Judge whether the function group is linear correlation sin 2t,cos t,sin t Are these three functions linearly related? How to prove them? If there are K1, K2, K3 which are not all zero such that K1 * sin 2T + K2 * cos t + K3 * sin t = 0 is constant on interval I, it is said that they are linearly correlated on interval I

Judge whether the function group is linear correlation sin 2t,cos t,sin t Are these three functions linearly related? How to prove them? If there are K1, K2, K3 which are not all zero such that K1 * sin 2T + K2 * cos t + K3 * sin t = 0 is constant on interval I, it is said that they are linearly correlated on interval I

Suppose that there are some numbers a, B, C which are not all zero such that asin2t + bsint + ccost = 0, the derivation is obtained
2acos2t + bCost csint = 0, and then the derivative is obtained
- 4asin2t bsint ccost = 0, let t = 0 in three expressions
c＝0,2a+b＝0,c＝0；
Let t = pi / 2, B = 0, - 2a-c = 0, - B = 0;
The final solution is a = b = C = 0, so it is irrelevant

The judgment of linear system
The input-output relationship of a system is as follows: Y (T) = | f (T) - f (t-1) | judge whether it is linear or time invariant?
Prove it for me. Thank you~~~

The linear proof assumes that a linear system should satisfy the following relation: when f (T) = a X1 (T) + B X2 (T) --- 1, y (T) = Y1 (T) + Y2 (T) --- 2, y (T) = | a (x1 (T) - X2 (T)) + B (x1 (T) - X2 (T)) | y (T) = a| X1 (T) - X2 (T) | can be deduced from relation 2

3 square decimeters 5 square centimeters = () square decimeters 4.6 liters = () cubic decimeters () milliliters 280 milliliters = () cubic centimeters = () liters
2.15 hours = () hours (expressed in fractions)

3 square decimeters 5 square centimeters = (3.05) square decimeters
4.6 L = (4) cubic decimeter (600) ml
280 ml = (280) CC = (0.28) l
2.15 hours = (2 and 1 / 4 or 9 / 4) hours (expressed in fractions)

Three views of a geometry, in which the front view and side view are equilateral triangles with side length of 2, and the top view is a circle with radius equal to 1,
Find the side area and volume of this geometry

It is a cone. From the top view, we can see that the bottom radius is 1. From the front view and side view, we can see that the bus length is 2, so the height h = √ 2 ^ 2-1 = √ 3
Side area s = π RL = 2 π
Volume v = 1 / 3SH = √ 3 / 3 π, please accept

Move the parabola y = x ^ 2 + BX + C upward by 3 units to y = x ^ 2-2x + 1 to find the value of B C

From the original formula, y = x ^ 2 + BX + C, move up three units, get y = x ^ 2 + BX + C + 3, this parabola is y = x ^ 2-2x + 1
B = - 2, C + 3 = 1, so B = C = - 2

How many cubic meters is a ton of sand

The bulk density of sand is usually 1.28 T / m3
The bulk density of stones is usually 1.48 T / m3
1 △ 1.28 ≈ 0.78 M3
One ton of sand is about 0.78 cubic meters

Calculate (- 7x) (the second power of X - 3x + 1)

The original formula = - 7x & sup3; + 21x & sup2; - 7x

(1) Let the parabola y = 2x square - 12x + 16 turn the vertex 180 degrees

Let the vertex turn 180 degrees, that is, the whole parabola turns 180 degrees. The analytical formula of the parabola is y = - 2x square + 12x-16

Questions about mass and density in Physics
Fill two identical circular containers (A and b) with two liquids of different densities (assuming that the two liquids are incompatible). The mass of the two liquids in cup a is half, and the volume of the two liquids in cup B is half. The total mass of the liquids in the two cups is m a and M B respectively. What is the mass relationship between them?

Let the density of the two liquids be P1 and P2 respectively, and the volume of the container be v
In a: (1 / 2m a) / P1 + (1 / 2m a) / P2 = v
It is concluded that m a / 2p1 + m a / 2P2 = v
In B: 1 / 2 VP1 + 1 / 2 VP2 = m b
It is concluded that (P1 + P2) square / (4p1p2) = M B / M a
The square of (P1 + P2) is greater than 4p1p2
So m a is less than m B

51 × 45 ingenious calculation

51×45
=(50+1)x45
=50x45+1x45
=2250+45
=2295