Do you know that the money spent is in inverse proportion to the money left?The money spent was not proportional to the money left. Because the sum of the money spent and the remaining money is fixed (for example, the total amount of money is 100 yuan, the amount of money spent + the remaining money = 100 yuan), and the inverse relationship is that the product of the two related quantities is fixed, so the money spent and the remaining money are not inverse.
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The proportion of first-class kindergarten in ShanghaiBy December 23,2022, the first online application forum revealed that there were 752 first-class and above high-quality kindergarten in Shanghai, accounting for 44.26% of the total number of kindergarten. In the 2019 - 2021 Shanghai City Three-Year Action Plan for Pre-school Education, it was proposed to increase the proportion of state-owned first-class kindergarten from 36% to 50%.
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Inverse proportional function, image and property classThe graph of the inverse proportional function was a hyperbola. Its properties were as follows:
** I. Quadrant distribution and monotonicity **
1. When the proportional factor is 0
- The two branches of the hyperbolas were in the first and third quadrants.
- In each quadrant, y decreases as x increases.
2. When the proportional factor is k < 0
- The two branches of the hyperbolas were in the second and fourth quadrants.
- In each quadrant, y increases with x.
- Note that the two branches of the hyperbola are infinitely close to the coordinate axis, but they can never intersect.
** 2. Symmetries **
1. A hyperbola is an axis-symmetrical figure, and the line y = x or y=-x is its axis of symmetries.
2. Hyperbolas were also symmetrical at the center, and the center of the center was the origin of the coordinates.
In the classroom, students can better understand the image and properties of the inverse proportional function by:
1. drawn image
- Choose different values of k (such as k = 2, k=-3, etc.) and list the corresponding values of x and y.
- According to the corresponding value table, the points were drawn in the coordinate system, and then the points were connected with a smooth curve to obtain the image of the inverse proportional function.
- Let the students observe the shape of the image, the quadrants, the relationship with the coordinate axis, and so on.
2. comparative analysis
- Comparing the inverse proportional function images with different k values, observe the effect of k values on the quadrants distribution and monotonicity of the images.
- For example, compare the images of <<y=<frac{1}{x}>> and <<y =-<frac{1}{x}>>. Ask the students to summarize the differences between the properties of <k>0> and <k> 0>.
3. with examples
- Some examples of inverse proportional relationships in real life can be cited, such as the relationship between speed and time when the distance is fixed (s = vl, when s is fixed, v = frac{s}{t}, v is inverse proportional to t), so that students can better understand the concept of inverse proportional function and its properties in reality.
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Inverse function means inverse? Why?Inverse function did not mean inverse.
By definition, an inverse function was a function that did the inverse operation on a fixed function. Assuming that the domain of a function was, and the range was, if there was a unique value corresponding to any value in the range, then the new function that was determined as an independent variable and a dependent variable was the inverse function of the original function.
In mathematics, the reciprocals referred to the number x multiplied by 1, which was recorded as 1/x. The two were fundamentally different in terms of concepts, calculations, and properties. They were not directly related.
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The difference between water inverse and metal inverseThe reverse of water and metal referred to the reversal of Mercury and Venus in the astronomical phenomena. The water reversal happened many times in the past year, while the metal reversal only happened once a year and a half. Water and metal would both affect interpersonal relationships and feelings, but based on the information provided, it was impossible to know the specific difference between water and metal.
Inverse ProblemThe C919 had a left-hand reverse thrust failure 100 hours before its operation. The reverse thrust device was used to shorten the sliding distance of the aircraft during landing. Normally, the reverse thrust generated by changing the direction of the gas jet would slow down the landing of the aircraft, but it was not the only landing deceleration device. The aircraft also had a brake system to ensure the safety of the landing. According to the Airworthy Standard for Transport Aircrafts, the aircraft could continue to fly and land safely when the thrust reverser was in any possible position. Failure of the thrust reverser was more common. The C919 used an " O-ring " thrust reverser. When it was not working, the thrust reverser channel was closed. When it was working, the thrust reverser channel was opened and the gas backward flow channel was closed. Part of the gas was sprayed forward to decelerate. This device could improve the thrust reverser efficiency and reduce the fuel consumption during thrust reverser. It was widely used in the new generation of civil airliners.
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Which function is the inverse function of the inverse trigonometer function?The inverse trigonometric-function was the inverse function of the trigonometric-function, which meant that the inverse trigonometric-function and the trigonometric-function were inverse functions of each other.
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The composition and proportion of the bleachersThe main components of the bleachers were calcium chopstick and calcium chloride.Among them, calcium chopstick was the active component and had strong oxidisation. The ratio of the bleaches could be determined according to different uses. For example, when used to deal with moldy floors, you can mix rinsing water and water in a ratio of 1:3. For household sterilization, you can mix 10 milliliters of rinsing water with 990 milliliters of clear water and dilute it in a ratio of 1:99. For cleaning and disinfecting excrement or secretions, you can mix 10 milliliters of rinsing water with 490 milliliters of clear water and dilute it in a ratio of 1:49. Different cleaning needs may require different proportions, so the proportion of the use of whiteness needs to be determined according to the specific situation.
Mix proportion of the castableThe mix ratio of the castables varied due to the different materials used and their uses.
For an important type of unshaped fire-resistant material such as the CA - 50 cement castable, if the grade-2 kiln was used to prepare the fire-resistant material and powder, the total amount of CA - 50 cement and fire-resistant material would be 27% - 30%, the amount of fire-resistant material would be 70% - 73%, and the amount of CA - 50 cement would be 10% - 20%. When used in medium-high temperature parts, the amount of cement should be reduced and the amount of fire-resistant powder should be increased. The grade of the fire-resistant powder should be the same as or one grade higher than that of the fire-resistant gravel. The fire-resistant gravel can be reasonably selected according to the service temperature of the kiln. The grain grading is usually two-grade grading or unified material.(The ratio of fine gravel to the whole gravel) is generally controlled at 0.45 - 0.55. The amount of water can be expressed by mass percentage, kilogram per cubic meter or water-cement ratio (the ratio of water to cement and powder). The principle is to reduce the amount of water as much as possible under the condition of ensuring the easiness of the castable mixture. The common mixing ratio should be determined by the test during production or construction according to the variety of raw materials and the use conditions. At the same time, it should be added as much as possible to improve the construction and fire resistance performance.
Castables made from aluminum clay:
- Binder: No. 625 and above aluminum cement, with a mixture ratio of 15% - 20%.
- "Agglomerate: made of Grade 2 and Grade 3 aluminum chamotte or Grade 1 and Grade 2 clay chamotte, waste high-aluminum bricks and waste fire-resistant clay bricks. The grain size of fine agglomerate is less than 5mm, and the mixing ratio is 30% - 40%. The grain size of coarse agglomerate is 5 - 15mm, and the mixing ratio is 30% - 40%.
- Powder (Admixture): The same as the gravel, not less than 70% of the grain size is less than 0.088mm, and the mixing ratio is 0 - 15%.
Phosphate-based casting material:
- Binder: 42.5 or higher grade cement, with a mixture ratio of 15% - 20%.
- "Agglomerate: made of Class I and Class II clay grog or waste firebricks. The grain size of the fine gravel is less than 5mm, and the mixing ratio is 35% - 40%. The grain size of the coarse gravel is 5 - 15mm, and the mixing ratio is 30% - 40%.
- Powder material: the same as the gravel, not less than 70% of the grain size is less than 0.088mm, and the mixing ratio is less than 15%.
In general, the formula of the fire-resistant casting material included fire-resistant material, fire-resistant binding agent, fire-resistant filling material, and other materials. The fire-resistant material is the main component, such as high-aluminum material and silica material, etc. The fire-resistant binding agent is composed of phosphorous acid, silica acid, aluminum acid, etc. The fire-resistant filling material is used to fill the gap of the material, such as mica, expanded pearlite, etc. The addition agent is used to improve the performance of the castable, such as enhancing the fire-resistant performance and increasing the density. Its formula needs to be adjusted and optimized according to the specific use environment and requirements.
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