It is known that triangle sword square equals 2.8, square plus circle equals 9.2, triangle plus circle equals three triangle sword Then the triangle equals [] A square equals [] Circle equals【

It is known that triangle sword square equals 2.8, square plus circle equals 9.2, triangle plus circle equals three triangle sword Then the triangle equals [] A square equals [] Circle equals【

Let △ be x, then 0 is 2x and □ is x-2.8
So there is: x-2.8 + 2x = 9.2
X=4
So the triangle equals [4]
Square equals [1.2]
A circle equals [8]
Help to prove the period of a function
Prove a periodic function and prove that the period of F (x) + F (x + a) + F (x + 2a) + F (x + 3a) + F (x + 4a) = f (x) f (x + a) f (x + 2a) f (x + 3A) f (x + 4a) is t = 5A. When I do f (x + a) * f (x + 2a) * f (x + 3a) * f (x + 4a) = 1, the quotient is t = 4A. Why is it not suitable
From: F (x) + F (x + a) + F (x + 2a) + F (x + 3a) + F (x + 4a) = f (x) f (x + a) f (x + 2a) f (x + 3a) f (x + 4a)
Substituting x + A, we get: F (x + a) + F (x + 2a) + F (x + 3a) + F (x + 4a) + F (x + 5a) = f (x + a) f (x + 2a) f (x + 3a) f (x + 4a) f (x + 5a)
By subtracting the two formulas, f (x) - f (x + 5a) = f (x + a) f (x + 2a) f (x + 3a) f (x + 4a) [f (x) - f (x + 5a)]
That is [f (x) - f (x + 5a)] [f (x + a) f (x + 2a) f (x + 3a) f (x + 4a) - 1] = 0
So there are two situations:
1) F (x) = f (x + 5a), then t = 5A
2) F (x + a) f (x + 2a) f (x + 3a) f (x + 4a) = 1
f(x+a)+f(x+2a)+f(x+3a)+f(x+4a)=0
Substitute x-a to get: F (x) + F (x + 2a) + F (x + 3a) + F (x + 3a) = 0
Subtraction of two formulas: F (x) - f (x + 4a) = 0
Let f (x) = f (x + 4a), then t = 4A
If t satisfies both 5A and 4a, then t = a is also its period
Obviously, if f (x) = 5 ^ (1 / 4) constant function, then any positive number is its positive period
Two circles are equal to three squares; a square and two triangles add up to a circle. How many times the mass of a circle is that of a triangle?
It's quality!
Two circles are equal to three squares; a square and two triangles add up to a circle. How many times the mass of a circle is that of a triangle?
2 circle = 3 positive
1 circle = 1.5 positive
1 circle = 1 positive + 2 Triple
2 three = 0.5 positive
6 three = 1 circle
6 △ 1 = 6 times
Six times
however... Is it quality?
On the proof of function periodicity
1. The function y = f (x) is symmetric with respect to two straight lines X = A and x = B. It is proved that t = 2|a-b|
2. For (a, 0) (B, 0) symmetry, it is proved that t = 2|a-b|
3. For a point (a, 0) and a line x = B symmetry, it is proved that t = 4|a-b|
4. Similarly, f (x + a) = - f (x) or one of - f (x). It is proved that t = 2A
A triangle plus a circle equals 75, then a triangle equals 4 circles, and finally a circle equals several, and a triangle equals several
Triangle x, circle y
x+y=75
x=4y
y=15
x=60
Triangle 60, circle 15
Circle equals 15, triangle equals 60
(five circles add up to 75)
∵1▲+1●=75，1▲=4●
∴4●+1●=5●=75，
The solution is 15
Then ■ = 75-15 = 60
Proof of periodic function
1,f（a+x）=-f（x）
2,f（a+x）=-f（x）^(-1)
3, f (a + x) = f (x) ^ (- 1) their periods are t = 2A
There is also functional symmetry
f（a-x）=f（a+x）
F (2a-x) = f (x) are symmetric with respect to x = a
1. Prove: because f (a + x) = - f (x), f [a + (a + x)] = - f (a + x) {substituting a + X as a variable x into f (a + x) = - f (x) to get} f (2a + X) = - f (a + x) = f (x) {from F (a + x) = - f (x)} that is, f (a + x) = - f (x) is a periodic function with period 2A. 2
A circle is equal to three triangles, a triangle is equal to two squares, a circle plus a triangle plus a square is equal to 72
A circle is three triangles
So a circle plus a triangle plus a square is four triangles and a square
One triangle is equal to two squares
So a circle plus a triangle plus a square is four triangles and a square, which is nine squares
That's nine squares, 72
So the square is 8
The triangle is 16
The circle is 48
X + 2x + 6x = 72 circle = 48 triangle = 16 square = 8
Square 8 circle 48 triangle 16
Circle = 3 triangle = 6 square
Then circle + triangle + square = 6 square + 2 square + 1 square = 9 square = 72
Block = 8
So triangle = 16
Circle = 48
If a circle equals 2 × 3 = 6 squares, then 6 + 2 + 1 squares = 72, squares = 8, circles = 48, triangles = 16
(3 * 2 + 2 + 1) squares equals 72
One square equals eight
One triangle equals 16
One circle is 48
A circle is equal to 3 * 2 = 6 squares. Let a square be X
6x+2x+1x=72
X=8
The circle is 48, the triangle is 16, and the square is 8
If the square is x, the triangle is 2x and the circle is 6x
A circle, a triangle and a square are 72
6X+2X+X=72
9X=72
X=8
Square is 8, triangle is 2 * 8 = 16, circle is 6 * 8 = 48
How to prove that the function f (x + 2) = 1 / F (x) is a periodic function and find its minimum positive period
Let x = x + 2, substitute f (x + 2) = 1 / F (x), get: F (x + 4) = 1 / F (x + 2), because f (x + 2) = 1 / F (x), so 1 / F (x + 2) = f (x), so f (x + 4) = 1 / F (x + 2) = f (x), so the minimum positive period is 4
Triangle plus square is 75, triangle plus circle is 100, circle plus square is 91, triangle, square and circle are equal to each other
Take 75 + 100 + 91 to get 2 triangles, 2 circles, 2 squares, 1 triangle, 1 circle, 1 square is 133, subtract 75's circle 58, subtract 100 to get square 33, subtract 91 to get triangle 42
Given the relation of a function, how to know its period?
F (x) = f (x + T) (t is a constant), this function is called periodic function, and t is the period of this function