Given the square of function y = x - 2x + 2 (x belongs to [T, t + 1]), if the minimum value of function y = f (x) is expressed by G (x), write out the analytic expression of G (T)

Given the square of function y = x - 2x + 2 (x belongs to [T, t + 1]), if the minimum value of function y = f (x) is expressed by G (x), write out the analytic expression of G (T)

The solution y = (x-1) ^ 2 + 1 when t + 1 "1, that is, t" 0 ", G (T) has the minimum value when x = t + 1, G (T) = f (T + 1) = T ^ 2 + 1 when t" 1, G (T) has the minimum value when x = t, G (T) = f (T) = (t-1) ^ 2 + 1 when t "1

Let the minimum value of function y = x square - 2x + 2, X ∈ [T, t + 1] be g (T), and find the analytic expression of G (T)

The original function can be written as: F (x) = (x-1) ^ 2 + 1
When t + 1

Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)

F (x) = x2-2x + 2 = (x-1) 2 + 1, so the symmetry axis of the image is a straight line x = 1, and the opening of the image is upward

Let the corresponding points of complex numbers Z1 and Z2 on the complex plane be a and B respectively, and | Z1 | = 4,4z12 + 2z1z2 + Z22 = 0, and o be the coordinate origin, then the area of △ OAB is
Why can we know from the condition that 2z1 / Z2 = cos π 3 ± isin π 3?

First of all, Z2 can't be 0, otherwise we will get 4z1 ^ 2 = 0 if we take it into that equation, because | Z1 | = 4. Then we divide Z2 ^ 2 on both sides of the equation, so we get the solution of the quadratic equation: 2z1 / Z2 = Cos2 π / 3 ± isin2 π / 3, then we get 2 | Z1 | / | Z2 | = 1, so | Z2 | = 8

100 kg of apples from fruit shop is 2 / 3 of pears. How many pears are there

150 kg of pears

1+1+2+3………… ... + 100 equals?

The first step is to reserve the first number 1 until the last calculation. The second step is to add the second number 1 and the last 100: 1 + 100 = 101. The third step is to add 2 and 99 = 101, and so on. The last 50 + 51 = 101, a total of 50 groups of 101, plus 1101 * 50 + 1 = 5051

I1 = I2 + I3, I2 + 4i1-i1 = 0, 2i3-i2 + 7 = 0 is the equation

Three unknowns, three sets of equations, have a unique solution. Let's work

As shown in the figure is a section of stairs, the height BC is 3 meters, and the length ab of the hypotenuse is 5 meters. If the stairs are paved with carpet, how many meters does the carpet need at least

Seven meters
According to Pythagorean theorem, the ground length (AB) = 4m
As the staircase is about this shape, it should be at least (3 + 4) M

In 1.2.3.4.5.6.7.8.10.15, () is the factor of 30, () is the factor of 45

1、2、3、5、6、10、15
1、3、5、15

Linear Algebra: why tr (A'ba) = tr (a'ab)? A 'is the transpose of A. TR is the trace of a matrix

tr(AB)=tr(BA)====>tr(A'AB)=tr(A'BA)
The first equation is a formula. Many mathematicians have proved it absolutely correct!