Finding the volume of regular hexagonal prism It is known that the longest diagonal of a regular hexagonal prism is 13 cm long and its side area is 180 square cm. The volume of this prism is calculated

Finding the volume of regular hexagonal prism It is known that the longest diagonal of a regular hexagonal prism is 13 cm long and its side area is 180 square cm. The volume of this prism is calculated

Let the length of the bottom edge be x and the length of the side edge be y,
X*Y＝180/6＝30
（2X)^2+Y^2=13^2
The solution is x = 6, y = 5
Then calculate the area of hexagon on the bottom of prism
The distance between the center point and the edge of a hexagon is 6 ^ 2-3 ^ 2 under the root sign, which is equal to 5
The area is 6 * 5 / 2 and * 6 = 90
Prism volume = 90 * 5 = 450 cubic centimeter

In the same rectangular coordinate system, we can draw the images of the functions y = x and y = 1 / X respectively, and try these two images to explain when x is larger than 1 / X and when x is smaller than 1 / X

One is an oblique line, the other is a hyperbola. And in their respective domains, one is an increasing function and the other is a decreasing function

How many tons of cement, sand and stone are needed to make 96 tons of concrete with cement, sand and stone in the ratio of 2:3:5?

96 × 22 + 3 + 5 = 19.2 (tons); 96 × 32 + 3 + 5 = 28.8 (tons); 96-19.2-28.8 = 48 (tons); a: 19.2 tons of cement, 28.2 tons of sand and 48 tons of stone are required

If 2A > b > 0, the minimum value of a + 4 / (2a-b) * B is?

Is one micron equal to one wire?
I just saw on the Internet that 1 wire = 1 meter = 0.01mm = 0.00001m = 10 micron

1 wire is our oral unit in mechanical design and processing, 1 wire = 0.01 mm = 10 micron

The average relative molecular mass ratio of H2 and O2 with volume ratio of a: B is that of H2 and O2 with volume ratio of a: B

The average molecular weight of H2 and O2 with volume ratio of a: B = (2a + 32b) / (a + b)
The average molecular weight of H2 and O2 with mass ratio a: B = (a + b) / (A / 2 + B / 32) = (32a + 32b) / (16a + b)

In the equation y = x square - BX + C, when x = - 2, y = 5; when x = - 1, y = 6, how much is the value of y when y = 2

It's a binary equation
Just bring it in
First, when x = - 2, y = 5; bring in 5 = 4 + 2B + C
When x = - 1, y = 6 is 6 = 1 + B + C
The solution is b = - 4, C = 9,
The original equation is the square of y = x + 4x + 9
Bring in the value of y = 2? Y? What's the situation?
If y = 2, there is no solution
It should be x = 2, y = 19
Yeah, how are you~

It is known that the vertex of the parabola is at the origin and the focus is on the negative half axis of the y-axis. The tangent equation passing through the point P (x0, Y0) (x0 ≠ 0) is y-y0 = 2ax0
(I) let the equation of parabola be x2 = - 2PY (P > 0),
From the tangent equation of passing point P (x0, Y0) (x0 ≠ 0) is y-y0 = 2ax0 (x-x0), we get that
∴y′|x=x0=-
x0p=2ax0,
So p=-
12a．
In the answer to the first question, | y ′| x = x0=-
x0p=2ax0,

In y '| x = x0 =, the symbols x = x0 are subscripts, which means that after the derivation of the function, x = x0 is substituted into the tangent slope
It is known that the tangent slope is 2 a x 0, and the result of derivation is x 0 P, so x 0 P = 2 a x 0

Calculation of pressure loss in ventilation duct
About 15 meters long pipeline, the front 6 meters is dn400, the back diameter is DN200, the air volume is 30000 m ^ 3 / h, how much is the pressure loss of the pipeline, and how much pressure should the fan use, thank you!
A lot of answers give me extra points~~~
It seems that roots blower can't reach such a large flow. It's dn400 pipeline that needs such a large flow. It's used for calibrating instrument

Under what conditions?
The velocity at DN200 is 265 meters per second!
Only constant volume fans (such as roots fans) can meet the demand
If it is to calibrate the instrument, it is short-term load and intermittent load
It is suggested that a steam drum should be equipped instead of a blower. It is also convenient to adjust the pressure and flow, which is much more convenient than adjusting the blower
After determining the time required for "calibration instrument", the required "gas volume" can be known. According to more than three times of the "gas volume" data, the volume of steam drum is selected, and the pressure reducing valve is equipped (to keep the pressure stable)
Specific pressure, I have no experience, may need to do several tests to determine
In my opinion, even if I need to make "30 cubic meters, 25 kg pressure" drum, I will not buy special high pressure fan, unless it is continuous load

How to simplify 99.9 * 99.9 operation

=(100-0.1)*99.9
=100*99.9-0.1*99.9
=9990-9.99
=9980.01