The minimum positive period of y = │ sin (PAI / 6-2x) + sin2x │ is（

The minimum positive period of y = │ sin (PAI / 6-2x) + sin2x │ is（

The minimum positive period is π / 4. Y = | sin (π / 6-2x) + sin2x | = | 2Sin (π / 12) cos (π / 6-4x) | Since the minimum positive period of F (x) = | cos (π / 6-4x) |, z = | cos (π / 6-4x) |
cos(pai/4+x)=3/5,17pai/12
cosπ/4cosx-sinπ/4sinx=3/5
cosx-sinx=3√2/5
square
cos²x+sin²x-2sinxcosx=18/25
1-2sinxcosx=18/25
sinxcosx=7/50
sinx+cosx=√2sin(x+π/4)
5π/4
（|x-4|-4）²=0
|x-4|-4=0
|x-4|=4
x-4=±4
x=4±4
So X1 = 8, X2 = 0
(9.8+x)/x=1/3
Multiply both sides by 3x
3（9.8+x)=x
29.4x+3x=x
2x=29.4
x=14.7
If the line y = KX + 1 (K ∈ R) and the ellipse X25 + y2m = 1 always have a common point, then the value range of M is ()
A. [1，5）∪（5，+∞）B. （0，5）C. [1，+∞）D. （1，5）
If y = KX + 1x25 + y2m = 1, then (M + 5k2) x2 + 10kx + 5-5m = 0, (m ＞ 0, m ≠ 5) ∵ the line y = KX + 1 (K ∈ R) and the ellipse X25 + y2m = 1 have a constant common point, that is, 100k2-20 (1-m) (M + 5k2) ≥ 0, then M2 + 5mk2-m ≥ 0, ∵ m ＞ 0, ∵ m ≥ - 5k2 + 1 ≤ 1, ∵ m ≥ 1 (m ≠ 5)
If the line y = KX + 1 (K ∈ R) and the ellipse X25 + y2m = 1 always have a common point, then the value range of M is ()
A. [1，5）∪（5，+∞）B. （0，5）C. [1，+∞）D. （1，5）
If y = KX + 1x25 + y2m = 1, then (M + 5k2) x2 + 10kx + 5-5m = 0, (m ＞ 0, m ≠ 5) ∵ the line y = KX + 1 (K ∈ R) and the ellipse X25 + y2m = 1 have a constant common point, that is, 100k2-20 (1-m) (M + 5k2) ≥ 0, then M2 + 5mk2-m ≥ 0, ∵ m ＞ 0, ∵ m ≥ - 5k2 + 1 ≤ 1, ∵ m ≥ 1 (m ≠ 5)
Given that the equation x2 | m | 1 + Y22 − M = 1 represents an ellipse with focus on the y-axis, then the value range of M is ()
A. M ＜ 2B. 1 ＜ m ＜ 2C. M ＜ - 1 or 1 ＜ m ＜ 2D. M ＜ - 1 or 1 ＜ m ＜ 32
X2 | m | 1 + Y22 − M = 1 represents the ellipse with focus on the y-axis. The solution of | 2-m | m | 1 | 0 is m ＜− 1 or 1 ＜ m ＜ 32, so D is selected
If the equation KX ^ 2 + y ^ 2 = 3 represents an ellipse with focus on the X axis, what is the value range of the real number k?
Divide two sides by three
x²/(3/k)+y²/3=1
Ellipse with focus on X axis
So 3 / k > 3
Zero
kx²+y²=3
x²/(3/k)+y²/3=1
Denotes ellipse k > 0
Focus on X-axis: 3 / k > 3, that is K
If the line y = AX-1 (a ∈ R) and the ellipse X25 + y2m = 1 with focus on X-axis always have a common point, then the value range of M is______ .
According to the meaning of the question, we can get y = AX-1 passing through the point (0, - 1). To make the straight line y = AX-1 and the ellipse X25 + y2m = 1 always have a common point, we only need to make the point (0, - 1) in the interior or on the ellipse, then m ≥ 1, and from the focus of the ellipse X25 + y2m = 1 on the X axis, then 5 > m; we can get 1 ≤ m < 5, so the answer is 1 ≤ m < 5
If the line y = KX + 1 (K ∈ R) and the ellipse X25 + y2m = 1 always have a common point, then the value range of M is ()
A. [1，5）∪（5，+∞）B. （0，5）C. [1，+∞）D. （1，5）
If y = KX + 1x25 + y2m = 1, then (M + 5k2) x2 + 10kx + 5-5m = 0, (m ＞ 0, m ≠ 5) ∵ the line y = KX + 1 (K ∈ R) and the ellipse X25 + y2m = 1 have a constant common point, that is, 100k2-20 (1-m) (M + 5k2) ≥ 0, then M2 + 5mk2-m ≥ 0, ∵ m ＞ 0, ∵ m ≥ - 5k2 + 1 ≤ 1, ∵ m ≥ 1 (m ≠ 5)
If the equation x22m-y2m-1 = 1 represents an ellipse with focus on the y-axis, then the value range of M is___ .
∵ the equation x22m-y2m-1 = 1 represents an ellipse with focus on the y-axis, ∵ the standard equation of the ellipse is y21-m + x22m = 1, satisfying 1-m ＞ 2m ＞ 0, and the solution is 0 ＜ m ＜ 13, so the answer is 0 ＜ m ＜ 13
If the focus of the ellipse x ^ 2 / M + y ^ 2 / 4 = 1 is on the X axis and the focal length is 2, then the value of the real number m is
C=1
M^2=C^2+B^2
M = root 5
Why do you ask?
The focal length is 2. That is to say, 2C = 2. C = 1
I know the focus is on the x-axis.
So m > 4 is for sure
According to a ^ 2 = B ^ 2 + C ^ 2, M = 4 + 1 = 5
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