There is a rectangular sheet of iron 40 cm in length and 30 cm in width. Cut out an equal small square at its four corners to make a cuboid uncovered sheet iron box 5 cm in depth (the thickness of welding joint is not included). What is the volume of the box?

40-5 × 2 = 30 (CM) 30-5 × 2 = 20 (CM) 30 × 20 × 5 = 3000 (cm3) a: the volume of the tin box is 3000 cubic centimeters

What's the difference between average speed and average speed?

1、 Definition: the average speed is the distance in unit time (the route passed); the average speed is the displacement in unit time (the vector of the first and last positions of the particle in this period)
2、 Velocity has only one size, which is scalar; besides size, velocity has direction, which is the tangent direction of the trajectory curve, which is vector;
3、 Formula: average speed = distance / time; average speed = displacement / time;
Maybe the above is more abstract. Let me give you an example
When you go to school in the morning, you make a detour to a snack bar for breakfast. That is to say, you first go from a to B and then to C. then your average speed is the total route you have traveled divided by the time you spent. But the average speed is the vector (equivalent to connecting line) / time spent from your home to school. That is to say, the average speed has nothing to do with the way we arrive
It should be noted that the velocity is the magnitude of the velocity, but the average velocity is not necessarily equal to the magnitude of the average velocity

It is known that the bottom radius of the cone is 3cm, the length of the generatrix is 9cm, and C is the midpoint of the generatrix Pb. On the side of the cone, the shortest distance from a to C is______ ．

: if the circumference of the bottom surface of a cone is 6 π, then 6 π = n π × 9180, n = 120 °, that is, the center angle of the cone side development is 120 °, APB = 60 °, ∫ PA = Pb, ∫ PAB is equilateral triangle, ∫ C is the midpoint of Pb, ∫ AC ⊥ Pb, ∫ ACP = 90 °, in the cone side development, AP = 9, PC = 4.5

Two ways to remove brackets in mathematical calculation
2 (X-2) - 3 (4x-1) = 9 (1-x) (write detailed process)
3x-2-8 * (1 / 4 x-1) = - 5 (write detailed process)

2 (X-2) - 3 (4x-1) = 9 (1-x) (write detailed process)
2x-4-12x+3=9-9x
2x-12x+9x=9+4-3
-x=10
x=-10
3x-2-8 * (1 / 4 x-1) = - 5 (write detailed process)
3x-2x+8=-5
x=-5-8
x=-13

It is known that the square area is 4 square centimeters, the area of the whole circle is () square centimeters, and the circumference of the circle is () centimeters

It is known that the square area is 4 square centimeters, the area of the whole circle is (3.14) square centimeters, and the circumference of the circle is (6.28) centimeters

As shown in the figure, in the straight triangular prism abc-a1b1c1, AC = BC = 12aa1, D is the midpoint of edge Aa1, DC1 ⊥ BD (1) proves that DC1 ⊥ BC (2) finds the size of dihedral angle a1-bd-c1

(1) It is proved that: in RT △ DAC, ad = AC, ∩ ADC = 45 ° similarly: ∩ a1dc1 = 45 °, ∩ cdc1 = 90 °; DC1 ⊥ DC, DC1 ⊥ BD ∩ DC = D ∩ DC1 ⊥ BCD ⊂ BCD ⊂ DC1 ⊥ BC (2) ≁ DC1 ⊥ BC, DC1 ∩ CC1 = C1, ∩ BC ⊥ acc1a1, ⊂ AC ⊂ AC

Given that the chord length is 600, the distance between chord and arc is 100, how much is the arc length

Given the chord length L = 600, the distance between the arc and the chord is h = 100, find the arc length C? The arc radius is r, and the center angle of the arc is A.R ^ 2 = (R-H) ^ 2 + (L / 2) ^ 2R ^ 2 = R ^ 2-2 * r * H + H ^ 2 + L ^ 2 / 42 * r * H = H ^ 2 + L ^ 2 / 4R = H / 2 + L ^ 2 / (8 * h) = 100 / 2 + 600 ^ 2 / (8 * 100) = 500A = 2 * arc sin ((L / 2) / R) = 2 * arc sin

A summation problem
One of the squares of 1 plus one of the squares of 2 plus one of the squares of 3 is added to one of the squares of N, and N approaches infinity. How much is this? I remember that it seems to be calculated by using the number of freields, and the answer seems to be a formula related to PI square. If I don't remember, I'd better have a calculation process

The result is pi ^ 2 / 6 and PI is pi
Detailed process can see the picture

The poetry of Guazhou

Berthing in Guazhou
Wang Anshi
There is a water room in Guazhou, Jingkou,
Zhongshan is only a few mountains apart
The spring breeze is green on the South Bank of the river,
When will the moon shine on me?
Jingkou and Guazhou are only a distance of water, and Zhongshan is only separated by several green mountains. The gentle spring breeze has greened the South Bank of the river, but the bright moon in the sky, when can you shine me home?

Positive proportion and inverse proportion function intersect at two points? These two points are symmetrical about the origin? What about inverse proportion and first-order function? What about positive proportion and first-order function
My question may not be standard, help me to answer it

It is true that the positive and negative proportion functions intersect at two points, which are symmetrical about the origin
But the intersection of inverse proportion and general first-order function is asymmetric; if there is one intersection of positive proportion and first-order function, it will not be symmetric

There is a rectangular sheet of iron 40 cm in length and 30 cm in width. Cut out an equal small square at its four corners to make a cuboid uncovered sheet iron box 5 cm in depth (the thickness of welding joint is not included). What is the volume of the box?