In a 12 cm long, 9 cm wide, 8 cm high cuboid container filled with water, the water soaked with a 6 cm long square iron block, when the iron block from the water After taking out, what will happen and what will the result be

In a 12 cm long, 9 cm wide, 8 cm high cuboid container filled with water, the water soaked with a 6 cm long square iron block, when the iron block from the water After taking out, what will happen and what will the result be

Volume of iron block: 6 × 6 × 6 = 216 cubic centimeter
Height of descent: 216 △ 12 × 9 = 216 △ 108 = 2cm
When the iron is removed from the water, the water will drop by 2 cm

A rectangular glass fiber reinforced plastic with a length of 26 cm, a width of 12 limi and a height of 20 cm is placed in a cube iron block with an edge length of 9 cm. When the iron block is taken out of the water, the water will go down a few centimeters

S cuboid bottom area = 26 * 12 = 312cm2
9*9*9=729cm^3
Descending height = 729 / 312 = about 2.33

The perimeter of a circle is 8 π cm, and the area of the circle is 16 π cm2______ ．

The radius of the circle is 8 π / 2 π = 4, and the area of the circle is 42 π = 16 π (cm2). A: the circumference of the circle is 8 π cm, which is 16 π cm 2 when you buy it

If the four line segments ABCD are proportional, that is, a of B = C of D, then AB = BC? Why?
The main reason is why, I know it is equal, but I don't know why
Conversely, if AB = BC, then a of B = C of D, why?

Yes
Ad = BC, correct it
b/a=d/c
It's a cross product
ad=bc
If you don't understand, look at it this way
b/a=d/c
Take both sides together
Namely
b/a×ac=d/c×ac
bc=da
And vice versa
ad=bc
ad÷ac=bc÷ac
d/c=b/a

In the square + 2x of polynomial - x, the coefficient of quadratic term is?

The quadratic term refers to the number of letters 2
In this polynomial, - x ^ 2
The coefficient is - 1

Given that the height of the cone is 42 and the radius of its bottom is 2, find: (1) the total area of the cone; (2) the center angle of the cone's side development

(1) ∵ the height of the cone is 42, the bottom radius is 2, ∵ the generatrix length of the cone is 6, the bottom perimeter is 2 × 2 π = 4 π, then the side area is 12 × 4 π × 6 = 12 π, the bottom area is π × 22 = 44 π, then the whole area is 12 π + π = 16 π. (2) ∵ the bottom radius of the cone is 2, ∵ the bottom perimeter of the cone is 4 π, The solution is n = 120. The center angle of the cone side expansion is 120 °

1^2+2^2+…… +The proving process of n ^ 2 Formula

Mathematical induction is a good choice, but we must first know the formula
In fact, we can use the high-order splitting term to sum
(k+1)³=k³+3k²+3k+1
3k²=(k+1)³-k³ - (3k+1)
3*1²=(2³-1³)- 4
3*2²=(3³-2³)-7
3*3²=(4³-3³)-10
.
3*n²=[(n+1)³-n³]-(3n+1)
Add
3*（1²+2²+3²+.+n²）
=[(n+1)³-1³]-(4+7+10+.+3n+1)
=n(n+1)(2n+1)/2.
1²+2²+3²+.+n²=n(n+1)(2n+1)/6

Let x, y, Z and K all be int type variables, then the value of X is () after executing the expression: x = (y = 4, z = 16, k = 32)
a、4
b、 16
c、 32
d、 52

C, 32
On the right side of "=" is an expression, which uses comma operation to calculate each quantity from left to right. The value of the whole expression is the value 32 of the last formula "k = 32", and 32 is assigned to X. therefore, the value of X is 32

My teacher's composition, about 400 words, to have examples

If someone asks me what a good teacher looks like in my mind, such a figure will immediately appear in my mind: in my thirties, tall figure, dark curly hair, some pretty face with a pair of glasses, so gentle, this is my Chinese teacher - Miss Zhao

If real numbers a and B satisfy a * a * a + b * b * B + 3AB = 1, then a + B =,

It is easy to understand the factorization of the formula A ^ 3 + B ^ 3 + C ^ 3-3abc
Decomposition of factor
(a+b-1)(a^2+b^2+1+ab-a-b)=0
The second factor = 0.5 ((a + b) ^ 2 + (A-1) ^ 2 + (B-1) ^ 2) is always greater than 0
therefore
a+b=1