A cuboid glass container is 20dm long and 15dm wide. The water depth in the container is 3.8dm Ask for guidance

It depends on how big the iron is
(V length + V iron) / (20 * 15) and then minus 3.8

A rectangular container with a side length of 8 cm and a height of 16 cm is used. The water in the container is 8 cm away from the container mouth,
After putting a spherical iron block into the container, the water surface rises 5 cm, and the volume of the spherical iron block is calculated

The volume of spherical block = the volume of water rising = the bottom area of container × the height of water rising
8 × 8 × 5 = 320 (cm3)

There is a cuboid with a bottom area of 300 square centimeters and a height of 10 centimeters. It contains 5 centimeters of water. Now immerse a stone in the water, and the water surface rises by 2 centimeters. What is the volume of this stone?

300 × 2 = 600 (cubic centimeter), a: the volume of this stone is 600 cubic centimeter

What is the relationship between the image of the original function and the image of the derivative function?

(1) If the image of the derivative function is a continuous curve, the interval of the independent variable x above the x-axis of the derivative function is often the monotone increasing interval of the original function, the interval of the independent variable x below the x-axis of the derivative function is often the monotone decreasing interval of the original function, and the intersection of the derivative function and the x-axis (also known as the zero point) is often the extreme point (Note: only the zero point of the sign changing is the extreme point, Left and right derivatives of zero point (different sign)
(2) If the image of the original function is continuous, then in the monotone increasing interval of the original function, the image of the derivative function is above the x-axis, in the monotone decreasing interval of the original function, the image of the derivative function is below the x-axis, and the value of the derivative function at the extreme point of the original function is zero

A mathematical problem about space vector
Find: (1) the equation of plane α passing through point P (3, - 1,2) and perpendicular to line L: X-Y + Z = - 1,2x-y + Z = 4; (2) the intersection of plane α and line L; (3) the distance from point P to line L
Do not do question (1), the answer is y + Z-1 = 0, only do question (2) (3)

(2) The simultaneous equations X-Y + Z = - 1,2x-y + Z = 4, y + Z-1 = 0, x = 5, y = 7 / 2, z = - 5 / 2 is the intersection m (5,7 / 2, - 5 / 2)
(3) The distance is the distance of PM. According to the distance formula between points in space, the solution is s = √ 178 / 2

As shown in the figure, in △ ABC, ab = AC, ∠ bad = 20 ° and AE = ad, then ∠ CDE=______ Degree

∵ AB = AC, ∵ let ∠ B = ∠ C = x degree, ∵ EDC = a, ∵ DEA be the outer angle of △ DCE, so ∠ DEA = x + A, in isosceles triangle ade, AE = ad, ∵ ade = x + A. in △ abd, x + 20 = x + a + A, the solution is a = 10, then ∠ CDE = 10 degree. So fill in 10

X ^ 2 + 3ax + 2A ^ 2-a-1 = 0 factorization process

x²+3ax+2a^2-a-1=0
x²+[(2a+1)+(a-1)]x+2a²-a-1=0
x²+(2a+1)x+(a-1)x+(2a+1)(a-1)=0
x[x+(2a+1)]+(a-1)[x+(2a+1)]=0
[x+(2a+1)][x+(a-1)]=0
x=-2a-1,x=-a+1

Given that the module of vector a is 4, the module of vector B is 5, and the angle between vector a and vector B is 60 degrees, then the module of 3-vector a-vector B =?
Why square the module first? (3a-b) · (3a-b) = 9a · A-6A · B + B · B

Because in this way, we can get the condition that "the angle between vector a and vector B is 60 degrees" by multiplying vector a by vector B
Module * cos of module * B of vector a multiplied by vector b = a
Is the angle between vector a and vector B

As shown in the figure, be and CF are bisectors of ∠ B and ∠ C in △ ABC, am ⊥ be at point m and an ⊥ CF at point n, respectively

Extend am to BC (or extension line) to P,
∵∠MBA=∠MBP,MB=MB,∠BMA=∠BMP,
∴ΔBMA≌ΔBMP,
∴AM=PM,
Extend an to BC (or extend) to Q, similarly: an = NQ,
The Mn is the median of Apq,
∴MN∥BC.

Factorization 3A ^ 2x ^ 3Y + 6AX ^ 2Y ^ 2-12ax ^ 2Y ^ 3
2.a^2(x-y)-2a(x-y)^2-(y-x)^3

3a²x³y + 6ax²y² - 12ax²y³
= 3ax²y(ax + 2y - 4y²)

A cuboid glass container is 20dm long and 15dm wide. The water depth in the container is 3.8dm Ask for guidance