Let F1 and F2 be the two focal points of hyperbola 42x-y2 = 1, p be on the hyperbola, and Pf1 · PF2 = 0, then the value of | Pf1 · | PF2 | is equal to

Let F1 and F2 be the two focal points of hyperbola 42x-y2 = 1, p be on the hyperbola, and Pf1 · PF2 = 0, then the value of | Pf1 · | PF2 | is equal to

Let: | Pf1 | = m, | PF2 | = n, then: M & # 178; + n & # 178; = (2C) & # 178; | M-N | = 2A, namely: (m-n) & # 178; = (2a) & # 178; by subtracting the two formulas, we can get: 2Mn = (2C) & # 178; - (2a) & # 178; = 4B & # 178; Mn = 2B & # 178; and then: the value of B can be calculated in this hyperbolic equation, and it can be substituted

The image of binary function is a surface, so what is the image of ternary function?

By analogy:
The image of a function of one variable y = f (x) is a curve in two-dimensional coordinates
The image of binary function z = f (x, y) is a surface in three-dimensional coordinates
The image of ternary function w = f (x, y, z) is three-dimensional in four-dimensional coordinates
Just because the real space is three-dimensional, it needs a little imagination to imagine the four-dimensional coordinates and the solid in the coordinates

After entering the expressway, the car will drive for 1.5 hours at the speed of 60 km / h, and then drive for 1.5 hours at the speed of 90 km / h to
Destination. The average speed of the car over the distance

Hello: average speed (60x1.5 + 90x1.5) / (1.5 + 1.5) = (90 + 135) / (3 = 225 ／ 3 = 75KM / H ~ if you agree with my answer, please click the [adopt as satisfactory answer] button in time ~ ~ the mobile phone questioner can comment on [satisfied] in the upper right corner of the client. ~ your adoption is the driving force for me to move forward ~ ~

How much is 48 times 99!
There are 25 times (40 + 4), 45 times 99 + 45, 45 times 99, 36 times 101-36, 36 times 101. You must give it to me before April 23, 2010, otherwise it won't be called points,

48×99=48×（100-1）=4800-48=475225×（40+4）=25×40+25×4=1000+100=110045×99+45=45×（99+1）=45×100=450045×99=45×（100-1）=4500-45=445536×101-36=36×（101-1）=36×100=360036×101=36×（100+1）=3...

The figure below is a figure obtained by cutting a cylinder vertically along its diameter. What is the surface area of this figure? (height 18 cm, bottom diameter 10 cm)

8 △ 2 = 4 & nbsp; & nbsp; & nbsp; 18 * 16 = 228 + 8 * 3.14 △ 2 = 12.56 * 16 + 4 * 4 * 3.14 = 379.2 (square centimeter)

Use 72 decimeter long wire to form a rectangle. The ratio of the length and width of the rectangle is 3:4. How many square decimeters is the area of the rectangle?

3 + 4 = 7 (shares), 72 △ 2 = 36 (decimeters), 36 × 37 = 1087 (decimeters), 36 × 47 = 1447 (decimeters), 1087 × 1447 = 1555249 (square decimeters). A: the area of this rectangle is 1555249 square decimeters

The following expressions are a factor of the polynomial 4x ^ 2 - (Y-Z) ^ 2: A: 4x-y + Z B: 4y-y-x C: 2x-y + X D: 2x-y-x

4x^2-(y-z)^2=(2x+y-z)(2x-y+z)
So choose C 2x-y + Z

We know the circle C; X + y-4x-14y + 45 = 0 and the point Q (- 2,3)
1. If point P (a, a + 1) is on circle C, find the length of line PQ and the slope of line PQ
2. If M is any point on the circle C, find the maximum and minimum of | MQ |

(1) Substituting P (a, a + 1) coordinates into X & # 178; + Y & # 178; - 4x-14y + 45 = 0 ① Get
a²+(a+1)²-4a-14(a+1)+45=0
The solution is a = 4
Then p coordinate is (4,5)
The length of segment PQ √ [(4 + 2) &# 178; + (5-3) &# 178;] = 2 √ 10
The slope of line PQ is (5-3) / (4 + 2) = 1 / 3
(2) The formula of (X-2) ² + (Y-7) ² = 8 is obtained from the formula of X & #178; + Y & #178; - 4x-14y + 45 = 0
The center C coordinate is (2,7), and the radius is 2 √ 2
Make a straight line CQ and intersect a and B
Linear CQ equation: (Y-3) / (7-3) = (x + 2) / (2 + 2), that is, y = x + 3 ②
① (2) the coordinates of a and B are (3 + √ 3,6 + √ 3) (3 - √ 3,6 - √ 3)
AQ length: √ [(3 + √ 3 + 2) &# 178; + (6 + √ 3-3) &# 178;] = 2 √ (10 + 4 √ 3)
The length of BQ is: √ [(3 - √ 3 + 2) &# 178; + (6 - √ 3-3) &# 178;] = 2 √ (10-4 √ 3)
Therefore: the maximum and minimum values are 2 √ (10 + 4 √ 3) and 2 √ (10-4 √ 3) respectively

On the mathematical problem of absolute value, when | x + 1 | + | X-2 | takes the minimum value, the value range of X

This can be understood as
|x-(-1)|+|x-2|
That is, the sum of the distances to x = - 1 and x = 2 on the number axis
So only between these two points, the minimum distance is 3
That is - 1 ≤ x ≤ 2

Given the function f (x) = 4x + 1, G (x) = 2x, the sequence {an} {BN} satisfies the condition A1 = 1, an = f (BN) = g (BN + 1) to find the general term formula of the sequence {an}

If the recurrence formula is: a (n) = 4 * B (n) + 1 = 2 * B (n + 1), then a (n + 1) = 4 * B (n + 1) = 2 * B (n + 2) is simultaneous: a (n + 1) = 2 * 2 * B (n + 1) + 1 = 2 * a (n) + 1B (n + 1) = 2 * B (n) + 1 / 2, a (n) = 2 * a (n-1) + 1 = 2 * (2 * a (n-2) + 1) + 1 =. = a (1) * 2 ^ (n-1) + 2 ^ (n-1) - 1B (n) = 2 * B (n-1) + 1