Through the focus of parabola x ^ 2 = 2PY (P > 0), make a straight line intersection at a (x1, Y1), B (X2, Y2) to prove: the vector OA * ob is a fixed value Through the focus of parabola x ^ 2 = 2PY (P > 0), make a straight line intersection at a (x1, Y1), B (X2, Y2) to prove: the vector OA * ob is a fixed value

Through the focus of parabola x ^ 2 = 2PY (P > 0), make a straight line intersection at a (x1, Y1), B (X2, Y2) to prove: the vector OA * ob is a fixed value Through the focus of parabola x ^ 2 = 2PY (P > 0), make a straight line intersection at a (x1, Y1), B (X2, Y2) to prove: the vector OA * ob is a fixed value

Focus f (0, P / 2)
Let y = KX + P / 2
Bring into parabola
x²-2pkx-p²=0
x1+x2=2pk
x1x2=-p²
Because y1y2 = (kx1 + P / 2) (kx2 + P / 2)
OA*OB=x1x2+y1y2；
It can be solved;

A pile of yellow sand was transported 5 / 1 of the total amount in the first day, 4 / 1 less than the next day. A total of 210 tons of yellow sand were transported in the two days. How many tons of yellow sand were originally transported

If x tons of original yellow sand are set, X / 5 tons are transported in the first day, and Y tons are transported in the second day, then x / 5 = y * 3 / 4, then y = 4x / 15
Furthermore, X / 5 + 4x / 15 = 210
Solution
x=450
Therefore, the original yellow sand 450 tons

The quadratic function of y = ax & sup2; + BX + C with respect to X-axis symmetry

Let's multiply every x on the right side of the equation by - 1
That is y = ax & sup2; - BX + C

Female workers account for 33% of the total number of workers in a factory, 102 less than male workers. How many male workers are there?

102 ÷ (1-33% - 33%) = 300 people (whole plant)
300 × 33% + 102 = 202 (male workers)

Given the circle C: x ^ 2 + y ^ 2-6x-4y + 4 = 0, the midpoint of the chord of line L1 cut by the circle is p (5,3)
Is there a constant B such that the midpoint of the chord of the line L2: x + y + B = 0 cut by the circle C falls on the line L1? If so, find out the value of B. if not, explain the reason

∵ x ^ 2 + y ^ 2-6x-4y + 4 = 0 can be transformed into (x-3) ^ 2 + (Y-2) ^ 2 = 3 ^ 2 ∵ the center of circle C is C (3,2), and the radius is 3. Suppose that there is a normal vector of M (x0, Y0) satisfying the meaning of L1, which is CP = (2,1) and a normal vector of L2, which is e = (1,1) obtained by PC ⊥ L1, that is, 2 (x0-5) + 1 (y0-3) = 0 by MC ⊥ L2

In class 5 (2), 2 / 5 of the students are boys, 3 / 4 of the girls are up to the standard in the physical test. How many of the girls are up to the standard in the physical test?

9/20

If real numbers x and y satisfy x2 + 4y2 = 4x, then the value range of S = x2 + Y2 is______ ．

From x2 + 4y2 = 4x, y2 = 14 (4x − x2), from y2 = 14 (4x − x2) ≥ 0, the solution is 0 ≤ x ≤ 4, substituting s = x2 + Y2, s = x2 + 14 (4x − x2) = 34x2 + x = 34 (x + 23) 2-13, X ∈ [0,4], s monotonically increases on [0,4], when x = 0, s gets the minimum value of 0; when x = 4, s gets the maximum value of 16, so the

There are 348 students in the fifth and sixth grades of Yucai primary school. The number of students in the sixth grade is 22 more than that in the fifth grade. There are () students in the fifth grade and () students in the sixth grade
Answer! RT!

This is a question of sum and difference,
A large number is equal to (sum plus difference) divided by two,
The solution to this problem is as follows:
(348 + 22) △ 2 = 185 (people) - grade 6
348-185 = 163 (people) - fifth grade
A: there are 185 students in sixth grade and 163 students in fifth grade
I hope this answer will help you

Does minus 14 have a square root?

No
Negative numbers have no square roots

The ratio of the three numbers of a, B and C is 4:7:9. The average of the three numbers is 40. What are the three numbers

Sum of three numbers = 40 × 3 = 120
4+7+9=20
A = 120 × 4 / 20 = 24
B = 120 × 7 / 20 = 42
C = 10 × 9 / 20 = 54