Can X be replaced by x = sin ^ 2 (T) in (0,1) definite integral

Can X be replaced by x = sin ^ 2 (T) in (0,1) definite integral

Yes. And the range of t only needs (0, PI / 4)

In the number - 5, - 2, - 4,5,2 arbitrarily take three numbers to multiply, where the largest product is -----, the smallest product is -----

The largest product may be:
(-5)×(-4)×5=100
The smallest product may be:
(-5)×5×2=-50

Solving x ^ 2-6x + 9 = (5-2x) ^ 2 by factorization

X^2-6X+ 9=(5-2X)^2
(x-3)^2=(5-2x)^2
Then: x-3 = 5-2x or x-3 = - (5-2x)
X = 8 / 3 or x = 2

Use the formula to show that the number on the ten digit is a and the number on the single digit is the two digit of B. then exchange the single digit of the two digit with the number on the ten digit
The sum of the calculated number and the original number. Can this number be divided by 11?

The number in the tens is a, and the number in the single is two digits of B
=A*10+B*1
=10A+B
After swapping the single digit of the two digit number with the number on the ten digit number, the two digit number is obtained
=B*10+A*1
=10B+A
The sum of the two numbers
=（10A+B）+（10B+A）
=11A+11B
=11*（A+B）
therefore
This number can be divided by 11!

4x-x + 1 / 32x + 1 / 3 solution of inequality system

(1)
4x-x+1/3

1. Verify these operation laws in many ways: addition commutation law addition combination law multiplication commutation law multiplication combination law multiplication allocation law (write two for each)
2. Is the operation law of integer operation tenable in decimal and fractional operation? Give an example

1.
Additive commutative law 2 + 3 = 3 + 2 12 + 13 = 13 + 12
Additive combination law (1 + 2) + 3 = 1 + (2 + 3) (11 + 12) + 13 = 11 + (12 + 13)
Commutative law of multiplication 2 * 3 = 3 * 2 12 * 13 = 13 * 12
Multiplicative Association Law (1 * 2) * 3 = 1 * (2 * 3) (11 * 12) * 13 = 11 * (12 * 13)
Multiplicative distributive law (1 + 2) * 3 = 1 * 3 + 2 * 3 (1-2) * 3 = 1 * 3-2 * 3
two
They are all established,
Decimals: replace the above example with decimals or fractions

Triangle ABC in the plane rectangular coordinate system, know ABC three-point coordinates, may I ask the center of gravity and vertical center and external center formula?

Let a (x1, Y1), B (X2, Y2), C (X3, Y3), then the coordinates of the center of gravity g of △ ABC are:
x=(x1+x2+x3)/3,y=(y1+y2=y3)/3.
The coordinate expressions of vertical center and external center are very complex, which are omitted here

If there are exactly six real numbers x satisfying | x2-6x-16 | - 10 | = a, then the value of real number a is equal to______ ．

As shown in the figure, when a = 10, two functions have six intersections, so a = 10

What is the derivative of ∫ f (x ^ 2) DX?
What about the derivative of F (e ^ x) DX?

The derivative of an integral is an original function
f(x^2)
e^x

What is the principle of detecting ozone concentration by ultraviolet absorption method?

The principle is that ozone has the maximum absorption sparsity for ultraviolet light with wavelength of λ = 254nm. Under this wavelength, ultraviolet light will attenuate through the ozone layer, which conforms to Lambert Beer's Law: I = IOE KLC: IO - incident light intensity without ozone; I - light intensity of light beam penetrating ozone; L - optical path length of ozone sample cell; C - ozone concentration; K - optical wavelength absorption coefficient of ozone
According to the formula, C value of ozone concentration can be determined by detecting I / Io value when K and L values are known
Ultraviolet absorption method has been used as the standard method of ozone analysis in the United States and other countries
According to the application, it can be divided into two types: air ozone detection and water-soluble ozone detection. Both of them can be detected continuously on-line with digital display and can be recorded and printed. The advantages are high detection accuracy, good stability and little interference from other oxidants. The disadvantages are high price
Due to the high content of nitrogen oxides produced by surface discharge type aeration tube and ceramic ozone generator, ultraviolet method should be used to detect the ozone concentration
As a modern technology product, the ozone ultraviolet detector (analyzer) has complete functions of lifting processing, light electricity conversion, data calculation, analysis and recording. The 8810 type ozone analyzer produced by Beijing analyzer factory has two kinds of products: 0-10ppm and 0-100pmm. In the United States, Japan, Germany and other countries, various specifications of ultraviolet analyzers are produced, and the maximum detection capacity is 20mg / L