In a square water tank full of water with 20 cm long edges, there is a rectangular iron block immersed in water, which is 10 cm long and 8 cm wide. When the iron block is taken out, the water level drops by 2 cm. What is the height of this rectangular iron block?

The volume of iron is 20 × 20 × 2 = 800 cubic centimeter
The height of the iron block is 800 (16 × 10) = 5cm
A: the height of this piece of iron is 5cm

In a water basin 5 decimeters long, 40 centimeters wide and 30 centimeters deep, the water depth is 20 centimeters. Now immerse a cube iron block with 20 centimeters long edge into the water,
How many centimeters will the water surface rise in the basin?

5 decimeters = 50 cm
20 × 20 × 20 = 8000 (CC)
8000 ÷ (50 × 40) = 4 (CM)
A: the water in the basin will rise by 4cm

A cuboid container is 0.5 meters wide and 12 decimeters high. Now the water depth is 6 decimeters. How many meters should the water depth be when a square iron block with an edge length of 2 decimeters is placed in the water?
What's the formula

2×2×2=8 ………… Volume of cube
8/（10×0.5）=1.6……………… The height of a cube after it is placed
1.6+6=7.6………… Depth after insertion

In space analytic geometry, how to find the coordinates of the intersection of two straight lines when the equations of two straight lines are known

It can be understood in this way
The equation of a surface in space is ax + by + CZ + D = 0
The so-called general equation of spatial straight line is defined by two intersecting planes
When learning solid geometry, I have seen two non parallel planes with only one intersection line
If two plane equations are established simultaneously, a straight line can be obtained. When two straight lines intersect at a point, it is equivalent to that three non parallel planes intersect at a point
So there are three linear equations of three variables, which have a unique solution (x, y, z)
It's almost like:
A1X+B1Y+C1Z+D1=0
A2X+B2Y+C2Z+D2=0
A3X+B3Y+C3Z+D3=0
Just solve the equation

The positive and negative proportion letter formula of grade 6
It's very comprehensive,

Y = KX -- K is constant, and Y is proportional to X;
Xy = k -- K must be, and X is inversely proportional to y

Solving exponential logarithm equation
(5^lgx)-(3^(lgx-1))=(3^(lgx+1))-(5^(lgx-1))

Let a = lgx,
So 5 ^ A-3 ^ (A-1) = 3 ^ (a + 1) - 5 ^ (A-1),
5*5^(a-1)+5^(a-1)=9*3^(a-1)+3^(a-1),
6*5^(a-1)=10*3^(a-1),
(5/3)^(a-1)=10/6=5/3,
So A-1 = 1,
So lgx = 2,
x=100.
After testing, x = 100 is the root of the original equation,
So the root of the original equation is x = 100

Parameter equation figure area proof!
Let C be a parametric equation
X = x (T), y = y (T) (t belongs to [a, b]) is given, y (T) is continuous, X (T) is differentiable and the derivative is not 0. Note α = x (a), β = x (b), then the area calculation formula of the figure enclosed by curve C, straight line x = α, x = β and X axis is
A=∫(a,b)|y(t)x'(t)|dt
How did you get this

A=∫{α,β}|y(t)|*|dx|=∫{x(a),x(b)}|y(t)|*|d[x(t)|=∫{a,b}|y(t)|x'(t)|dt；
B ≥ a, but α = x (b) is not necessarily greater than β = x (a), that is, DX is not necessarily greater than 0, so DX takes the absolute value;

Fourth grade mathematics summer homework problems!
1: In a division formula, the sum of divisor, divisor, quotient and remainder is 85. If the divisor is known to be 4, find the sum of divisor, remainder and quotient
2: Chicken and rabbit in the same cage, a total of 80 heads, 260 feet, how many chickens? How many rabbits?
3: The average score of Xiaoming's previous math tests is 84. This time, he has to take the test with 100 points to raise the average score to 86?
4: In a pan, you can fry up to two pancakes at the same time. It takes 6 minutes to cook one pancake (3 minutes for both sides). How many minutes does it take at least to cook three pancakes?
5: When Xiaoqing is doing a subtraction, he writes the six mistakes on the minus ten digits as 9, and the nine mistakes on the subtracted digits as 6. The difference is 577. What's the correct answer to this question?
6: There are a total of 2012 red, white and black beads, which are worn in the order of 5 red, 4 white and 3 black. What color is the last bead?
7: On both sides of a 100 meter long highway, plant a tree every five meters from the beginning to the end. How many trees should be planted?
8: Smile, mischievous, clever three people, only one person did good, wisdom grandfather came to them to verify the situation
He said with a smile, "it's mischievous."
Naughty said: "I didn't do it."
Little smart said, "I didn't make it."
Only one of them told the truth. Who did it? Tell me your reason
Everybody, when you help me to solve the problem, please talk about your thinking, why do you want to write this formula, what is your thinking! The reward points will not be less for you

1. The quotient of the remainder divided by 64 is 16
2. Chicken 30, rabbit 50
3. The 8th time
4.12 minutes
five point six one zero
6. White
7.21*2
8. Naughty? I don't know
I'm just saying what's in my head
1. I move Calc to calculate 85-4, set the remainder 1, and the answer becomes this
260-80 * 2 = 100, 100 divided by 2 = 50, there are 50 rabbits
3. Calc is also used to calculate. At the beginning, 84 * 5 + 100 and then divide by 6 is very close to 86, but it's either going on or 8
4. This person with high Chinese level knows that it's only two cakes at the same time
5. If the subtracted number 6 is wrongly written as 9, then the difference is + 30, because the subtracted number 9 is written as 6 + 3
6.5 + 4 + 3 = 12 2012 = 167 * 12 + 8 what is the eighth number
7.100 divide by 5, then + 1, then multiply by 2, because the starting point cannot be forgotten
8. What's the topic? Inference: there is only one right. The first one says it was done by the second one, but the second one says it's not. The third one also says it's not. Then the third one should be the person who does it, and the second one is right. What should I say about this topic?

lg2=a,lg7=b,lg35=?
There are rewards for RT fast online

lg35=lg5*7=lg7+lg10/2=lg7+1-lg2=b-a+1

Is there a real number α such that sin α + cos α = 3 / 2?

When α = π / 4, sin α + cos α = 2 √ 2 > 3 / 2, so it must exist

In a square water tank full of water with 20 cm long edges, there is a rectangular iron block immersed in water, which is 10 cm long and 8 cm wide. When the iron block is taken out, the water level drops by 2 cm. What is the height of this rectangular iron block?