In a 12 cm long and 8 cm high rectangular water tank, submerge a cube with an edge length of 6 cm, and the water surface rises by 2 cm. What is the width of the rectangular water tank?

In a 12 cm long and 8 cm high rectangular water tank, submerge a cube with an edge length of 6 cm, and the water surface rises by 2 cm. What is the width of the rectangular water tank?

6 × 6 × 6 ^ (12 × 2), = 216 ^ 24, = 9 (CM); answer: the width of this cuboid tank is 9 cm

There is a cuboid glass jar with a length of 20 cm and a water depth of 10 cm. Now a piece of iron with a length of 10 cm, a width of 8 cm and a height of 5 cm is made of wood

The description of the problem is not clear
Under the premise of ignoring the glass thickness, the glass tank volume = 20 * 20 * 20 = 80 cubic cm, the water depth of 10 cm = half of the glass tank edge length of 20 cm, that is to say, the water storage and idle account for 50% and 40 cubic cm respectively. The iron block volume = 10 * 8 * 5 = 40 cubic cm, which is exactly half of the glass tank volume. After the iron block is put into the tank, the water will completely submerge the iron block and fill the tank mouth

In a glass jar with a length of 25 cm and a width of 20 cm, there is a cube iron block with an edge length of 10 cm. At this time, the water depth is 15 cm. If the iron block is taken out of the jar, what is the water depth in the jar?

25 × 20 × 15-10 × 10 = 7500-1000 = 6500 (cubic centimeter) 6500 △ 25 × 20 = 6500 △ 500 = 13 (centimeter) answer: the water depth in the tank is 13 centimeter

If the intersection of the line y = 3x-1 and y = x-k is in the fourth quadrant, then the value range of K?

First, in the fourth quadrant, x > 0, y

It is proved that f (x, y) at point (0,0) is continuous and partial derivative exists, but not differentiable
f(x,y)=x^2y^2/(x^2+y^2)^(3/2)

There should be similar examples in the textbook
1) due to
　　　|[(x^2)(y^2)]/(x^2+y^2)^(3/2)|
　　

What is the probability that at least one of the three people in group A, two in group B and one in group C will be in group B?

At least one of the probabilities in group B is
1-C(4,2)/C(6,2)
=1-6/15
=1-2/5
=3/5

How to find the range of quadratic function?

First, find the ordinate of the parabola vertex, if a > 0, then the range is [vertex ordinate, positive infinity], if a < 0, then the range is (negative infinity, vertex ordinate]. Premise: the definition field is r

It is known that parabola y ^ 2 = 4x and ellipse x ^ 2 / 8 + y ^ m = 1 have the same focus F
1, find the value of M
2. There is a moving point P on the parabola. When the distance AP between the moving point P and the fixed point a (3,0) is the smallest, the coordinates of P and the minimum value of PA are obtained

1.y^2=4x F(1,0) c=1 8-m=1 m=7
2. Let P (x, y), then | AP | & # 178; = (x-3) & # 178; + Y & # 178; = x & # 178; - 2x + 9 = (x-1) & # 178; + 8 > = 8, so | AP | has a minimum of 2 roots. In this case, x = 1, y = 2 or - 2
So p (1,2) or (1, - 2)

Factorization (A2-1) (b2-1) - 4AB

In △ ABC, the bisector of ∠ C intersects AB at point D, passes through point D as the parallel line of BC, and intersects AC at point E, if BC = a, ab = B, de =?

AB = B should be AC = B, otherwise it is not easy to do
Because CD bisects ACB
Therefore, ACD = BCD
Because de / / BC
Therefore, CDE = BCD
Therefore, CDE = ACD
So de = CE
Let CE = de = X
Because de / / BC
So de / BC = AE / AC
So x / a = (b-X) / X
The solution is: x = AB / (a + b)
That is, de = AB / (a + b)