What is the function of induction formula in senior high school mathematics compulsory 4

What is the function of induction formula in senior high school mathematics compulsory 4

1. Easy to solve math and physics problems;
2. Solve the problems in life;
3. To appreciate the beauty of mathematics
College entrance examination
The general formula of 1,8 / 5,15 / 7,24 / 9
(n^2+2n)/(2n+1)
((n+1)^2-1)/(2n+1)
General term formula of 1,3,3,5,5,7,7,9,9 ··
An=n+[(-1)^n+1]/2
A mathematical problem about work efficiency. I'm confused,
Tap A can fill a water tank in 25 minutes,and Tap B can fill the same tank in 20 minutes.
(a)If the volume of the tank is 5000cm^3,find the rate of flow of water(in cm^3/min)for
(i)Tap A,and
(ii)Tap B,
(b)Both taps(Tap A and Tap B )are used to fill up the tank at the same time.
(i)Calculate the total volume of water in the water tank after 10 minutes.
(ii)Will the water overflow if both Tap A and Tap B are turn on for 10 minutes.
[title] it takes 25 minutes for single tap a to fill the pool, while it takes 20 minutes for single tap B to fill the same pool. (a) if the volume of the pool is 5000 cubic centimeters, calculate (I) the flow rate of tap a and (II) the flow rate of tap B; (b) if both tap a and tap B are opened at the same time, (I) calculate the total volume of water in the pool after 10 minutes
As shown in the figure, the power supply voltage is 4.5V, resistance R1 = 5 Ω, the maximum resistance of rheostat R2 is 20 Ω, the range of ammeter is 0 ~ 0.6 a, and the range of voltmeter is 0 ~ 3 V. in order to protect the ammeter from damage, what is the resistance range of rheostat access circuit?
It can be seen from the circuit diagram that the sliding rheostat R2 is connected in series with the resistance R1. The voltmeter measures the voltage at both ends of the sliding rheostat, and the ammeter measures the total current of the circuit. When the current expression number is I1 = 0.6A, the resistance of the sliding rheostat connected to the circuit is the smallest. According to Ohm's law, the voltage at both ends of the resistance R1: U1 = i1r1 = 0.6A × 5 Ω
Because of the good cooperation, the work efficiency of Party A is one tenth higher than that of Party B. the work efficiency of Party A and Party B is one fifth higher than that of Party B. Party A and Party B work together for four hours, completing two fifths of the whole work. The next day, Party B work alone for four hours, leaving 13 / 30 of the work unfinished. How many hours does it take for Party A to work alone?
We need to formulate
If Party A completes in a hour and Party B completes in B hour, then when Party A and Party B cooperate,
The efficiency of a is 11 / 10A, and that of B is 1 / b * (1 + 1 / 5)
（11/10a+6/5b）* 4= 2/5
4/b+2/5=1-13/30
b=24
Substituting into the original formula, a = 22
A bulb marked with "36V, 36W" is connected to the circuit with a voltage of 220 v. in order to make it shine normally, a resistor of -------- should be connected in series. When the lamp shines normally, the power consumed by the circuit is----------
From P = UI, 36W = 36V * I lamp, I lamp = 1a, from u = RI, r = 220V / 1A = 220ohm, from W lamp = u square / R lamp
R lamp = 36 ohm r resistance = R total - R lamp = 220-36 = 184 ohm
From P = UI = 220 V * 1A = 220 w
In order to light normally, the power should be 36W. Because the resistance value is certain, the voltage should be 36V, so the resistor should be connected in series. At this time, the current is 36W / 36V = 1a. The total resistance is 220V / 1A = 220 ohm. So the resistance is 220-36 ^ 2 / 36 = 184 ohm. The total power is 220W
Answer: 184
Two hundred and twenty
To make the bulb shine normally, the voltage at both ends of the bulb should be 36V.
The value of resistance R in series should be 220 × 36 △ (R + 36) = 36
∴R=184Ω
When the lamp lights normally, the power consumed by the circuit is: P = 36 + 184 & # 178; △ 184 = 220W
It takes t hours for Party A to complete a task, and it takes one hour less for Party B to complete the same task than Party A. what is the efficiency of Party B?
1/(t-1)/(1/t)
=t/(t-1)
T-1
What is the efficiency formula? Thank you. If all work items are set to 1, then a completes 1 / X every day, and B completes 1 / (x + 5) every day. The following is the formula listed according to the title
Help me with the formula,
It is known that the total contact area between the car wheel and the horizontal ground is 1500 square centimeters, the total mass between the goods and the car is 6T, the total contact area between the bicycle wheel and the horizontal ground is 20 square centimeters, the mass of the cyclist is 75kg, and the mass of the bicycle is 10kg. Please judge whether Xiaoming's statement is correct through calculation according to the data provided (G is 10N / kg)
Xiao Ming's view is: trucks are so heavy, the effect on the road must be greater than bicycles
Xiaoming's view is wrong, the effect on the road depends on the pressure; the pressure of trucks on the ground P1 = M1 × g / S1 = 6000 × 10 / 0.15 = 400 (PA) the pressure of bicycles on the ground P2 = M2 × g / S2 = 75 × 10 / 0.002 = 275000 (PA) because P2 > P1, the pressure of bicycles on the ground is greater than that of trucks on the ground
The ground pressure is calculated
P car = f car / s car = m Car * g / s car = 6000kg * 10N / kg / 0.15m2 = 4 * 10 ^ 6pa
P bike = f Bike / s bike = m bike * g / s bike = 85kg * 10N / kg / 0.0002 M2 = 4.25 * 10 ^ 6pa
Because P bicycle > P car
Therefore, the effect of bicycles on the road is greater than that of cars. Xiao Ming's view is wrong. ... unfold
The ground pressure is calculated
P car = f car / s car = m Car * g / s car = 6000kg * 10N / kg / 0.15m2 = 4 * 10 ^ 6pa
P bike = f Bike / s bike = m bike * g / s bike = 85kg * 10N / kg / 0.0002 M2 = 4.25 * 10 ^ 6pa
Because P bicycle > P car
Therefore, the effect of bicycles on the road is greater than that of cars. Xiao Ming's view is wrong. Put it away
Theoretically, the effect of pressure is determined by the pressure divided by the force area. It is wrong to say that the effect of truck on the road must be greater than that of bicycle, but the specific values of several physical quantities are given in this question. Therefore, it can be judged whether the statement is correct through calculation and comparison, that is, the effect of truck on the road is greater than that of bicycle It's possible. Formula: F = g = mg, P = f / s. As for the calculation, you can do it yourself. It's better to exercise more. I only provide the method
Theoretically, the effect of pressure is determined by the pressure divided by the force area. It is wrong to say that the effect of truck on the road must be greater than that of bicycle, but the specific values of several physical quantities are given in this question. Therefore, it can be judged whether the statement is correct through calculation and comparison, that is, the effect of truck on the road is greater than that of bicycle It's possible, formula: F = g = mg, P = f / s. As for the calculation, you can do it yourself. It's better to exercise more. I only provide the method ~ ~ ~ put it away
You can calculate the pressure of the car and bicycle on the ground: the pressure of the car on the ground is 0.4MPa, the pressure of the bicycle on the ground is 0.425mpa, so the effect of the bicycle on the ground is stronger
Xiao Ming's statement is not correct. Pressure is the physical quantity of force effect, so the comparison of force effect should compare the size of pressure, not the size of pressure.
Pressure of truck on road: P1 = 6000kg * 10N / kg / 0.15 = 400000pa
Pressure of bicycle on road: P2 = (75 + 10) kg * 10N / kg / 0.002 = 425000pa
Because P2 > P1
So bicycles have a great effect on the road. ... unfold
Xiao Ming's statement is not correct. Pressure is the physical quantity of force effect, so the comparison of force effect should compare the size of pressure, not the size of pressure.
Pressure of truck on road: P1 = 6000kg * 10N / kg / 0.15 = 400000pa
Pressure of bicycle on road: P2 = (75 + 10) kg * 10N / kg / 0.002 = 425000pa
Because P2 > P1
So bicycles have a great effect on the road. Put it away
1500 square centimeter = 0.15 square meter, 6T = 6000 kg, 20 square centimeter = 0.002 square meter
P (card) = f / S = 6000 kg / 0.15 M2 = 40000 pa
P (self) = f '/ S = 85kg / 0.002 M2 = 42500pa
Xiao Ming is wrong
Mathematical efficiency ratio
When the master and the apprentice process a batch of parts, the work efficiency ratio of the master and the apprentice is 4:3. It takes 8 days for the master to process alone, and how many days for the apprentice to process alone?
4：3=8：
=24
=6
It takes six days for the apprentice to be alone
Let the engineering quantity be x (x > 0) and the apprentice use y (Y > 0) days, then the apprentice efficiency are x / 8 and X / y respectively, so
x/8/（x/y）=4/3
How to use primary school knowledge?