Given that the length of the line segment l passing through point P (2,3) and cut by two parallel lines 3x + 4y-7 = 0 and 3x + 4Y + 8 = 0 is d 1), find the minimum value of D, 2) when the line L and 2) When the line L is parallel to the X axis, try to find the value of D

Given that the length of the line segment l passing through point P (2,3) and cut by two parallel lines 3x + 4y-7 = 0 and 3x + 4Y + 8 = 0 is d 1), find the minimum value of D, 2) when the line L and 2) When the line L is parallel to the X axis, try to find the value of D

1）d=3
2) d=5
Given the function f (x) = 4 to the - x power (x is less than or equal to 0), f (x-1) (x > 0), if the equation f (x) = x + A has and only has two unequal real numbers
Given the function f (x) = 2 to the power of - x (x is less than or equal to 0), f (x-1) (x > = 0), if the equation f (x) = x + A has and only has two unequal real roots, then the value range of real number a is?
Let f (x) = f (x) - (x + a) = the - x power - X - a of 2;
Then its derivative f '(x) = - LN2 · 2 to - x power - 1
When f '(x) = 0, the - x power of (- LN2) · 2 is 1;
X power of 2 = - LN2;
X = log with base 2 (- LN2);
In this case, a = - 1 / LN2 log is the logarithm of base 2 (- LN2);
Then: if a ＞ - 1 / LN2 log is logarithm of base 2 (- LN2), then the equation f (x) = x + A has and only has two unequal real roots
The distance between two parallel lines 3x-2y + 1 = 0 and 6x-4y-5 = 0 is a concrete analysis
Analysis:
3x-2y + 1 = 0 and 6x-4y-5 = 0, i.e
6x-4y + 2 = 0 and 6x-4y-5 = 0,
therefore
The distance between them
d=|2+5|/√[6^2+(-4)^2]
=7 / √(36+16)
=7 / √52
=7√52 /52
=7√13 / 26
The area of the triangle formed by the vertex of the image of the function y = x ^ 2-4x + 3 and its two intersections with the X axis is --- square unit
The distance between two parallel lines 3x-2y-1 = 0 and 3x-2y + 1 = 0 is
3x-2y-1=0→y=1.5x-0.5 3x-2y+1=0 →y=1.5x+0.5
Draw an image and get a distance of 2 according to the similarity theorem
- radical 5
Five
There are three intersections between the image of quadratic function y = 4x ^ 2-3x-10 and the two coordinate axes. The area of the triangle composed of these three points is
Three points (- 5 / 4,0) (2,0) (0, - 10)
Bottom 5 / 4 + 2 = 13 / 4 height 10
The area of triangle is 1 / 2 * 13 / 4 * 10 = 65 / 4
The point of intersection on x-axis is (2,0), (- 5 / 4,0) on Y-axis is (0, - 10)
S = 1 / 2x bottom x height = 1 / 2x13 / 4x10 = 65 / 4
Three points (- 5 / 4,0) (2,0) (0, - 10)
Bottom 5 / 4 + 2 = 13 / 4 height 10
The area of triangle is 1 / 2 * 13 / 4 * 10 = 65 / 4
The distance between two parallel lines 3x-2y + 1 = 0 and 3x-2y-2 = 0
Formula of distance between parallel lines:
ax+by+c1=0
ax+by+c2=0
d=(|c1-c2|)/(√a^2+b^2)
The distance between two parallel lines 3x-2y + 1 = 0 and 3x-2y-2 = 0
D = | 1 - (- 2) | / radical (3 ^ 2 + 2 ^ 2) = 3 / radical 13 = 3 / 13 radical 13
Note: (^ 1 / 2) denotes the root sign
Formula: D = | C1-C2 | / ((a * a + b * b) ^ 1 / 2)
So: D = | - 2-1 | / (3 * 3 + (- 2) * - 2)) ^ 1 / 2 = 3 / (13 ^ 1 / 2)
If the intersection of X-Y and X-Y is X-1
The intersection with a point on the x-axis indicates that the point y = 0;
Taking y = 0 into y = 4x-1
X = 1 / 4;
Take x = 1 / 4 and y = 0 into y = - x + M
The result is: M = 1 / 4
Y = 4x-1 and X-axis intersect at (1 / 4,0),
Substituting (1 / 4,0) into y = - x + m, we get,
-1/4+m=0，
So m = 1 / 4
1/4
Y = 4x-1 and X-axis intersect at (1 / 4,0),
Substituting (1 / 4,0) into y = - x + m, we get,
-1/4+m=0，
So m = 1 / 4
1/4
It is known that the integer part of x = √ 2 + 1 is a and the decimal part is B. find 1. A & # 178; - B & # 178; 2. AB & # 178; X & # 178;
a=2,b=√2 -1
So. A & # 178; - B & # 178; = 1 + 2 √ 2
AB & # 178; X & # 178; = 2 (because BX = 1)
If the image of the function y = - x + m2 and y = 4x-1 intersects on the X axis, then the value of M is ()
A. 12B. 14C. ±12D. ±14
When y = 0, 4x-1 = 0, the solution is x = 14, the intersection of two straight lines and X axis is (14, 0), and the solution is M2 = 14, M = ± 12