Given that the image of the function y = | x2-1 | / X-1 has exactly two intersections with the image of the function y = KX, then the value range of K is? I just want to know if the range of K can go to 2

Given that the image of the function y = | x2-1 | / X-1 has exactly two intersections with the image of the function y = KX, then the value range of K is? I just want to know if the range of K can go to 2

y=|x²-1|/(x-1)
① X > 1 or X ≤ - 1, y = (X & # 178; - 1) / (x-1) = x + 1
② -1

For the function y = f (x), if there exists x0 such that f (x0) = x0 holds, then x0 is called the fixed point of y = f (x). Given that f (x) = ax * x + (B + 1) x + B-1 (a is not equal to 0), for any real number B, f (x) always has two different fixed points, then the value range of a is?
Come on, I'm in a hurry

The equation AX * x + (B + 1) x + B-1 = x has two solutions
The discriminant of ax * x + BX + B-1 = 0 is greater than 0
b*b-4ab+4a>0
Let f (b) = b * b-4ab + 4a
Parabolic opening upward and always greater than 0
Discriminant 16A * a-16a

If there is a point P (- 1,1) in the ellipse x ^ 2 / 4 + y ^ 2 / 3 = 1, f is its left focus, and a point m on the ellipse minimizes the value of MP + 2mf, then the coordinate of point m is?

Make the vertical line of the left standard line through M, and the vertical foot is e,
Because the eccentricity of the ellipse x ^ 2 / 4 + y ^ 2 / 3 = 1 is 1 / 2, there is a
ME=2MF,
MP+2MF=MP+ME,
According to the geometric relationship,
Obviously, when MP and me are collinear, the minimum value is taken
So the ordinate of M is 1, so the coordinate of M is (- 2 √ 6 / 3,1)
[the minimum value is - 1 - (- 4) = 3 (the left collimator is at x = - 4)]

Zui new (2010 test) remember, to all Oh

People's education press primary school grade 5 Volume 2 final mathematics examination paper
(time: 90 minutes)
1、 Think hard, I will fill in. (20 points)
1. The product of 5.04 × 2.1 is () decimal places; the quotient of 22.6 △ 0.33 is ()
2. Will keep two decimal places is (), keep three decimal places is ()
3. Put ">" in the circle below“

In the system of mathematical equations {1, kx-y-4 = 0, when k is the value, the system of equations has only one real root 2,4x * x + 18y * y-18 = 0

From Formula 1, y = kx-4
Substituting the above formula into formula 2, we get the following result:
4X^2+18(KX-4)^2-18=0
4X^2+18K^2X^2-144KX+288-18=0
(4+18K^2)X^2-144KX+270=0
∵ this system of equations has only one set of real roots, (4 + 18K ^ 2) x ^ 2-144kx + 270 = 0 should have only one real root
That is: (- 144K) ^ 2-4 (4 + 18K ^ 2) 270 = 0
144×144K^2-4×270(4+18K^2)=0
96K^2-5(4+18K^2)=0
96K^2-90K^2-20=0
6K^2-20=0
K^2=10/3
K=±√30 /3
Conclusion: the method is simple

Fourth grade volume II mental arithmetic problem card 18

Where is the homework, what is the name of the book, what version did not say oh, only trouble
Let's talk about the topic or cheer on ourselves
Hope it helps you, huh

If the side length of a square garden is increased by 4 meters, the area will be increased by 96 square meters. What is the original area of the square garden?

Derivation of the period formula of simple pendulum (calculus)

Let the length of pendulum be l and the angle between cycloid and vertical direction be θ, then the motion formula of simple pendulum is D & sup2; θ / dt & sup2; + G / L * sin θ = 0, let ω = D θ / DT, and the above formula be rewritten as: ω D ω / D θ + G / L * sin θ = 0 ω & sup2; = 2G / L * cos θ + C. given the initial conditions, θ = α (0 ≤ α ≤ π), ω = 0, then the special solution is: ω & sup2; =2G / L * (COS θ - cos α) = 4G / L * (Sin & sup2; (α / 2) - Sin & sup2; (θ / 2)) so t = ∫ D θ / ω = 1 / 2 * √ (g / L) * ∫ [0, θ] d θ / √ (Sin & sup2; (α / 2) - Sin & sup2; (θ / 2)) do the transformation sin (θ / 2) = sin (α / 2) sin φ, then t = √ (L / g) * ∫ [0, φ] d φ / √ (1-sin & sup2; (α / 2) * Sin & sup2; φ) = √ (L / g) * f (φ, Sin (α / 2)) above is the formula for a simple pendulum to swing from any position to any angle. When a simple pendulum starts to swing from any position to a vertical position, θ = α, then φ = π / 2, then t = 4T = 4 √ (L / g) * f (π / 2, sin (α / 2)) = 4 √ (L / g) * k (sin (α / 2)), where α is the commonly known swing angle, Now let's look at the influence of different pendulum angles on the period. The approximate formula of simple pendulum is t = 2 π √ (L / g), the exact formula is t = 4 √ (L / g) * k (sin (α / 2)), and the relative error is e (α), then E (α) = (2k (sin (α / 2)) - π) / (2k (sin (α / 2))
It is calculated by Maple
Within 10 degrees, e= sine=l/g 　　e（1）=0.0019% 　　e（2）=0.0076% 　　e（3）=0.0171% 　　e（4）=0.0305% 　　e（5）=0.0476% 　　e（6）=0.0685% 　　e（7）=0.0933% 　　e（8）=0.1218% 　　e（9）=0.1542% 　　e（10）=0.1903% 　　e（11）=0.2303% 　　e（12）=0.2741% 　　e（13）=0.3217% 　　e（14）=0.3730% E (15) = 0.4282% e (16) = 0.4872% e (17) = 0.5500% e (18) = 0.6165% e (19) = 0.6869% e (20) = 0.7611%. Generally, the laboratory takes α ≤ 5, so the relative error is not more than 0.05%. Generally speaking, the accuracy is relatively high

There is a rectangular iron sheet 80 cm in length and 60 cm in width. The same square is cut off at four corners to make a uncovered cuboid with a bottom area of 1500 square cm
What is the side length of the truncated small square

Let the side length of a small square be X
(80-2x)(60-2x)=1500
x1=15,x2=-55
∵x≥0
∴x=15
A: the side length of the truncated small square is 15

The difference between average velocity and average velocity

Average speed = displacement / time, average speed = distance / time. For example, people use speed V1 from a to B, and speed V2 from B to A. because the displacement is 0, the average speed is 0, the distance is not 0, the time is not 0, and the average speed is not 0. It can be calculated as follows: V1 is the speed V1, V2 is the speed v2