, you make sure that there are 12 cards of the same color.

OK, the answer is out.

If you draw up to 44 cards, you are guaranteed that 12 of them are of the same color.

In other words, if you draw 44 cards, you're sure that 12 cards are of the same color.

x+4x=

4x=x=.x=

x = x divided by 6 = 25

15x=25×6

x=10×（x+5）=6×（x-4）

3x+15=6x-24

6x-3x=15+24

3x=39x=13

There are no unknowns about this.

If so4 (then.

x=1-7/10+1/10x=1/6x

1/6x-1/10x=3/10

1/15x=3/10x=

There is no independent variable for this either.

3/5x=1/30+1/60

3/5x=1/20

x=1/12

8. (8x+4) divided by 4+1=8

2x+1+1=8

2x=6x=3

First of all, it is impossible to tell whether it is an unknown number or a multiplication sign; Again, the equations are so simple that you can do it with the time you need to know what to ask. Little sister has to study seriously!

1.A total of 42-12=30 students donated 5 yuan and 10 yuan. A total of 229-12*2=205 yuan was donated.

If there are x people who donate 5 yuan, there are 30-x people who donate 10 yuan.

5x+10(30-x)=205

5x=95x=19

There were 19 students who donated 5 yuan and 11 students who donated 10 yuan.

2.If there are x adults and 100-x children.

4x+（100-x)/4=100

Multiply both sides by 416x+100-x=400

15x=300

x=20100-20=80 people.

There are 20 adults and 80 children.

5 yuan 19 people, 10 yuan 11 people.

Adult 20 Infant 80

The survival rate is 85% So, the mortality rate is: 1-85% = 15% so the death rate is:

500x15%=75 (trees).

20 more trees died in the spring than in the fall.

So the fall dies is:

75-20=55 (trees).

The mortality rate in the autumn is:

So the tree planted is:

55 10% = 550 (trees).

Let's say x trees were planted in the spring, y trees were planted in the fall, and z trees were planted in the fall

Equation: x=500*;

y=z*;Solve the equation to get x=425; z=950;y=855;

Answer: x+y=1280

∵∠a=∠b

ac=bc=5

de‖bc∠ade=∠b=∠a，∠bcf=∠cfe∴de=ae=3

CF bisects ACB

ecf=∠bcf=∠cfe

ef=ec=ac-ae=5-3=2

df=de-ef=3-2=1

1) ABC is an isosceles right triangle, BAC=90° AB=AC

The same goes for ae=ad

bac=∠ead=90°

BAC+ CaE= EAD+ CAE, i.e. BAE= CAD AABE ACD

2)cd⊥be

abc is an isosceles right triangle, bac=90° b= acb=45°

abe≌△acd

acd=∠b=45°

bcd=∠acd+∠acb=90°

cd⊥be

Here's the answer:

1。After E to do EH vertical CF at H, extend CF to AB at G, let AG=X, then EH=2X 5, AB=2X, AD AB=AE AC=3 5

So ad=6x 5

gd=ad-ag=6x/5-x=x/5

It's easy to prove DGF efh

So there is ef df=eh dg=(2x 5) (x 5)=2 and because de=ae=3

So df=1

2.(1) The proof is as follows

bae=90+∠cae

cad=90+∠cae

bae=∠cad

And because: ab=ac

ae=ad△abe≌△acd

2) Because of ABE ACD

So acd= abc=45

And because acb=45

So acd= acb= acd=90

So vertically.

, de bc, ae ac=de bc, de = 3, de bc, ce is 24(1).ad=ae,(2).CD vertical BE, triangle ABE is all equal to triangle ACD,< ACD = < ABC = < ACB = 45 degrees, < BCD =