It is known that the periodic function f (x) is an odd function defined on R, f (3 / 2-x) = f (x) If f (1) > - 2, f (2009) = M-3 / m, find the value range of M

It is known that the periodic function f (x) is an odd function defined on R, f (3 / 2-x) = f (x) If f (1) > - 2, f (2009) = M-3 / m, find the value range of M

F (x) is an odd function defined on R, f (x) = - f (- x)
And f (3 / 2-x) = f (x), so f (3 / 2-x) = - f (- x)
That is, f (3 / 2 + x) = - f (x)
f(x+3)=f((3/2+x)+3/2)=- f(3/2+x)= f(x).
So the period of the function is 3
f（2009）=f(670×3-1)=f(-1)=-f(1)

It is known that the function f (x) defined on R is an odd function and satisfies f (3 / 2-x) = f (x)

Using the assignment method, we know that f (3 / 2-x) = f (x) 1 ∵ f (x) is an odd function, and substitute ∵ f (3 / 2-x) = - f (x-3 / 2) into ∵ f (x) = - f (x-3 / 2) 2. Change x into x-3 / 2 ∵ f (x-3 / 2) = - f (x-3) 3. Change x into x + 3 by ∵ f (x) = f (x-3), that is, the period of F (x + 3) = f (x) ∵ f (x) is 3

As shown in the picture, there is a 1 meter wide zigzag path in a rectangular grassland. How many square meters is the lawn area?
The length is 18m and the width is 12m

Ah, there is no picture. I think it should be like this: 18 * 12 - (18 * 1 + 12 * 1-1 * 1) = 187 square meters

Answer to question 3 on page 27 of mathematics exercise book of grade 6 Volume 1
In the 14th Busan Asian Games and the 15th Doha Asian Games, the top athletes of our country won 315 gold medals. The ratio of gold medals won by our athletes in these two Asian Games is 11:10?
Hurry!

315×（11/11+10）=165
315×（10/11+10）=150

Sequence an = 2A (n-1) + 2 ^ n + (- 1), A1 = 5, if {(an + P) / 2 ^ n} is an arithmetic sequence, find the real number P
The standard answer is - 1

an=2a(n-1)-1 +2^n
an -1 = 2(a(n-1) -1 ) + 2^n
(an-1)/2^n - (a(n-1) -1)/2^(n-1) = 1
p= -1

A house needs to be paved with square bricks. It needs 480 square bricks with an area of 0.09 square meters. If it uses square bricks with a side length of 0.6 meters, how many are needed?

0.09 × 480 ^ (0.6 ×. 6) = 0.09 × 480 ^ 0.36 = 43.2 ^ 0.36 = 120 (pieces) a: 120 pieces are needed

Simplify the ratio [write the process] 40:100, 24:8 / 3, 0.36:5.6, 2 / 9:5 / 6, 145:15

40:100=4:10=2:5=2/5
24:8 / 3 = 72:8 = 9:1 = 9
0.36:5.6=36:560=9:140=9/140
Two out of nine: five out of six = 4:15 = 4 / 15

Cos (x + quarter) = 4 / 5, X ∈ (- Π / 4,0), then sin (x)=

∵x∈(-π/4,0)
∴x+π/4∈(0,π/4)
∵cos(x+π/4)=4/5
∴sin(x+π/4)=3/5
sinx=sin(x+π/4-π/4)
=sin(x+π/4)cosπ/4-cos(x+π/4)sinπ/4
=(3/5)*(√2/2)-(4/5)*(√2/2)
=-√2/10

As shown in the figure, BD is the middle line of △ ABC, ab = 6cm, BC = 4cm, then what is the perimeter difference between △ abd and △ BCD?

∵ BD is the middle line of △ ABC, ∵ ad = CD, ∵ abd and △ BCD circumference difference = (AB + AD + BD) - (BC + CD + BD), = AB + AD + bd-bc-cd-bd, = ab-bc, ∵ AB = 6cm, BC = 4cm, ∵ abd and △ BCD circumference difference = 6-4 = 2cm

1.Tan300°+sin450°=
2. Given the function f (x) = √ 3sinxcosx + sin2x-1 / 2 (x belongs to R) (1) find the period of function f (x); (2) how can the image of function f (x) be obtained from the image of function y = SiNx
3. A rectangular storage room with a floor area of 20 m2 and a wall height of 3 m should be built. A door is installed on one side of the four walls (the area of the door and the area of the wall are designed according to a certain proportion). It is known that the average cost of one side is 300 yuan / m2, the cost of the other three sides is 200 yuan / m2, and the cost of the roof is 250 yuan / m2, What's the minimum
4. Given the function f (x) = 2 sin2x (π / 4 + x) - √ 3cos2x, X belongs to [π / 4, π / 2], (1) find the maximum and minimum of F (x); (2) find the monotone interval of F (x)
5. Given that f (x) = xlnx, G (x) = - x2 + ax-3, (1) find the minimum value of F (x); (2) for all x belonging to (0, positive infinity), 2f (x) ≥ g (x) is constant, find the value range of real number a; (3) prove that for all x belonging to (0, positive infinity), there is LNX, > 1 / EX-2 / ex
establish

1. The original formula = - tan60 ° + sin90 ° = - √ 3 + 1 = 1 - √ 32: using the double angle formula F (x) = √ 3 / 2sin2x + sin2x-1 / 2 = (√ 3 / 2-1) sin2x-1 / 2, so the period = 2 π / 2 = π has f (x) = SiNx, the abscissa compresses 1 / 2, the ordinate does not change, and then the ordinate expands