Total differentiation: z = xcos (X-Y) $(acontent)

Total differentiation: z = xcos (X-Y) $(acontent)

z=xcos(x-y)
zx=cos(x-y)-xsin(x-y)
zy=xsin(x-y)
therefore
dz=zxdx+zydy=[cos(x-y)-xsin(x-y)]dx+xsin(x-y)dy

How to find the total differential of arctan (Y / x)

How to understand the definition of differential?
 

Even in books, some details are not dealt with strictly. I have checked some materials before, and the descriptions in many places are different. However, the differential representation in books is not strict, which is caused by the vague use of some concepts. Maybe the course of advanced mathematics was written for science and engineering, Bias and application. So many places are not as strict as mathematics

Is the work done by the metal bar to overcome the ampere force Joule heat of the metal bar or Joule heat of the whole circuit

The metal rod overcomes the ampere force to do work, that is to say, the ampere force does negative work, which will reduce the kinetic energy of the metal rod (if there is no other force), so the reduced kinetic energy will be converted into the electric energy in the circuit where the metal rod is located
As for whether the electric energy will be converted into Joule heat in the whole circuit, it also depends on whether there is other power supply in the circuit. If there is no other power supply or motor in the circuit, the electric energy will be consumed in the whole circuit in the form of Joule heat

4AB & # 178; △ 2A ^ - 2b & # 179; calculation

4ab²÷（-2a^-2b)³
=4ab²÷(-8a^-6b^3)
=-1/2a^7b^-1
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The resistance of the winding coil of a DC motor is 8 ohm. When it is connected to a 110 V circuit, it works normally,
If the friction between the shaft and the bearing of the motor is neglected, the electric power consumed by the motor is (), and the power converted into heat energy is

Power consumption: 2 * 110 = 220W
Conversion to heat: (2 ^ 2) * 8 = 32W

A street lamp is high h, and a person is high h. a person walks forward in a straight line at a constant speed V directly under the street lamp. What motion does the shadow of the head do?

Let's assume that the distance between man and lamp is x at the beginning, and the distance from shadow to lamp is y. by drawing, we can know that shadow and man lamp are similar in two triangles, i.e. Y-X / y = H / h. The solution is y = HX / (H-H). After time t, the distance from man to lamp is x + VT, and the distance from shadow to lamp is s

The basic unit of the international system of units
To define the unit symbol, what physical quantity it represents and its symbol
There are bonus points after answering

Length unit: M
Time unit: seconds (s)
Weight unit: kg
Current unit: Ampere (a)
Thermodynamic temperature: on (k)
The unit of mass of a substance: mole (mol)
Luminous intensity: candela (CD)
In October 1983, the 17th International metrology conference held in Paris adopted a new definition of meter: "meter is the length of light travel in vacuum in the interval of 1 / 299792458 seconds". In this way, the definition of meter based on spectral line wavelength is replaced by the new definition of meter, Meter is defined as the distance that light travels in 0.000000003335640952 seconds measured by a platinum atomic clock (the reason for this particular number is that it corresponds to the historical definition of meter - the distance between two scales on a specific platinum rod kept in Paris)
The unit of time, second, is the basic unit of time in the international system of units. The symbol is s. sometimes it is labeled as sec by using the English abbreviation. The prefix of the international system of units is often combined with seconds to make more subtle division, such as MS (millisecond), US (microsecond, millionth of a second) and NS (nanosecond), Although the Si prefix can also be used to amplify time, such as KS (thousand seconds), MS (million seconds) and GS (billion seconds), it is rarely used in this way. People are still accustomed to using the 60 base minute, hour and 24 base day as the second expansion
The world recognized second: under the current international system of units, the 13th International Conference on weights and measures held in 1967 defined second as the duration of 9192631770 cycles of radiation corresponding to the transition between two hyperfine energy levels of cesium 133 atomic ground state. The cesium atom mentioned in this definition must be stationary at absolute zero, The second defined in this case is equivalent to the second defined in the astronomical almanac
The kilogram (symbol kg or kg) is the basic unit of mass measurement in the international system of units. The kilogram is also one of the most commonly used basic units in daily life. The definition of the kilogram is the mass of the original international kilogram, which is almost equal to the weight of a liter of water. The kilogram is the only basic unit with the prefix of the international system of units, It is also the only international unit that still uses artifact as its definition
Since 1889, the weight of "kilogram" has been defined by a cylinder of platinum iridium alloy (90% platinum, 10% iridium) placed in BIMP, France. Its height and diameter are about 39 mm. The alloy was made in 1879 and carefully adjusted to meet the weight of "kilogram" since the French Revolution in the 18th century. It was adopted 10 years later, The kilogram is the unit of mass, and the mass is equivalent to how heavy a thing is. However, mass is actually a property with "inertia"; that is to say, a thing tends to maintain its existing speed without external force. When an object with a mass of one kilogram is under the action of a Newtonian force, the mass of one kilogram will increase, It will accelerate at an acceleration of one meter per second (about one tenth of the acceleration of the earth's gravity). The weight of matter depends entirely on the local gravitational strength, while the mass does not change (assuming that the mass does not move relative to the observer at relativistic speed), Under microgravity, astronauts can lift the object in the capsule without any force, because the object "has no weight". However, the object still retains its mass under microgravity, and the astronauts need to exert ten times the force to accelerate the object with ten times the mass at the same acceleration
Ampere is the international unit of current, abbreviated as ampere, and the symbol is A. It is defined as: when two infinite parallel straight wires with a distance of 1 meter in vacuum are connected with equal constant current, when the force on each meter of wire is 2e-7n (2 × 10 ^ (- 7) n), the current is constant, The current on each wire is 1 ampere. The current smaller than ampere can be expressed in milliampere, microampere and other units. 1 ampere = 1000 milliampere (MA) 1 milliampere = 1000 microampere (μ a) the common unit on the battery is MAH (milliampere hour). For example, 500mah means that the battery can provide 500mA × 1hr = 1800C (Coulomb, referred to as "library"), That is to provide a 500mA power consumption of electrical appliances for one hour
Kelvin, the thermodynamic temperature scale or absolute temperature scale, is the unit of temperature in the international system of units. It was invented by William Thomson, the first generation of Irish Lord Kelvin. Its name is Kelvin according to the inventor's title. The symbol is k, but without "°". In 1927, the Seventh International Conference on Metrology took the thermodynamic temperature scale as the most basic temperature scale
Kelvin thermometer (abbreviated as "K") is widely used in scientific work. The Kelvin temperature scale is established by an ideal gas, and its zero point is called absolute zero. According to the kinetic theory, when the temperature is at absolute zero, the Kelvin temperature scale is established by using an ideal gas, The kinetic energy of gas molecule is zero. For convenience, the scale interval of Kelvin thermometer is consistent with that of centigrade thermometer. That is to say, one degree on Kelvin thermometer is equal to one degree on centigrade thermometer, the freezing point of water is 0 ℃ on centigrade thermometer, and 273.15k on Kelvin thermometer
Mole, formerly known as mole or gram atom, is one of the seven basic units in the international system of units. It represents the amount of matter, and the symbol is mol. every mole of any substance contains particles with Avogadro constant (about 6.02 × 10 ^ 23). When using mole, the basic particles should be specified, which can be atoms, molecules, ions and other particles, or a specific combination of these particles
In science, the collective containing 6.02 × 10 ^ 23 particles is regarded as a unit, which is called mole. It is the unit representing the amount of matter (the symbol is n), which is called Mo for short. The unit symbol is mol. 1mol carbon atom contains 6.02 × 10 ^ 23 carbon atoms, and the mass is 12g. 1mol sulfur atom contains 6.02 × 10 ^ 23 sulfur atoms, and the mass is 32g, The mass of any substance, in grams, is numerically equal to the relative atomic mass of that atom
Candela unit of luminous intensity. It is one of the seven basic units of the international system of units (SI). The symbol CD is the luminous intensity of a light source in a given direction. The light source emits monochromatic radiation with a frequency of 540 × 10 to the 12th power Hertz, and the radiation intensity in this direction is 1 / 683 watt per sphericity. The luminous intensity unit was originally defined by a candle, In 1948, the 9th International Conference on Metrology decided to use the blackbody at the freezing point temperature of platinum as the benchmark of luminous intensity, and named it candela, which was once called new candela. In 1967, the 13th International Conference on Metrology made a more rigorous definition of candela, In 1979, the 16th International Conference on Metrology decided to adopt the current new definition. Luminous intensity is abbreviated as luminous intensity. The international unit is short for candela cd.Lcd When the radiation of the light source is uniform, the light intensity is I = f / Ω, Ω is the solid angle, and the unit is sphericity (SR), f is the luminous flux, and the unit is lumen, For the point light source, I = f / 4. Brightness is the brightness of the light-emitting surface, which refers to the ratio of the luminous intensity of the light-emitting surface in the specified direction to the area of the light-emitting surface in the vertical and specified direction, in candela / m2

As shown in the figure, on a rough horizontal plane, there are two pieces of wood 1 and 2 with mass M1 and M2 respectively. In the middle, they are connected by a light spring with original length L and stiffness coefficient K. the sliding friction coefficient between the block and the ground is μ. Now, a horizontal force is used to pull the block 2 to the right. When the two blocks move at a constant speed, the distance between the two blocks is ()
A. L+μkm1gB. L+μk（m1+m2）gC. L+μkm2gD. L+μk（m1m2m1+m2）g

Study on block 1. Block 1 is subjected to gravity, spring pull, ground support force and friction force. According to the balance condition, the spring force F = μ m1g & nbsp; & nbsp; and the spring elongation length x = FK = μ m1gk is obtained by Hooke's law. Therefore, the distance between two blocks is s = L + x = L + μ km1g when two blocks move at a uniform speed together. Therefore, select a

How many hectares is an acre

1 ha = 15 mu, i.e. 1 mu = 1 / 15 ha, i.e. about = 0.06667 ha