If the sum of five consecutive positive integers is a complete cubic number and the sum of three middle integers is a complete square number, then what is the minimum value of the smallest one

In fact, this is an analysis problem: let the number in the middle be x, then there is 5x = y ^ 3, 3x = Z ^ 2. Since y and Z are all positive integers, it is easy to know that x contains at least 5 * 5 and at least 3 * 5, and that 5x can open to the third power, so at least 3 * 3 * 3 and 3x can open to the second power, so x must contain the product of even 5

∫ e ^ (x ^ 1 / 2) DX range 0 to 1

Do variable substitution t = x ^ (1 / 2) x = T ^ 2 DX = 2tdt
The original integral is replaced by ∫ 2Te ^ TDT in the range of 0 to 1 = [2 (t-1) e ^ t] (t = 1) - [2 (t-1) e ^ t] (t = 0) = 0 - (- 2) = 2

Beibei's round table is 1 meter in diameter. Now it needs to be covered with tablecloth
A. 100 cm × 80 cm B, 120 cm × 80 cm
C. 80cm × 80cm D, 120cm × 120cm
Is it perimeter or area?

Beibei's round table is 1 meter in diameter. Now we need to lay a tablecloth on it
The length of other answers is too short
The diameter of round table is 1 meter, which means that the side length of tablecloth should be at least 1 meter × 1 meter

A cylindrical timber is 5 meters long. After sawing it into two identical small cylindrical timber, its surface area increases by 0.18 square meters
What's the volume of this wood?
2. The railway between stations a and B is 620 km long. A passenger train goes from station a to station B, while a freight train goes from station B to station A. after 4 hours, the two trains meet. How many kilometers does a passenger car travel per hour and a freight car travel per hour

There are two sections
The sectional area is: 0.18 △ 2 = 0.09 square meters
The original volume is: 0.09 × 5 = 0.45 cubic meters
If you don't understand, please ask

Modify the sick sentence. Use the modifier to modify the following sentence
1. We should constantly improve learning methods and enhance learning efficiency
2. All couplets are full of revolutionary optimism
3. I think of many beautiful things in the past
4. China has the largest population in the world
5. Mr. Wang was honored as "model head teacher"
6. I like to read both primary school students' Mathematics and children's daily

The title is to be modified with a modifier, that is to say, in the original sentence

It is known that Y1 = e ^ 3x-xe ^ 2x; y2 = e ^ x-xe ^ 2x; Y3 = - Xe ^ 2x are three solutions of a second order linear differential equation with constant coefficients
The conditions of these two questions are the same (please ignore the second half of question 13). Why do we get different general solutions

The two are actually the same
Let's first look at the special solution, which is - Xe ^ (2x), both of which are the same
The first part is C1 * e ^ (3x) + (c2-c1) * e ^ x, and the second part is C1 * e ^ (3x) + C2 * e ^ X
The reason why it looks different is that the first one is to make the two parts orthogonal, while the second one is to make it easier to read
In fact, the second method is to replace c2-c1 with C2. For example, in the first method, when C1 = 3 and C2 = 7, the second method corresponds to C1 = 3 and C2 = 4
Because the value range of C is complex, C1 can be written as C1 ^ 2, sin (C1), C1 * C2, whatever

What is the bulk density of rice

Hello, vangsionfer
It's not the density (specific gravity) of a grain of rice, but the density (specific gravity) of a bag of rice or a pile of rice
In the past, rice was measured by bucket or liter. A liter of rice was 1 cubic decimeter, weighing 1.5 Jin (old system, market Jin) or metric system
75 kg
Therefore, the specific gravity of bulk rice is 0.75kg △ 1dm & sup3; = 0.75kg/dm & sup3;, which is lighter than that of water and packed in plastic bags
If it doesn't leak, it's floating in the river. If you don't believe it, try it
As for the specific gravity of each grain of rice is more than 1kg / DM & sup 3;, it is heavier than water, and a single grain of rice is heavy
Good luck and goodbye

777 out of 7777 and 7777 out of 7777
I need a detailed problem-solving process

7777 out of 777

If the value range of the independent variable X of the function y = KX + B is - 2 ≤ x ≤ 6, and the value range of the corresponding function y is - 11 ≤ x ≤ 9, the analytic solution of the function value is obtained
Analytical expression

Because the image of a function is a straight line, it determines that the maximum and minimum values of a function in a certain interval can only appear at the two ends of the interval. Case 1: x = - 2, y = - 11x = 6, y = 9 are substituted into the function, and the solution is k = 5 / 2, B = - 6. Case 2: x = - 2, y = 9x = 6, y = - 11 are substituted into the function, and the solution is k = - 5 / 2

The volume of a cuboid is 6 cubic meters, the bottom area is 12 / 5 square meters, how many meters is the height

6 △ 12 / 5 = 5 / 2 decimeter
The answer is 2 / 5 decimeters higher

If the sum of five consecutive positive integers is a complete cubic number and the sum of three middle integers is a complete square number, then what is the minimum value of the smallest one