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What does ∈ mean mathematically?
A symbol in mathematics
We usually use capital Latin letters a, B, C Represents a set, using the lowercase Latin letters a, B, C Represents an element in a collection
If a is an element of set a, it is said that a belongs to (along to) set a, denoted as a ∈ a; if a is not an element of set a, it is said that a does not belong to (not along to) set a, denoted as a &; a
When expressing this symbol mathematically, we can directly use the word "belong"
For example, a ∈ a can be read as: small a belongs to large a
In solid geometry, this symbol is used to indicate the position of a point (note! Only for points)
A quadratic trinomial formula x2 + 2x + 3 is multiplied by a binomial formula ax + B. if there is no quadratic term in the product and the coefficient of quadratic term is 1, the value of a and B can be obtained?
(x2 + 2x + 3) × (AX + b) = AX3 + bx2 + 2ax2 + 2xb + 3ax + 3B = AX3 + (bx2 + 2ax2) + (2xb + 3ax) + 3b, there is no first-order term in the product, and the coefficient of second-order term is 1, ∧ 2A + B = 1, 2b + 3A = 0, ∧ B = - 3, a = 2
What is the meaning of positional relation in mathematical geometry
The position relation refers to the relations of intersection, parallel and vertical, and the quantity relation is greater than, less than and equal to the length
Is there a real number a such that the maximum value of y = sin ^ 2x + A * cosx + 5 / 8a-3 / 2 on [0, π / 2] is 1?
(sinx)^2=1-(cosx)^2
So y = - (cosx) ^ 2 + acosx + 5 / 8a-1 / 2
0
If the equation (SiNx) ^ 2 - (2 + m) SiNx + 2 = 0 of X has two real roots on [- π / 6,5 π / 6], find the range of real number M
Let t = SiNx t ∈ [- 0.5,1]
If the original equation is changed to T ^ 2 - (2 + m) t + 2m = 0, one of them must be t = 2
sinx=t=2,
There's no need to answer in order to do the task
If the equation 4sinx-sin2x + M-3 = 0 of X has a real number solution, then the value range of real number m is ()
A. [1，+∞）B. [-1，8]C. [1，5]D. [0，8]
Let t = SiNx, then - 1 ≤ t ≤ 1. So the original equation is equivalent to - T2 + 4T + M-3 = 0, that is, M = t2-4t + 3. Because y = t2-4t + 3 = (T-2) 2-1, when - 1 ≤ t ≤ 1, the function y = t2-4t + 3 = (T-2) 2-1 decreases monotonically, so 0 ≤ y ≤ 8
If the equation sin2x + cosx + k = 0 has a solution, then the range of K is ()
A. -54≤k≤1B. -54≤k≤0C. 0≤k≤54D. -1≤k≤54
The equation sin2x + cosx + k = 0 has a solution, which is equivalent to k = - sin2x cosx. The range of K is the range of y = - sin2x cosx, and y = - sin2x cosx = cos2x-cosx-1 = (cosx-12) 2-54
θ is the third quadrant angle, and the curve represented by the equation x2 + y2sin θ = cos θ is ()
A. Hyperbola with focus on Y-axis B. hyperbola with focus on X-axis C. ellipse with focus on Y-axis D. ellipse with focus on X-axis
∵ θ is the third quadrant angle, ∵ Sin & nbsp; θ < 0, cos & nbsp; θ < 0, ∵ x2 + y2sin θ = cos θ, ∵ x2cos θ + y2sin θ cos θ = 1, and ∵ cos & nbsp; θ < 0, sin θ cos θ > 0, ∵ equation X2 + y2sin θ = cos θ represents hyperbola with focus on Y axis
Given the curve X = 4 cos α, y = 2Sin α and the point m (2,1), the linear equation of the chord with m as the trisection point is obtained
There is a parametric equation
The curve equation is
Ellipse of x ^ 2 / 16 + y ^ 2 / 4 = 1
Let y = K (X-2) + 1
(1) When K does not exist
Obviously not qualified
(2) When k exists
LIANLI Kede
(4k^2+1)x^2+(-16k^2+8k)x+16k^2-16k-12=0
From the discriminant > 0
We can see that this inequality is always true
x1+x2=-b/a=（16k^2-8k)/(4k^2+1)
x1x2 = c/a= (16k^2-16k-12)/(4k^2+1)
xm=(x1+x2)/3
ym=(y1+y2)/3
It can be concluded that
k^2=1/12
So k = + radical 1 / 12 or K = - radical 1 / 12
The linear equation comes out
It is known that the equation of ellipse C is x ^ 2 / A ^ 2 + y ^ 2 / 2 = 1 (a > 0), its focus is on the X axis, and the point Q (√ 2 / 2, √ 7 / 2) is a point on the ellipse
(1) Find the scale (2) of the ellipse, set the moving point P (x0, Y0), satisfy the vector OP = vector om + 2 vector on, where m and N are the points on the ellipse C, the product of the slope of the line OM and on is 1 / 2, and prove that x0 ^ 2 + 2y0 ^ 2 is the fixed value
(1) Q point into the elliptic C equation can be (√ 2 / 2) ^ 2 / A ^ 2 + (√ 7 / 2) ^ 2 / 2 = 1, the solution is a = 2 ∪ elliptic equation is: x ^ 2 / 4 + y ^ 2 / 2 = 1 (2) let vector OP = (x0, Y0), vector om = (x1, Y1), vector on = (X2, Y2) ∪ vector OP = vector om + 2, vector on ∪ x0 = X1 + 2x2, Y0 = Y1 + 2Y2 and ∫ point m, N on the elliptic C
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- 18. 1. If G (x) = f (x + a) + F (x-a), the domain of function g (x) is obtained 2. Find the domain of the function f (x) = root sign (x-2k) + 1 / root sign (X & # 178; - 4) I don't think I understand the function. I hope the great God can give me some advice or experience I will ask if I don't understand. I hope you can answer patiently~
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- 20. If the quadratic equation (3sin θ) x ^ 2 - (4cos θ) x + 2 = 0 with respect to X has two real roots, find the value range of θ Don't you consider that 3sin θ is not equal to 0?