Let a straight line passing through the focus of the parabola y2 = 2px (P > 0) intersect with the parabola. Let the coordinates of the two intersections be a (x1, Y1) and B (X2, Y2) respectively. Prove: (1) y1y2 = - P2 (2) x1x2 = p24

Let a straight line passing through the focus of the parabola y2 = 2px (P > 0) intersect with the parabola. Let the coordinates of the two intersections be a (x1, Y1) and B (X2, Y2) respectively. Prove: (1) y1y2 = - P2 (2) x1x2 = p24

It is proved that: (1) let the linear equation be x = my + P2, and substitute y2 = 2px, y2-2mpy + P2 = 0, y1y2 = - P2 (2) x1 · x2 = y12p · y22p = p24

How to make 95% alcohol into 75% alcohol

Based on the constant mass of alcohol, 100 g 95% alcohol is assumed
100*95%=75%*（100+x）
X is the mass of water

Factors of 76 and 80

The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 80 are 1, 245, 8, 10, 16, 20, 40, 80

Finding indefinite integral | LNX | DX

The integral of LNX is not analytic
It can't be expressed as elementary function

The mass of a hollow aluminum ball is 27g. After the hollow part is filled with alcohol, the total mass is 48g

It is known that: m aluminum = 27g & nbsp; m = 48g & nbsp; ρ aluminum = 2.7g/cm3 & nbsp; ρ alcohol = 0.8g/cm3, find: V ball =? The mass of alcohol in the hollow part is m alcohol = M-M aluminum = 48g-27g = 21g, ∵ ρ = MV, and the volume of the hollow part is v air = V alcohol = m alcohol ρ alcohol = 21g 0.8g/cm3 = 26.25cm3

The following defines an "f operation" on a positive integer n:
① When n is odd, f = 3N + 5; when n is even, the result is f = n × 12 × 12 × (where f is odd), and the operation is repeated. For example, take n = 26, as shown in the figure, if n = 50, then the result of the 2013 "f operation" is______ ．

The first time: 50 × 12 = 25, the second time: 3 × 25 + 5 = 80, the third time: 80 × 12 × 12 × 12 = 5, the fourth time: 3 × 5 + 5 = 20. It can be seen that from the third time, the odd number of times is 5, and the even number of times is 20, so the result of the 2013 "f operation" is 5 if n = 50

The part of plane x + Z = a contained in cylinder x ^ 2 + y ^ 2 = a ^ 2, ∫ (x + Z) ds =?
(radical 2) π a ^ 3
Σ is the part of plane x + Z = a contained in cylinder x ^ 2 + y ^ 2 = a ^ 2, ∫∫Σ (x + Z) ds =?

What is the difference between transfer and transformation in physics

Transfer: for example, the process of heat transfer is the transfer of internal energy from a high temperature object to a low temperature object
Transformation: after the football leaves the foot, it rolls more and more slowly on the field, and finally stops. Here, the mechanical energy of the ball is transformed into internal energy. Another example is the power stroke of the internal combustion engine, which transforms the internal energy of the gas into the mechanical energy of the machine. The form of energy has changed
Conversion: when learning the direction of the magnetic field, the direction of the magnetic field is determined by the north pole direction of the small magnetic needle. That is, the phenomenon that cannot be directly observed is converted into the imagination that we can see; another example is whether the electric current is determined by whether the light bulb emits light

Given that the lengths of the two right sides of a right triangle are exactly the two roots of the equation 2x square - 5x = - 2, we can find the length of the oblique side of the right triangle

2X squared - 5x = - 2
2x^2-5x+2=0
So X1 + x2 = 5 / 2
x1*x2=1
So X1 ^ 2 + x2 ^ 2 = (x1 + x2) ^ 2-2x1 * x2 = 25 / 4-2 = 17 / 4
So oblique side length = √ (x1 ^ 2 + x2 ^ 2) = √ (17 / 4) = √ 17 / 2

It is known that in the quadrilateral ABCD, ab = BC = DC = 1, Da = root 3, angle B is the area of the quadrilateral with degree BCD of 90 degrees

Link to AC
Because AB = BC = 1 and angle B = 90 degrees
So AC = root 2, angle ACB = 45 degrees
Because DC = 1, Da = root 3,
Easy to get DC square + AC square = Da square
So ACD = 90 degrees
So angle BCD = angle ACB + angle ACD = 45 ° + 90 ° = 135 °
S quadrilateral = s △ ABC + s △ ACD = 0.5ab × BC + 0.5ac × CD = 0.5 + 0.5 radical 2