Math Problems Math Teacher Enter!! Math Master!! Thank you!!

The result is equal to:

Above (2 3 x 3 2) 2002 x1 5 1 1 5

The calculation method is to combine the first two items to synthesize the same power, and then divide by (-1) to the 2004th power, the even power of the negative number is a positive number, and the 2004th power of (-1) is equal to 1, so the answer to this question is.

i.e. 3 2, this proposes a 3 2, the original formula is equal to.

2 3) to the power of 2002 * (3 2) to the power of 2002 * 3 2 divided by 1

So the final result is: 3 2;

The answer is —1) The 2004 power is 1, divide the 2003 power of ( by the 2002 power of ( multiply by the 2002 power of ( ) by the 2002 power (2 thirds of the 2002 power ) by 1, and that's it.

ef‖ab,afiibe

ABEF is a parallelogram.

ad‖bc,∠aeb=∠ead

Because bae= ead

So, aeb= bae

So ab=be

So ABEF is diamond-shaped.

Adiice, quadrilateral aecd is trapezoidal.

In the triangle abe, aeb= bae, b=60°, so aeb= bae= b=60°

Therefore ab=be=ae

And ab=cd

So ae=cd

So the quadrilateral aecd is an isosceles trapezoid.

The quadrilateral ABEF is a parallelogram ( bae= eaf= bea= aef so af be).

The quadrilateral aecd is an isosceles trapezoidal ( abe is an equilateral triangle so ae cd).

Let the original number n=10a+b (both a and b are positive integers).

Then the number obtained after the said change is: a+5b

10 times larger: 10A+50B

If this number is divisible by 7, it is a multiple of 7.

Then subtract 49b from this number (49b is of course a multiple of 7) to get 10a+b, which is of course divisible by 7.

Because 2 are multiples of 7, the difference obtained is also a multiple of 7, OK?

It is understood as follows: from the front view, you can see that the removed cuboid is in the direction of the front line of sight, and from the side view, you can see that the removed cuboid is on the left side of the original cuboid

[Analysis].

This question examines the relationship between the three views of a geometric body, paying attention to memorizing and understanding the meaning of "length is right, height is level, and width is equal";

Analyze the position of the removed box from the front and side views, and then determine the correct shape for the top view.

Answer] A b

c d solution: from the front view, you can know the direction of the removed cuboid in the front line of sight, from the side view, you can see that the removed cuboid is on the left side of the original cuboid, from the description of the above views, it can be seen that the top view conforms to the c option, so choose c

On this topic, I will give you a picture. The physical object can be determined based on the main and left views, and then the top view can be determined based on the physical object.

Don't think of this geometry as a box in the corner).

Make a rectangular carton and draw the line squarely.

You get the idea.

For students with poor spatial imagination, they can make the model by hand.

Is it a triangular platform? Make a top view.

Let the area of the upper bottom surface be s and the height be h, then the area of the lower bottom surface is 4s

So the original volume is 7 3sh. After segmentation, the large volume was (4+3) 3sh. The small volume is 7 3sh-(4+ 3) 3sh=(3- 3) 3sh.

The ratio of the volume of the two parts is (15+7 3) 6

+ 8^(-x) = 2^3x + 2^(-3x)[2^x+2(-x)]^2=2^2x + 2^(-2x) +2 = a^2

2^2x + 2^(-2x) = a^2-2[2^2x + 2^(-2x)]*2^x+2^(-x)) = 8^x+8(-x) +2^x+2^(-x) = a(a^2-2)

So 8 x+8(-x) = a(a 2-2) -a2 x+y=12 xy=9 x（x^1/2-y^1/2）/（x^1/2+y^1/2）=(x^1/2-y^1/2)^2/（x^1/2+y^1/2）* x^1/2-y^1/2)

x+y-2(xy) 1 2) (x-y)(x-y) 2 = (x+y) 2 - 4xy, x-y < 0 The rest of the substitution is fine.

1.The cube sum formula: a 3 + b 3 = (a + b) * (a 2 - ab + b 2).

8^x+8^(-x)=(2^x)^3+[2^(-x)]^3=[2^x+2^(-x)]*a^2-2+1)=a*(a^2-1)

2.(x 1 2-y 1 2) (x 1 2+y 1 2) = (x-y) (x+y+2 root number xy) = (root number 3) 3

According to the coordinates of a and b, the angle between a, b and x-axis can be obtained as 30°, and the history of Lu Qi is 60°, so a b, x +2) 1=(-y) Sihe (1 x-1), obtain.

1,Y=f(x):

y=x -x+2-1 x,2 When x 1, find the minimum value of the function y=f(x) 1, because the function increases monotonically at x 1 2.

It can be seen as a superposition of two functions, y=x -x+2 and y= -1 x.

1) The modulo of vector a is closed = 1, the modulo of vector b is 2, vector a 2 = 1, vector b 2 = 4, and vector a * vector b = 0, that is, vertical.

Vector c*vector d=-ya 2+(x 2+2)(1 x-1)b 2 (should be followed by a string of what a*b, because a*b=0, so omitted, you can judge the cheating to write it out) = 0

y=4x-4x2+8x-8

2) Derive y=4x-4x2+8 x-8 first. In the calculation, it's very simple.

modulo of vector a = 1, modulo of vector b = 2, vector a 2 = 1, vector b 2 = 4, and shouting to Lu Hu the quantity a * vector b = 0, that is, straight to Hayano Nao.

Vector c*vector d=-ya 2+(x 2+2)(1 x-1)b 2 (it should be followed by a string of what a*b, because a*b=0, so you can write it out) = 0

y=4x-4x2+8x-8