Some problems about induction formula For example, cos (3 π - 60 °). At this time, use formula 3 (COS (- a)) to round off 3 π directly, or use formula 4 (COS (π - a)) to calculate?

Some problems about induction formula For example, cos (3 π - 60 °). At this time, use formula 3 (COS (- a)) to round off 3 π directly, or use formula 4 (COS (π - a)) to calculate?

With formula 4, it can be seen that cos (2tt + (tt-a)) 2tt is equal to the original function and turns a circle, so it can be rounded off first and then becomes cos (tt-a)

The system of inequalities 0.5x + 0.2 (50-x) ≤ 19 ① 0.3x + 0.4 (50-x) ≤ 17.2 ②

0.5x+0.2（50-x）≤19 ①
0.5x+10-0.2x≤19
0.3x≤9
x≤30
0.3x+0.4（50-x）≤17.2②
0.3x+20-0.4x≤17.2
-0.1x≤-2.8
x≥28

1, let x > 0, find the minimum value of (2x & # 178; + 5x + 3) / X
2. Prove that "in the inscribed rectangle of a circle with radius r, the square with the largest area is equal to 2R & # 178;
3. Cut a square piece of white iron with a side length of a into a small square at each corner (the four small squares cut out are equal), and then bend it into a box without a cover. Q: when the side length of the square cut out is multi baked, is the volume of the box made the largest?

The original formula is 2x + 5 + 3 / x, because a + B & gt; = 2 * radical (a * b), so the result of the original formula is 5 + 2 * radical (6) 2. The diagonal divides the garden into four parts, and the area of the garden is a * b * Sina / 2 & nbsp; & nbsp;, & nbsp; Sina = sin (3.14-a). The area of the two diagonal triangles is equal, and the side length is R / 2 & nbsp

The proof of mathematical inequality
A square plus 7 is greater than 5A
A squared a is greater than 2a-1
A square + 1 is greater than 2A
The fourth power of 4a is greater than or equal to 4A Square-1
Square a plus square B is greater than or equal to 2 (AB + a-b) - 1
3 (a square + 2B Square) greater than or equal to 8ab
How to verify

1.
(A^2+7)-5A=(A-5/2)^2-25/4+7
=(A-5/2)^2+3/4
＞0
two
A^2-(2A-1)=A^2-2A+1=(A-1)^2≥0
three
It's the same as 2
four
4A^4-（4A^2-1）=（2A^2）^2-2（2A^2）+1=（2A^2-1）^2≥0
five
（A^2+B^2）-[2（AB+A-B）-1]
=（A^2-2AB+B^2）-2（A-B）+1
=（A-B）^2-2（A-B）+1
=（A-B-1）^2≥0
six
3（A^2+2B^2）-8AB
=3A^2+6B^2-8AB
=（√3A）^2+（√6B）^2-8AB
=（√3A-√6B）^2+2（√3√6）AB-8AB
=（√3A-√6B）^2+2（√18-√16）AB
≥0

The proof of inequality
Given a1a2a3... An = 1, prove A1A2 + a2a3 +... + a (n-1) an + ana1

It can't be proved, because there is a hypothesis that A1 = - 1, A2 = - 1. An = - 1, when n is an even number, the left side is equal to N, and the right side is less than 0, so the inequality doesn't hold! If you want to get this aspect, go to the ranking inequality and Cauchy inequality ~ when an > 0, there are A1 = 1 / 4, A2 = 2, A3 = 2, A1 * A2 + A2 * A3 + a3 * A1 = 1 / 2 + 4 + 1 / 2 = 5, a1 + A2 + a3 = 1 / 4

Proving mathematical inequality
(1) a²+b²+5≥2(2a-b)
(2) If a and B are positive numbers, and a ≠ B, the proof is given
(a³)²+(b³)²>(a²)²b²+a²(b²)²
I don't know if I can see clearly. The above ones were originally 6-th and 4-th power. I split them into 2-th and 3-th power

1. A and B are 60 kilometers apart. A and B respectively ride bicycles and motorcycles from a to B. It is known that a starts one hour earlier than A. as a result, B arrives one hour earlier than A. B's speed is three times that of A. what's the speed of a and B?
2. Given x-6y = 5, x + 2Y = - 2, find the value of x ^ 2-4xy-12y ^ 2

First question:
Let a V; X, B V: y
The equations are: 60 / X-60 / y = 2,3x = y
Substituting y = 3x into the first formula, we get 60 / X-60 / 3x = 2
If 60-60 / 3 = 2x, 40 = 2x, x = 20
Y=3X=3*20=60
A
Second question:
(X-6Y)(X+2Y)=X^2-6XY+2XY-12Y^2=x^2-4xy-12y^2
So x ^ 2-4xy-12y ^ 2 = (x-6y) (x + 2Y) = 5 * - 2 = - 10

Come on, mathematician
On tree planting day, the sales department and the students took 123 saplings to plant trees. When they got to the hillside, they saw that there were two open spaces for planting. They immediately measured them. As a result, they learned that one plot was 9 meters long and four and a half meters wide, and the other plot was 6 meters long and three and a half meters wide. If all the trees were planted according to the size of the area, how many saplings should each plot have?

Area ratio 9 × 4.5:6 × 3.5 = 27:14
123×27÷(27+14)=81
123×14÷(27+14)=42
A: 81 trees in the first block and 42 trees in the second block

If the terminal edge of angle a passes through point P (1, - 2), then the value of tan2a is

The value of Tana can be obtained from point P. Tana is the slope of angle A
Tan α = - 2, then Tan 2 α = 4 / 3
Please feel free to use, if you have any questions, please ask
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Help! Space vector
Three known triangle points a = (1,0,0) C = (0,0,1) o = (0,0,0)
Find the normal vector of this plane
The reference answer is the normal vector E = (0,1,0) of the plane OAC
How do we get this? Instead of taking the normal vector, we take the point product of two intersecting lines in the plane equal to 0. This e = (0,1,0)
(2010 Hubei 18 questions)

This is very simple. Draw a space rectangular coordinate system, and you can see that OA is the unit vector of X axis, OC is the unit vector of Z axis, then ob must be the unit vector of Y axis (0.1.0). This is the simplest method