Please give me a math problem, and then teach me how to think! Teach you how to think

Known: y = (x + 1) / (x ^ 2 + 1), solve the value range of Y
First of all, you need to know how to solve the range! Common methods are quadratic function analysis, inequality method, function image method! Variable separation method, substitution method, and discriminant method! And you need to know the object of these methods!
This topic has is uses the discriminant method!
That is, the deformation is: x ^ 2-xy + 1-y = 0, it can be seen that it is a quadratic function about X. by using the discriminant! Y ^ 2-4 (1-y) is greater than or equal to 0, the value range of value range y can be solved!

A mathematical geometry problem has a way of thinking
Question: in ⊙ o, D and E are the points on radius OA and ob respectively, and ad = be, point C is a point on arc AB, connecting CB and CE, ∠ AOC = ∠ BOC
Verify CD = CE
The thinking is as follows:
Triangle AOC, BOC,
If the edges are equal, the congruence can be proved
It can be proved that the third side is equal, that is, CD = CE

In ⊙ o, radius OA = ob, because ad = be, so oa-ad = ob-be, that is od = OE
Because ∠ AOC = ∠ BOC and OC = OC, the triangle doc and the triangle EOC are congruent,
So CD = CE

Find the rules. [4.5] [7.9] [9.12] [7.7] what is the question mark?

【4.5】【7.9】【9.12】【?.7】
The first two differ by 1, the second two differ by 2, the third two differ by 3, so the fourth two differ by 4
The fourth answer may be 3 or 11. The difference is 4 anyway
There may be two answers. Choose one

The power arm of a lever is 60cm, and the resistance arm is 20cm. It is used to raise the weight of 300N by 2cm at a uniform speed. Regardless of the self weight and friction of the lever, we can find: (1) what is the power? (2) what is the moving distance of the power action point? (3) how much work is done by the power?
Please give me a brief idea

(1) According to the balance condition of lever, f1l1 = f2l2, F1 * 60cm = 300N * 20cm, F1 = 100N
(2) According to the principle of work, f1s1 = f2s2, 100N * S1 = 300N * 2cm, S1 = 6cm = 0.06m
(3) According to the formula of work, w = f1s1 = 100N * 0.06m = 6J

Two physics problems in junior three, please help
1. (1) please design an experiment plan, measure the air density in the classroom, and write down the equipment and measurement plan required for the experiment
(2) What should be paid attention to when selecting equipment and conducting laboratory test (at least write two points)
2. In the laboratory, students measure the density of a small ore by using balance, measuring cylinder, small ore, thin wire, beaker and water. In the experiment, Yu Xiaoying accidentally broke the measuring cylinder, but there is no measuring cylinder in the laboratory, so the teacher added an overflow cup to him. Please help her find a way to measure the volume of the small ore and write down the brief experimental steps
thank you

1. Weigh the beaker mass M1 with a balance;
2. Fill the overflow cup with water, and prepare the beaker to receive water below;
3. Tie the small ore with a thin thread and slowly put it into the overflow cup;
4. Weigh the mass m2 of beaker with overflow water by balance;
5. Calculate the mass of overflow water M = m 2-m 1, and then calculate the volume of water according to the density of water, that is, the volume of small ore

Xiao Ming had a pair of wooden chess. In order to know the density of the wooden material, he took a measuring cylinder and read out the scale value corresponding to the water surface as 180ml. Then he put a chess piece into the measuring cylinder and floated on the water surface after it was stable. He read out the scale value corresponding to the water surface as 192ml. Finally, he pressed the chess piece into the water with a thin wire to make it completely submerged, After the water surface is stable, read out the corresponding scale value of 200ml. Please help Xiao Ming calculate the density of the wood material according to the above data. The density value you calculated is ρ=______ (take g = 10N / kg)

When the pieces float, the volume of boiled water is 192ml-180ml = 12ml = 12cm3 = 12 × 10-6m3; the buoyancy of the pieces is equal to its own gravity, g = f floating = ρ water, GV row = 1000kg / m3 × 10N / kg × 12 × 10-6m3 = 0.12n, the weight of the pieces is m = GG = 0.12n10n / kg = 0.012kg; the volume of the pieces is 200ml-180

Two physics problems in junior three are in trouble!
1. A cubic block of wood with a side length of 10cm and a density of 0.44 * 10 cubic kilograms per cubic meter floated on the water surface and pressed it into the water at a constant speed. How much work has been done by its vertical distance of 5m
2. A 30 kW motor is used to drive the pump to pump water to supply a water tank 30 meters above the water surface. The known volume of the water tank is 60 cubic meters, and the mechanical efficiency of the pump is 60%
1. The quality of water in the tank after the tank is full of water
How long does it take to fill the empty tank with water

1. A cubic wooden block with a side length of 10cm and a density of 0.44 * 10 cubic kilogram per cubic meter floated on the water surface and pressed it into the water at a constant speed. How much work has been done by its vertical distance of 5m? 2. A motor with a power of 30kW is used to drive the water pump to pump water to supply a water tank 30 meters above the water surface

1. When measuring the force, it is necessary to measure the force in a straight line with uniform speed. What if the speed is not uniform? What if the force is pulled obliquely?
2. F floating = g, f floating = g row, which pair (floating or floating)
3. It seems that both floating and floating are f-floating = g. when an object is floating or floating, should the formula f-floating = G be used to calculate the buoyancy, or should f-floating = p-liquid GV be used to calculate the buoyancy?
Which units are j?
What's the difference between F and f (force)

1. When measuring the force, it is necessary to measure the force in a straight line with uniform speed. What if the speed is not uniform? What if the force is pulled obliquely?
If the speed is not uniform, there will be acceleration or acceleration motion, which makes the numerical transformation uncertain or inaccurate
The oblique pull can only measure the component of the original force (this is about the composition and decomposition of the force, learned in high school), so the measurement is not accurate
2. F floating = g, f floating = g row, which pair (floating or floating)
It's all right. If you don't believe it, you can do it all over again
3. It seems that both floating and floating are f-floating = g. when an object is floating or floating, should the formula f-floating = G be used to calculate the buoyancy, or should f-floating = p-liquid GV be used to calculate the buoyancy?
Can, that depends on the question, how simple how to calculate
4. Which units are j?
Unit of heat: Joule
5. What is the difference between F and f (force)
Generally, small f is resistance, but you can also use F, but write the corner mark, such as f resistance

Third grade physics, please answer
Xiaoli makes millet porridge at home. She puts 3kg of water into a 500g iron pot, and first heats the water from 20 ℃ to boiling. How much heat does it need to provide? {note: the specific heat capacity of iron is 460j / (kg. C)}
Note: please write the detailed steps, including the formula!

According to the formula: Q suction = cm (t0-t), we get
Heat absorbed by iron: Q1 = 460 x 0.5 x (100-20) = 18400 (J)
Heat absorbed by water: Q2 = 4200 x 3 x (100-20) = 1008000 (J)
Total heat to be provided: q = Q1 + Q2 = 18400 + 1008000 = 1026400 (J)

When an expedition member goes to a certain place, the bar magnet is not horizontal. The north pole of the bar magnet almost only faces the sky, so where is he?
A. Arctic
B. Antarctica
C. In iron ore
D. Can't judge
What is the reason?

B correct

Please give me a math problem, and then teach me how to think! Teach you how to think