If f (x) = sin (x + Pai / 3) + asin (x-pai / 6) (x belongs to R), then the value of a is? Please give a specific solution, not just the answer,

Because the axis of symmetry is half π
So f (0) = f (π)
sin(π/3)-asin(π/6)=-sin(π/3)+a(5π/6)
√3/2-a1/2=-√3/2+1/2a
a=√3

There are two solutions to the equation sin (x + Pai / 3) = m / 2, which is greater than or equal to 0 and less than or equal to Pai?

Let f (x) = sin (x + Pai / 3) the function image is obtained by moving g (x) = SiNx image by π / 3 units to the left
Let H (x) = m / 2 (the image is a horizontal line parallel to the X axis) so that it has two intersections with F (x)
√3≤m

In the plane, the product of the distances from a moving point P to two fixed points a and B is equal to the square of half of the distance between the two fixed points

Let a (- A, 0), B (a, 0), (a > 0)
P(x,y)
It can be concluded from the question setting that:
√[(x+a)²+y²]×√[(x-a)²+y²]=a²
[(x²+y²+a²)+2ax]×[(x²+y²+a²)-2ax]=a^4
(x²+y²+2a²)(x²+y²)=4a²x²
(x²+y²)²=2a²x²-2a²y²
hold
x=ρcosθ
y=ρsinθ
On behalf of the people, you can get
ρ²=2a²cos2θ

For the factorization of quadratic trinomial, if the final result can be reduced by multiplying the coefficient, do you have to multiply it? For example, the correct factorization of 4x square + 4x-1 is () a, 4 (x + 2 / 1 + radical 2) (x + 2 / 1-radical 2) B, (2X + 1-radical 2) (2x + 1 + radical 2)

The process is: 4x & # 178; + 4x-1 = 4 (X & # 178; + x) - 1 = 4 (X & # 178; + 2 × 1 / 2x + 1 / 4) - 2 = 4 (x + 1 / 2) & # 178; - 2 = {2 (x + 1 / 2) + root 2} {2 (x + 1 / 2) - root 2} = (2x + 1 + root 2) (2x + 1-root 2)

The people's Republic of China was founded on October 1, 1949, and it will be the 63rd anniversary of the founding of the people's Republic of China in 2012

Fill in the operation symbol or bracket on the horizontal line to make the equation hold
①4_ 4_ 4_ 4_ =1
②4_ 4_ 4_ 4=2
③4_ 4_ 4_ 4_ =3
④4_ 4_ 4_ 4=4

①(4+4)/(4+4)=1
②4*4/(4+4)=2
③(4+4+4)/4=3
④(4-4)/4+4=4

The National Day in 2007 is Monday. What day is the National Day in 2010

This is about the calculation of mod
The difference between the two dates is 3 years. In 2008, there are 366 days in leap year, which is (365 * 3 + 1) days
（365*3+1） MOD 7 =4
So: 2010 National Day is Friday

What is the area formula of the ring in letters?

π（R2-r2）

What's 5 out of 13 times 26?

It should be equal to 10

[simple mathematical problem] let's change the expression of a first-order function into that of a second-order function
How can y = - 10x + 200 be transformed into the square of y = - 10x + 320x-2400
[simple question] the cost price of a flower is 12 yuan per pot. In sales, the functional relationship between the selling price x (yuan) of each pot and the daily sales volume y (pot) is y = - 10x + 200
What is the maximum profit per day when the price is fixed?

Y = - 10x square + 320x-2400
=-10(x^2-32x+240)
=-10(x-12)(x-20)
=(-10x+20)(x-12)
Y = - 10x + 200 multiplied by (X-12) can be converted to the square of y = - 10x + 320x-2400

If f (x) = sin (x + Pai / 3) + asin (x-pai / 6) (x belongs to R), then the value of a is? Please give a specific solution, not just the answer,