As shown in the picture, a ladder is 25 meters long, leaning against a wall, and the bottom B of the ladder is 7 meters away from the wall 【1】 How high is the top of the ladder from the ground? [2] if the top of the ladder falls 4 meters, how many meters does the bottom of the ladder move horizontally?

As shown in the picture, a ladder is 25 meters long, leaning against a wall, and the bottom B of the ladder is 7 meters away from the wall 【1】 How high is the top of the ladder from the ground? [2] if the top of the ladder falls 4 meters, how many meters does the bottom of the ladder move horizontally?

(1) The top of the ladder is (25 ^ 2 - 7 ^ 2) ^ (1 / 2) = 24 meters above the ground
(2) If the top of the ladder falls 4 meters, the bottom of the ladder moves horizontally
(25 ^ 2 - 20 ^ 2) ^ (1 / 2) - 7 = 8M

A ladder is 25 meters long, leaning against a wall. It is known that the bottom of the ladder is 7 meters away from the wall. If the top of the ladder falls 9 meters, then the bottom of the ladder is drawn horizontally
How many meters?

The top height of the ladder before sliding is √ (25 & # 178; - 7 & # 178;) = 24m
24-9=15
Distance from the bottom to the wall after sliding √ (25 & # 178; - 15 & # 178;) = 20m
The sliding distance at the bottom is 20-7 = 13m

A ladder is 10 meters long, leaning against a wall, and the bottom of the ladder is 6 meters away from the wall
1) How high is the top of this ladder from the ground?
2. If the top of the ladder falls 1m, how many meters does the bottom of the ladder slide horizontally?
3. If the top of the ladder falls 2m, how many meters does the bottom of the ladder slide horizontally?
What conclusions can you draw from 2 and 3
How high is the top of the cone from the ground?

1. The ladder and the wall form a right triangle
Height h = √ (10 ^ 2-6 ^ 2) = 8M
2. If the slide is 1m, the height is 7m
Distance L = √ [10 ^ 2-7 ^ 2] = √ 51 = 7.14m
Moving 7.14-6 = 1.16M
3. If the slide is 2m, the height is 6m
Distance L = √ [10 ^ 2-6 ^ 2] = √ 64 = 8M
Moving 8-6 = 2m
4. Let XM be the slide, then the height = 8-xm
Distance L = √ [10 ^ 2 - (8-x) ^ 2] = √ (36 + 16x + x ^ 2) = √ (18-x) (2 + x) M
Mobile L-6 = √ (18-x) (2 + x) - 6 m
The sliding height is not proportional to the horizontal sliding distance

Given the two equations 2x & # 178; - 2 (2m-1) x + (M + 2) = 0 in the interval (- 3,3), find the value range of M!

2x^2-2(2m-1)x+(m+2)=0
Four conditions should be met according to the meaning of the title
1.△=4(2m-1)²-8(m+2)>=0
That is: 4m & # 178; - 4m + 1-2m-4 > = 0
4m²-6m-3>=0
(3-√15)/4

Equations x + 2Y = m, 2x + y = 1_ The solution of 2m satisfies that 3x + 2Y is greater than 0, and the value range of M is obtained

x+2y=m
2x+y=1-2m
Add up and down 3 (x + y) = 1-m
x+y=(1-m)/3
2x+y=1-2m
Add up and down 3x + 2Y = 4 / 3-7 / 3M > 0
4-7m>0
7m

If the root of the equation is a positive integer and M is an integer, the value of M is obtained

(1) When m = 0, the original formula is - 2x + 2 = 0, x = 1, so m = 0
(2) When m is not zero, because the equation has a heel, so we are greater than or equal to zero, that is, b-4ac is greater than or equal to 0, and m of the solution is greater than or equal to - 2
According to the meaning X1 + x2 = negative a / b = 3 + m / 2} = 0, x1x2 = A / C = 1 + m / 2} = 0, the above two expressions are positive integers, so m = 1 or positive and negative 2. (because 2 divided by M is an integer, so m is positive and negative 1 or positive and negative 2, but M = - 1 does not meet the requirement of greater than or equal to 0,)
Synthesis (1) (2), then M = 0,1, + - 2

The equation MX & sup2; - (M & sup2; + 2) x + 2m = 0 (2) if the equation has two integer roots, find the value of M

According to Weida's theorem, the product of two integer roots is 2m / M = 2, so the two can only be 1,2 or - 1, - 2
So (M & sup2; + 2) / M = ± 3, M = ± 1

If x = 1 − 1m is the root of the equation mx-2m + 2 = 0, then the value of x-m is ()
A. 0B. 1C. -1D. 2

Substituting x = 1-1m into the equation: m (1-1m) - 2m + 2 = 0, the solution is: M = 1, х x = 0, х x-m = 0-1 = - 1, so C

The intersection of the quadratic function y = x & # 178; - 5x-6 and the Y axis is___ The point of intersection with the x-axis is______ ;
Parabola y = - 2x & # 178; + 4x + 1 the length of the line cut on the x-axis is___ .

x=0
y=-6
Intersection with y axis (0, - 6)
y=0
x²-5x-6=0
(x+1)(x-6)=0
X = - 1 or x = 6
The point of intersection with X axis is (- 1,0) (6,0)
-2x²+4x+1=0
x1+x2=2,x1x2=-1/2
Length = | x1-x2 | = √ [(x1 + x2) &# 178; - 4x1x2]
=√（4+2）
=√6

If the quadratic function y = x2-2x-m has no intersection with the X axis, then the value range of M is the same______

Y = x & # 178; - 2x-m has no intersection with X axis
That is, when y = 0, X & # 178; - 2x-m = 0 has no root
Since there is no root, the discriminant of root