How many points are excellent in mathematics?

How many points are excellent in mathematics?

Full Score 150 points need 127.5 points, 120 points need 102 points, 100 points need 85 points

December 10, 2006!

Application of equation
Engineering problems
Score application questions
Percentage application
Concentration problem
Cooperation issues
That should be it!

Y = 2x / 3, x + y = 200, how to solve the system of linear equations with two variables?

X + y = 200 can be converted to x = 200-y
Then we bring in the first formula
y=2x/3
y=2（200-y）/3
After simplification
y=(400-2y)/3
5y=400
y=80
Then we take y = 80 into the second formula
x+y=200
x+80=200
x=120
So x = 120
y=80

If the system of homogeneous equations has only 0 solution, why is the rank of coefficient matrix equal to the number of unknowns

Theorem 4 on page 77 of Tongji 5th Edition:
A necessary and sufficient condition for a homogeneous equation AX = 0 with n variables to have nonzero solutions is R (a) = n
If a is an M * n matrix, then R (a)

Given X & # 178; - 7x + 1 = 0, find the value of X & # 178; + 1 / X & # 178

x²-7x+1=0
x-7+1/x=0
x+1/x=7
x²+1/x²
=(x+1/x)²-2
=7²-2
=49-2
=47

Given that the absolute value of x plus 2 and the absolute value of y plus 7 are opposite to each other, find the value of negative x + y

｜X+2｜+｜y+7｜=0
Then x = - 2, y = - 7
-(X+Y ）= -（-9）=9

For the equations of X, y {2x-y = 3., 2kx + (K + 1) y = 0} whose solutions are opposite to each other, what is k = then?

Y=-X
So 3x = 3, x = 1, y = - 1
2K - (K + 1) = 0, so k = 1

The integral of square x Times Square X of e

The indefinite integral of ∫ x ^ 2 * e ^ (x ^ 2) DX and ∫ x ^ 2 * e ^ (- x ^ 2) DX can not be expressed by elementary function, but the definite integral of ∫ x ^ 2 * e ^ (- x ^ 2) DX on [0, + ∞) can be obtained
∫(0→+∞)x^2*e^(-x^2)dx
=∫(0→+∞)(-1/2)x*e^(x^2)d(-x^2)
=(-1/2)∫(0→+∞)x*d[e^(-x^2)]
=(-1/2){[x*e^(-x^2)]|(0→+∞) - ∫(0→+∞)e^(-x^2)dx}
=(1/2)∫(0→+∞)e^(-x^2)dx
=√π/4=(1/4)√π

Necessary and sufficient conditions for coplanar vectors
What kind of linear combination?

Two vectors must be coplanar
In short, if the vector is coplanar, then the vector is on the straight working plane
If three vectors are coplanar, then a = MB + NC
That is to say, B and C are regarded as a group of bases, and a can be represented by MB + NC. Then a, B and C are coplanar
Multiple vectors are the same

lim(n→∞)(sin(n+√(n^2+n)))^2
lim(n→∞)(1/n!(1!+2!+… +n!))

1) First of all, {sin [π √ n (n + 1)]} ^ 2 = {sin [π √ n (n + 1)]} ^ 2 - [sin (π n + π / 2)] ^ 2 + [sin (π n + π / 2)] ^ 2, and {sin [π √ n (n + 1)]} ^ 2 - [sin (π n + π / 2)] ^ 2 - [sin (π n + π / 2)] ^ 2