Who knows this sophomore math? 70

A1D BC and A1DCB are in the same plane, so the dihedral angle B A1C D is a flat angle!!

If the question is correct.

That could be arccos (-1 3).

I'm also a sophomore in high school, but the dihedral corner you wrote doesn't seem right.

1. Proof of: [(a b) 2] 2-(a 2+b 2) 2=(a 2+2ab+b 2-2a 2-2b 2) 4

a 2-2ab+b 2) 4 -(a+b) 2 4 because.

a+b) 2 is greater than or equal to 0, so -(a+b) 2 4 is always less than or equal to 0, i.e. [(a b) 2] 2 is less than or equal to (a 2+b 2) 2.

2. Proof: According to the title, it is necessary to prove 2AB (A+B) "Root Number AB, as long as it proves [2AB (A+B)] 20, AB>0, as long as it proves 4AB-(A+B) 2<0, that is, -(A-B) 2<0, because A, B are both positive numbers, and A is not equal to B, the conclusion is obviously valid, so 2AB (A+B) "Root Number AB."

Three, prove: 1/1 plus 2/2 of 1/b is 2AB of A + B, so.

1/1 of A plus 2/2 of 1/B is less than or equal to AB under the root sign (proof 2 is slightly changed: A b).

2.Under the root number, ab is less than or equal to 2/2 of a+b, (a+b) 2-root number ab (root number a - root number b) 2 2, (root number a - root number b) 2 constant "= 0, so (a+b) 2> = root number.

Fractions of a + b is less than or equal to 2 of the A side under the root number plus the dust of the B square, 2 of the A side under the root number plus B square of the dry bridge - 2 of a + B under the root number (A-B) 2 4, because (A-B) 2> = 0, so 2 of a + B is less than or equal to 2 of the A side plus B square under the root number.

The written expression is limited, and it can't be as standardized as the usual homework, so please forgive me.

1,d2,a is not equal to zero and b is not equal to zero, then a squared is not equal to b squared.

Let the top angle of the cross-sectional triangle (two waists as the busbar) be , then.

s=1 2·sin ·l l 2 (since the cone angle of the original cone of the roller shed is 120°, "=" can be taken).

Or 7 the radius of the height of the two circular surfaces is , so the distance from the center of the sphere to the section is respectively.

5 -3 = 4 and 5 -4 = 3

When two sections are on the same side, the cross-section distance is |3-4|=1

When the two cross-sections are matched on the ulnar side, the cross-sectional distance is |3+4|=7

Count all small cubes, the number of which is 10 = 1000;

All unstained small cubes, the number of which is 8 = 512;

So the number of at least one of these small cubes painted red is 1000-512 = 488.

Let the length, width, and height of the cuboid be a, b, and c, respectively.

ab+bc+ca)·2=22 ，(a+b+c)·4=24

So 2ab+2bc+2ca=22 a+b+c=6

The diagonal length is a +b +c = a+b+c) -2ab-2bc-2ca= 6 -22= 14

According to the similar triangle, it is easy to obtain that the length of the conical bus bar before being intercepted is 3 4 = 12cm, so the length of the intercepted round bus bar is 12-3 = 9cm

Hope to add points, thank you!

2) Find the size of the dihedral angle b-ap-c;

3) Find the distance from the point C to the plane apb.

1) Proof: take the midpoint E of AB and connect PE, CE, AB=BC

ce⊥abap=bp

PE ABAB surface PCE

PC ab2) take the midpoint F of the PA and connect BF and CF

bp=ab，af=pf

BF APAC = BC = 2, ACB = 90 degrees.

ab=pb=ap=2√2

pc ac again, so pc=ac=2

CF AP stands for BFC is what is sought.

CF=AP2=2,BF=(22)(3=6,BC=2BC2+CF2=BF2=6,i.e., BCCccos BCCos BCC=3:3

bfc=arccos(√3/3)

3) Let the distance from C to the plane APB be D

bc⊥cf，bc⊥ac

BC Plane APC

v(b-apc)=v(c-apb)

bc*s△apc=d*s△apb

2*(2*2/2)=d*[√3*(2√2)^2/4]d=2√3/3

v in v(b-apc) = v in v(c-apb) this should be the volume.

Might as well set a1 to x1'=a1-1, xi=ai-a(i-1) for i=2,3,…，12，x13'=30-a12

then x1'+x2+x3+…+x12+x13'=30-12 where x1'=a1-1 indicates the number of elements in S before a1, and xi=ai-a(i-1) indicates the number of elements in S between a(i-1) and AI, x13'=(30-a12) indicates the number of elements in S after A12, obviously the left and right sides of the above equation are the number of elements in S but not in T, so they are equal.

and x1'≥0，x13'≥0 , xi ：i=2,3,…, 10 out of 12 satisfy 1 and one equals 0 , so that x1 = x1'+1，x13=x13'+1。Consider setting xk=0, 1

<> didn't laugh at this dry touch.

<> for the dismantling of the tape code to participate in the test. Yes.

Set the art group x people, the calligraphy group y people, then the equation system:

x/(y+x)=3/8……（1）

x+36)/(y+x)=7/12……(2) then (2) (1) gets:

x+36)/x=(7/12)/(3/8)1 + 36/x=14/9

36/x=7/9

x=81……（3）

Substitute (3) into (1) to get:

81/(y+81)=3/8

y=135 so there are 81 people in the art group and 135 people in the calligraphy group.