Factorization of (6x ^ 2-7x) ^ 2-25

Factorization of (6x ^ 2-7x) ^ 2-25

（6x^2-7x)^2-25
=(6x^2-7x+5)(6x^2-7x-5)
=(6x^2-7x+5)(3x-5)(2x+1)

Factorization of 6x ^ 2-7x-24

2 3
×
3 -8
So the original formula = (2x + 3) (3x-8)

Given that the square difference of two numbers is 195, find these two numbers
At least three sets of values are obtained

x^2-y^2=195
(x+y)(x-y)=195*1
x+y=195
x-y=1
The solution is x = 98, y = 97
(x+y)(x-y)=65*3
x+y=65
x-y=3
The solution is x = 34, y = 31
(x+y)(x-y)=39*5
x+y=39
x-y=5
The solution is x = 22, y = 17
(x+y)(x-y)=15*13
x+y=15
x-y=13
The solution is x = 14, y = 1

It is known that y ^ 2 = 4x, f is the focal point, a and B are two points on the parabola
The angle AFB is 120 degrees. M is the midpoint of AB, and N is the projection of m on the directrix

Let a (x, y) and a, B be symmetric about X axis
∵∠AFB=120°
It can be specialized ∠ AFM = 30 degree
And ∵ AF = x + 1
∴FM=x+1/2
Then find ab

What is the weight of 1 cubic meter of water? How to calculate?

1000kg M = Ρ (flexible) v = 1000kg / m ^ 3 * 1m ^ 3 = 1000kg

A, B, C, D four people sit
On the four sides of a square table, five different prizes were given to him
How many kinds of prizes are there in total
Different ways?

Taking into account the primary school mathematics, do not arrange the combination of knowledge
If the same prizes (5 kinds) are given to a and C (face to face), there are 4 points for B and 4 points for D. there are 5 * 4 * 4 points based on the principle of multiplication
If a and C are given different prizes, there are 5 * 4 points. There are 3 points for B and the same 3 points for D. there are 5 * 4 * 3 * 3 points based on the principle of multiplication
There are 5 * 4 * 4 + 5 * 4 * 3 * 3 methods

Let y = y (x) be determined by the equation x ^ 3 + y ^ 3 = e ^ XY, and find the value of dy / DX! X = 0
Such as the title, the process

For x ^ 3 + y ^ 3 = e ^ XY, derive 3x & sup2; + 3Y & sup2; * y '= e ^ (XY) * (XY)'3x & sup2; + 3Y & sup2; * y' = e ^ (XY) * (y + X * y ') 3x & sup2; + 3Y & sup2; * y' = e ^ (XY) * y + e ^ (XY) * x * y'y '= [3x & sup2; - e ^ (XY) * y] / [e ^ (XY) * x-3y & sup2;] that is dy / DX = [3x & sup2; - e ^ (XY) * y] /

How to convert the density of water from 1g / cm cubic to 10 cubic / M cubic?

Conversion of composite units:
In 1g / cm ^ 3: 1g = 0.001kg, 1cm ^ 3 = 10 ^ - 6m ^ 3
So: 1g / cm ^ 3 = 0.001kg/10 ^ - 6m ^ 3
Multiply the numerator and denominator by 10 ^ 6 at the same time to get: 1g / cm ^ 3 = 1 × 10 ^ 3kg / m ^ 3
I don't know what to ask

The relationship between factorization and integral multiplication

The two are opposite to each other
Factorization is to write a polynomial into the product of several polynomials,
Integral multiplication is to write the product of several polynomials into a polynomial

The triple integral ∫ ∫ (x ^ 2 + y ^ 2) ^ (- 0.5) DV is calculated, where V is the solid surrounded by the sphere x ^ 2 + y ^ 2 + Z ^ 2 = 4 and the paraboloid z = (x ^ 2 + y ^ 2) / 3
If you want to use polar coordinates, the answer is 5 * 3 ^ (0.5) / PI. I feel that the answer is wrong. Please calculate,
The integral of his answer is DRD θ DZ. I think he wrote less R, which should be rdrd θ DZ
Or do you think you're right

It should be cylindrical coordinates, polar coordinates are for binary graphics
V is the solid surrounded by the sphere x ^ 2 + y ^ 2 + Z ^ 2 = 4 and the paraboloid z = (x ^ 2 + y ^ 2) / 3, that is, the upper surface is a sphere and the lower surface is a paraboloid. Therefore, the range of Z is (x ^ 2 + y ^ 2) / 3 ≤ Z ≤ √ (4-x ^ 2-y ^ 2), and the upper half of the sphere Z is greater than 0
Change to cylindrical coordinates as (ρ ^ 2) / 3 ≤ Z ≤ √ (4 - ρ ^ 2)
The intersection plane of x ^ 2 + y ^ 2 + Z ^ 2 = 4 and z = (x ^ 2 + y ^ 2) / 3 is Z = 1, x ^ 2 + y ^ 2 = 3
Therefore, when the figure is projected to the xoy plane, the figure is ρ = x ^ 2 + y ^ 2 = 3
So the range of ρ, θ is: 0 ≤ ρ ≤ √ 3,0 ≤ θ ≤ 2 π
dV=ρdρdθdz
Therefore, the accumulation is divided into two parts
I=∫∫∫(x^2+y^2)^(-0.5)dv
=∫∫∫(1/ρ)ρdρdθdz
2π √3 √(4-ρ^2)
=∫ dθ ∫ dρ∫ dz
0 0 (ρ^2)/3
√3
=2π*∫ [√(4-ρ^2)- (ρ^2)/3]dρ
0
=2π（2π/3+√3/6）
I'm not the same as the answer, maybe there's a problem with the answer or my last integral
It's not easy to play for such a long time