Math Puzzle Urgency Mathematics Puzzle Urgency

1.(2 to the power of 2004-1) (2-1).

Let s = 1 + 2 + 2 squared + 2 cubic + ......2 to the power of 2002 + 2 to the power of 2003 (1).

2s = 1 + 2 + 2 squared + 2 cubic + ......2 to the power of 2002 + 2 to the power of 2004 (2).

2)-(1) gives s = (2 to the power of 2004-1) (2-1).

2.(x-100 to the power of x) (x-1).

Let s = 1 + x + x square + x cubic + x cubic + ......x to the 98th power + x to the 99th power (1).

xs = 1 + x + x square + x cubic + x cubic + ......x to the 99th power + x to the 100th power (2).

2)-(1) gives s = (x to the power of 100 -1) (x-1).

The problem of the number series is put ??

I forgot the formula, but it shouldn't be that hard

Take one out of the box where the label is a 5-a-6.

Because the label is wrong, if you take out 5 grams, there are two 5 grams inside.

Then the label is two 5-gram boxes, that is, two 6-gram labels are two 6-gram boxes, that is, a 5, a 6 If you take out 6 grams, then the box is two 6-gram labels, and the label is two 6-gram boxes, and there are two 5-gram boxes.

The label is inside two 5-gram boxes, one is a 5, and one is a 6

Solution: Suppose number 1 is 5g 5g, number 2 is 6g 6g, and number 3 is 5g 6g

There are two cases where the label is incorrect:

a) No. 1 is 66, No. 2 is 56, No. 3 is 55b) No. 1 is 56, No. 2 is 55, No. 3 is 66 Li Ping opened the box of No. 3 and took out any one of them to weigh, if it is 5g, then the label is a case;

If it's 6G, then the label is B.

The weight ratio of sugar to water is 1:2

So water accounts for 2 (1+2)=2 3

So the weight of water = 42 * 2 3 = 28 grams.

1.Move 16 units to the right from A to the right, this point is +16, and move 7 units from A to the right of A, this point is +7

Move 14 units to the right from A to A, this point is +14 to move 1 unit from A to the left of A, this point is -1

2.The distance traveled on this day is: 16 + 9 + 7 + 15 = 47km fuel consumption = 47 100 * liters.

Bets on the number line - 1, 0, 7, 14, 16

A total of 47 km was walked, which seems like this.

The first question is not for me to draw.

Total distance l=16+16+9+9+7+7+15=79km ;

Fuel consumption is ( = liters.

The answer on the first floor is correct, but the process is wrong, and it is estimated that it is copied from someone else's process The mean is not used incorrectly.

Let the slope of the straight line be k, according to the point slope then.

The equation for a straight line is y-1=k(x-2) and k<0pa|*|pb|

Root number. -2(k^2+1)/k

2(-k-1/k)

2（-k²-1）/k

k>0 -1/k>0

There is according to the mean inequality.

k)+(1/k)>=2

Take an equal sign if and only if -k=-1 k, i.e., k=-1.

From this, it can be derived from the muffled chain.

pa|*|pb|The minimum value is 1

In this case, the linear equation is y-1=-(x-2), i.e. y=-x+3

The equation for a straight line is y-1=k(x-2) and k<0pa|*|pb|Root number.

2(k^2+1)/k

2(-k-1/k)

k>0 -1/k>0

k)+(1 k)>=1 2 If and only if -k=-1 k, i.e., k=-1, take the equal sign.

pa|*|pb|The minimum value is 1, and the scattered straight line square shirt is y-1=-(x-2), that is, y=-x+3

First, let the linear equation y=ax+b pass the point p and bring in 2a+b=1 let point a(0,y) b(x,0) bring in to get y=b x=-b a丨pa丨 丨pb丨=x y =-b 2 a and 2a+b=1 so b=1-2a bring in to get 丨pa丨 丨pb丨=-(1 a-4+4a) If you want to be hungry pa丨 丨pb丨minimum So when you want 1 a=4a, that is, a=-1 2 (its fierce key is really a branch is late and positive or negative) But according to this problem, it is negative. So there is the equation for a straight line y=-1 2x +3

I don't know if it's right, please teach me with a high finger.

What is a bad topic,,, ,,, good to take,,。 Zhenghui rides... Neither is the figure.

From the first encounter to the second encounter, A and B walked twice the distance between AB, because the speed did not change, the time taken must be twice as long as the first encounter, and the distance they walked must be twice as long as before the first encounter.

From the first encounter to the second encounter, A walked 80 + 50 = 130 kilometers.

So the first time Qianjia walked 65 kilometers, that is to say, when they met for the first time, the meeting point was 65 kilometers away from City B.

Use equations first, then change them to non-equations. I've done this before. Advice is welcome!