English translation

I'm a graduate student, so I don't have any English textbooks on hand. If you want to send the original text, I'll translate it for you

Translation of the last paragraph of section B 2B

It's a good way to relax by surfing the Internet or watching game shows, but we think the best way is through exercise. It's good for both physical and mental health. For example, sports activities are fun. When you exercise together, you can spend time with friends and family. Please remember: "old habits are hard to change". So start exercising before it's too late!

Translation of three essays in Section B 2B, unit 3, Grade 8,

My mother told me a good friend is like a mirror. I'm quiet and more serious than most kids.That 's why I like reading books and I study harder i...

How to prove that for any two positive integers m, n (M > n), m ^ 2 + n ^ 2, m ^ 2-N ^ 2, 2Mn, these three numbers are a group of Pythagorean arrays
Reading Pythagorean array and Fermat's second natural paragraph

a=m^2+n^2
b=m^2-n^2
c=2mn
b^+c^2=(m^2-n^2)^2+(2mn)^2
=m^4-2m^2*n^2+n^4+4m^2*n^2
=m^4+2m^2*n^2+n^4=(m^2+n^2)=a^2
That is: B ^ 2 + C ^ 2 = a ^ 2
Therefore, m ^ 2 + n ^ 2, m ^ 2-N ^ 2, 2Mn are Pythagorean arrays

In a division formula, the sum of divisor, divisor and quotient is 240, the quotient is 3, and the divisor is 240

Divisor = 3 divisor
So 3 divisor + divisor + 3 = 240
The divisor is 237 / 4
The divisor is 237x3 / 4 = 177.75

Vertical proof of space rectangular coordinate system
Example: given m (a, a, a) n (a, 2a, 2a) a (0,0,2a) B (2a.2a.0) C (0,2a, 0) verification: Mn is perpendicular to the plane ABC. Please try to be simple

Vector Mn = (0, a, a);
The vector AB = (a, 2a, - 2A);
Vector BC = (- 2A, 0,0)
Vector Mn * vector AB = 0; vector Mn * vector BC = 0
So Mn vertical AB; Mn vertical BC;
Obviously AB and BC intersect
So Mn is perpendicular to plane ABC

It is known that sin α = 35, α is the second quadrant angle, and Tan (α + β) = 1, then the value of Tan β is______ ．

Because α is the second quadrant angle, sin α = 35, so according to sin2 α + Cos2 α = 1, we get: cos α = - 45, then Tan α = sin α, cos α = - 34; and because Tan (α + β) = Tan α + Tan β 1 − Tan α, Tan β = 1, we substitute the value of Tan α = - 34 into − 34 + Tan β 1 + 34tan β = 1, namely - 34 + Tan β = 1 + 3

Composition, my hobby, about dance, 400 words, now

1. My hobby is dance. When I was in grade one, one day in music class, the teacher said, "those who want to go to the cygnet dance class come here to sign up." so I went to the teacher to sign up. Next Tuesday, Friday and Saturday, I will go to the cygnet dance class to learn dance

Mathematical problems of log
2 + log 2 (bottom) 4 = 3x-1

Log 2 (bottom) 4 = 2 this is a formula! Brother!
2 + log 2 (bottom) 4 = 3x-1
==》
2 +2 =3x-1
==》
5=3x
==?
x=5/3

Why B = {y | y ≥ (4ac-b & # 178;) / 4A} when a > 0, and when a

a> When a is greater than 0, B = {y | y ≥ (4ac-b # 178;) / 4A}
a

English translation