If equation (m-1) x ^ 2 + 2Y ^ 2 + m ^ 2-2m-3 = 0 represents ellipse, then the value range of real number m

If equation (m-1) x ^ 2 + 2Y ^ 2 + m ^ 2-2m-3 = 0 represents ellipse, then the value range of real number m

m-1>0,
m>1
m≠3
m^2-2m-3

It is proved that there must be prime number between P + 1 and P square~

Obviously p ^ 2 > 2 (P + 1)
Bertrand Chebyshev theorem shows that: if the integer n > 3, then there is at least one prime P, which conforms to n < p < 2n &; 2. Another weaker argument is that for all integers n greater than 1, there is a prime P, which conforms to n < p < 2n
So p + 1 and 2 (P + 1)

Given that the monotone decreasing interval of function f (x) = x ^ 3 + BX ^ 2 + CX + D is [- 1,2], find the value of B and C
The derivative function f '(x) = 3x ^ 2 + 2bx + C has been calculated
But how do you get in

f'(-1)=0
f'(2)=0
The rest is to solve the equation

Let f (x) = LG (2 / 1-x + a) be an odd function, then the value of a is?
The answer is - 1. How did you get it?

Because it is an odd function, all f (x) = - f (- x);
lg(2/1－x +a)=-lg(2/1+x +a)=lg(2/1+x+a)^-1
That is 2 / (1-x + a) = (1 + X + a) / 2
The solution is a = - 1

The sum of a prime number and its 8 times is 45. What is the prime number?

5

The probability density f (x, y) = e ^ - y, 0 of two-dimensional random variable (x, y)

D is the area of shadow in the figure

Given that the quadratic function f (x) satisfies f (2-x) = f (2 + x), and the intercept of the image on the Y axis is 0, the minimum value is - 1, the analytic expression of the function f (x) is obtained

∵ f (x) satisfies: F (2-x) = f (2 + x), the axis of symmetry of the function f (x) is x = 2. Let f (x) = a (X-2) 2 + B. and ∵ the intercept on the Y axis is 0, and the minimum value is - 1. ∵ a > 0, 4A + B = 0, B = - 1. The solution is a = 14, B = - 1. ∵ f (x) = 14x2-x

Find the following greatest common factors 12 and 24 10 and 18 9 and 4

12 and 24:12
10 and 18:2
9 and 4:1
All greatest common factors: 1

For rational numbers a and B, define the operation a △ B = 3A + B / a-3b, and calculate 7 △ (- 6)
How can I get this formula!

A, B in a △ B = 3A + B / a-3b are replaced by 7, - 6
7 △ (- 6) = 3 × 7 + (- 6) / 7-3 × (- 6) = 21-6 / 7 + 18 = 38 and 1 / 7
I think it should be a △ B = (3a + b) / (a-3b)
7△（－6）=[3×7+（-6）]/[7-3×（-6）]=15/25=3/5

How the Geometer's Sketchpad makes a section in a frustum, a cylinder or a cone, and it can rotate
The key is rotation!

In the existing software random lesson, some sections are pyramid and pyramid, there is no ready-made cross-section of frustum or cylinder or cone. You can use the Geometer's Sketchpad, solid geometry platform to make
In the strongest Chinese version of 5.03 updated on August 31, tools that point the custom tool folder to the installation path will add tools such as solid geometry, some of which can do 3D