A stone with a volume of 8 cubic decimeters is put into a cuboid container containing water. It is found that the water surface rises from 5 decimeters to 7 decimeters. Find the volume of original water Find the volume of original water

The volume of the object in the water is equal to the rising volume of the water. According to this, we can calculate the bottom area of the original container: 8 (7-5) = 4 square decimeters
We also know that the original height of water is 5 decimeters, so the volume of original water = 4x5 = 20 cubic decimeters

A cuboid fish tank has a bottom area of 20 square decimeters and a water depth of 4.3 decimeters. If you put a stone with a volume of 30 cubic decimeters, the water doesn't overflow. How high is the water now

Here are my steps and explanations:
① Volume of fish tank: 20 × 4.3 = 86 (DM & # 179;)
② Find the total volume: 86 + 30 = 116 (DM & # 179;)
③ Find the present height: 116 △ 20 = 5.8 (DM)
It's simple and clear. I hope you can reply as soon as possible,

A real matrix of order 3 satisfying (A-E) (a-2e) (a-3e) = 0 is proved to be similar diagonalized

Since (A-E) (a-2e) (a-3e) = 0, the eigenvalues of a can only be 1,2,3 (1). If 1,2,3 are all eigenvalues of a, then a matrix of order 3 has three different eigenvalues, so a can be diagonalized. (2) if two of 1,2,3 are eigenvalues of a, the other one is not

Do you use singular or plural to have some difficulty

"Have some difficulties" means "have some difficulties" and "have some difficulties" means "have some difficulties"!
Have some difficulty in doing sth
There is some difficulty in doing

The bookstore sells a batch of fairy tale books, 20% of which are sold on the first day, 120 on the second day, and 240 left. How many of these fairy tale books are there in total?

Suppose there are x books in this batch, 20% of which are sold on the first day, and the remaining x-0.2x = 0.8x; 120 books are sold on the second day, and 240 books are left
So 0.8x-120 = 240, x = 450

As shown in the figure, if the quadrilateral efgh is △ ABC inscribed square, BC = 21cm, height ad = 15cm, what is the side length of the inscribed square efgh?

Let the intersection of AD and Hg be m. from the meaning of the title, we know that the ∵ quadrilateral efgh is ∵ ABC inscribed square, ∥ Hg ∥ BC, ∥ AHG ∥ ABC, ∥ hgbc & nbsp; = & nbsp; AMAD, hg21 & nbsp; = & nbsp; 15 − hg15, and the solution is Hg = 354, so the side length of the inscribed square efgh is 354

English translation
for one's convenience
for convenience's sake
at one's convenience
be convenience for sb to do sth
Don't translate it to me from the online translator, because I've translated it, but it's not smooth

For your convenience, you can pay it in check

There are three cuboids, 10 cm long, 8 cm wide and 4 cm high. How to make a cuboid with the largest surface area? How many square centimeters is the largest surface area?

Put together the largest surface area of the cuboid, then three in a row
The first two and the last two 8 * 4 faces are connected, and a total of 4 faces are reduced
The total surface area of three: 3 * 2 * (10 * 8 + 10 * 4 + 8 * 4) = 912 square centimeters
Surface area after splicing: 912-4 * 8 * 4 = 784 square centimeters

The cube abcd-a'b'c'd'diagonal BD 'is perpendicular to the plane PMN (P is the midpoint of a'B', M is the midpoint of AD, n is the midpoint of CC ')

Then B (0,2,0), d '(2,0,2), P (0,1,2), m (1,0,0), n (2,2,1) vector BD' = (2, - 2,2), vector PM = (1, - 1, - 2), vector PN = (2,1, - 1) let the normal vector of plane PMN be vector n = (x, y, 1), then: X

How to make a true friend,

A true friend is a friend in need.In the conteporary society,one shall learn to differ the bad ones from those who may give you support both whenever you are in need of help.He who would not leave you alone when you are in trouble

A stone with a volume of 8 cubic decimeters is put into a cuboid container containing water. It is found that the water surface rises from 5 decimeters to 7 decimeters. Find the volume of original water Find the volume of original water