It is known that a ^ 2 + B ^ 2 = 1, x ^ 2 + y ^ 2 = 1, where a, B, X and Y belong to R. it is proved by vector method that: - 1 ≤ ax + by ≤ 1 (complete process is required)

It is known that a ^ 2 + B ^ 2 = 1, x ^ 2 + y ^ 2 = 1, where a, B, X and Y belong to R. it is proved by vector method that: - 1 ≤ ax + by ≤ 1 (complete process is required)

Let: vector a = (a, b), vector b = (x, y), then: | a | = 1, | B | = 1
AB = ax + by = | a | B | cosx
We get: ax + by = cosx
Because: 0 ≤ x

It is proved that the vector field a = (x ^ 2-y ^ 2 + x) I - (2XY + y) J is a planar harmonic field, and its force function u and potential function v are obtained

Let P = x ^ 2-y ^ 2-2-y ^ 2 + X, q = (2XY + y) let P = x ^ 2-2-y ^ 2 + X, q = (2XY + y) let P = (2XY + y + y) be p \35; \\35\\\\\35\\\\\\\\\35\; Q \\\\\\\\\\\\\\\\\\ (range 0 to y

As shown in the figure, it is known that angle 1 is equal to angle 2 and angle c is equal to angle D. try to explain that angle a is equal to angle F

Angle 1 equals angle 2 (known)
And ∵ equal to vertex angle)
1 = ∠ 3 (equivalent substitution)
Ψ BD parallel to CE
The two straight lines are flat and the same angle is equal
And ∵ ∠ C = ∠ D (known)
■ ∠ abd = ∠ D (equivalent substitution)
The BD is parallel to CE (the internal stagger angles are equal, and the two lines are parallel)
The angle a is equal to the angle f

Take the ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to form three three digit numbers and one single digit number, and make the sum of these four numbers 999. We require the maximum three digit number to be as small as possible, so what is the maximum three digit number?

It is required that the maximum three digits of the composition should be as small as possible, that is, the three three digits should be as close as possible, and the closer they are, the smaller they are; because 999 △ 3 = 333, the hundreds of the three digits should be 2, 3, 4, so the three digits are relatively small; if the maximum three digits of the composition are as small as possible, the three digits at the beginning of 4 are the smallest, only 40A; let the three digits be 40a, 3bC, 2DE, one digit f; a, B , C, D, e, f belong to 1, 5, 6, 7, 8, 9; 999-40a-3bc-2de-f = 99-a-bc-de-f = 99-bc-de-a-f = 0; 99 △ 2 = 49, so one of B and D must be less than 4; let B = 1, then 99-1c-de-a-f = 89-c-de-a-f = 0; because 5, 6, 7, 8, 9, take four different numbers and add up to 26, 27, 28, 29, 30; let d = 6, then there is 89-c-6e-a-f = 29-c-e-a-f = 0, C, e, a, F have solutions, a chooses the smallest 5. So the biggest three digit is 405

It is known that the speed of the local train is 56 times that of the express train. The two trains are going towards each other at the same time from station a and B, and they meet at the place 4 kilometers away from the midpoint. How many kilometers is the distance between station a and B?

(4 × 2) / (65 + 6 − 55 + 6) = 8 / 111, = 88 km. A: the distance between the two stations is 88 km

Known: as shown in the figure, in the quadrilateral ABCD, ∠ a = ∠ D, ∠ B = ∠ C, try to judge the position relationship between AD and BC, and explain the reason

The position relationship between AD and BC is parallel. Reasons: ∵ the sum of the internal angles of the quadrilateral ABCD is 360 °, and ∵ a + ∵ B + ∵ C + ∵ d = 360 °, and ∵ a = ∵ D, ∵ B = ∵ C, ∵ a + ∵ B + ∵ B + ∵ a = 360 °, and ∵ a + ∵ B = 180 °, and ∵ ad ∥ BC (the internal angles of the same side are complementary and the two lines are parallel)

For a pile of chemical fertilizer, 25% of the total weight is transported in the first time, the remaining 59 tons are less than 10 tons in the second time, and the remaining 74 tons are transported in the third time. How many tons are there in total?

(74-10) △ [1-25 - (1-25) × 59], = 64 △ 415, = 240 (tons); answer: there are 240 tons of chemical fertilizer in this pile

Mean inequality what is "one positive, two definite, three equal" and why?

Q let me give a simple example. First of all, there must be two positive numbers. Why? If there are two negative numbers, using the mean inequality, we will get the result (- 4) + - 9) > = 12. Three phases ensure that the equal sign can be obtained, such as 4 + 9 > = 12. At this time, the condition of equality is not satisfied. 4 is not equal to 9, so only 4 + 9 = 13 > 12. As for the second definite, I haven't thought of a good solution. I'll let you know later

The railway between Party A and Party B is 480 km long. Passenger cars and freight cars leave from both places at the same time and meet each other after 4 hours
It is known that passenger cars travel 65 kilometers per hour, and freight cars travel x kilometers per hour. The incorrect equations are (). A, 65 × 4 + 4x = 480 B, 4x + 65 = 480 C, 65 + x = 480 △ 4 D, (65 + x) × 4 = 480 C, 65 + x = 480 D, and 65 + x = 480 x = 480 D

The answer is B

Solve the system of inequalities: {- 2 ≤ 3-2x 3-2x ≤ 4

{-2≤3-2x ①
{3-2x≤4 ②
The solution is 2x ≤ 5
x≤5/2
Solution 2 is - 2x ≤ 1
x≥-1/2
So - 1 / 2 ≤ x ≤ 5 / 2