There are 8 comic books. Story books are half of comic books and interesting mathematics. Interesting mathematics is equal to the number of comic books and story books. How many story books?

There are 8 comic books. Story books are half of comic books and interesting mathematics. Interesting mathematics is equal to the number of comic books and story books. How many story books?


Storybooks account for 1 / 2 of the total: 1 / 2 (1 / 2 + 1) = 1 / 3
Interesting mathematics accounts for 1 / 2 of the total
Then comic strips account for 1-1 / 2-1 / 3 = 1 / 6 of the total
The total number is: 8 △ 1 / 6 = 48 copies
Story book: 48 × 1 / 3 = 16



Two interesting math problems of grade one, hee hee, let's see which math genius can answer them!
1. Observe the law of the formula, and calculate (- 1) + 2 + (- 3) + 4 + (- 5) + 6 + +100=?
2. Observe the law of the formula and calculate | 1 / 3 + (- 1 / 2) | + | 1 / 4 + (- 1 / 3) | + | 1 / 5 + (- 1 / 4) | + +|1 / 2010 + (- 1 / 2009) | =?
These two questions are similar to the arithmetic series. Please observe these two questions carefully. Thank you here. But please note that you can't just put a number. Can you write down the process of doing the questions? Thank you here!


1. The original formula = (2-1) + (4-3) + (6-5) + +(100-99)
=1×(100÷2)=1×50=50
2. Original formula = 1 / 2-1 / 3 + 1 / 3-1 / 4 + 1 / 4-1 / 5 + +1/2009-1/2010
=1 / 2-1 / 2010
=1004/2010
=502/1005



Mr. Zhang bought 4 copies of interesting mathematics and 4 copies of Story King, paid the salesperson 20 yuan and recovered 7.6 yuan
6 yuan, then how much is each story king? Use the equation to make it clear


Set X Yuan for each story
4(1.6+x)=20-7.6
x=1.5



Finding integral ∫ ((x ^ 2) / sqrt (x ^ 2 + X + 1)) DX


The following two indefinite integral formulas can be proved by trigonometric substitution
∫√(x^2+a^2)dx=(x/2)√(x^2+a^2)+(a^2/2)ln[x+√(x^2+a^2)]+C,
∫dx/√(x^2+a^2)=ln(x+√(x^2+a^2)+C,
The original formula = ∫ (x ^ 2 + X + 1) DX / √ (x ^ 2 + X + 1) - (1 / 2) ∫ (x + 1) DX / √ (x ^ 2 + X + 1) - (1 / 2)) ∫ DX / √ (x ^ 2 + X + 1)
=∫√(x^2+x+1)dx-(1/2)∫(d(x^2+x+1)/√(x^2+x+1)-(1/2)∫dx/√(x^2+x+1)
=∫√[(x+1/2)^2+3/4]d(x+1/2)-(1/2)(x^2+x+1)^(-1/2+1)/(-1/2+1)-∫d(x+1/2)/√[(x+1/2)^2+3/4]
=(1/2)*(x+1/2)√(x^2+x+1)+(3/8)ln[x+1/2+√(x^2+x+1)]-√(x^2+x+1)-(1/2)ln[x+1/2+√(x^2+x+1)]+C
=(1/2)*(x+1/2)√(x^2+x+1)-(1/8)ln[x+1/2+√(x^2+x+1)]-√(x^2+x+1)+C.



0, - 3,8, - 15,24, (), () and - 11, - 6,4,9,19, (), () find the law


The rule of 10, - 3,8, - 15,24, (- 35), (48) is to take these numbers as absolute values, then the difference is an odd number sequence starting with 3, 0, 3, 8, 15, 24, 35, 48, and the difference is 357 9 11 13, then according to the above rule, a positive number, a negative number, a positive number, and a negative number



Integers that are not zero can be regarded as false fractions whose denominator is one___ (judge right or wrong)


All integers that are not zero can be regarded as false fractions whose denominator is 1



The range of integer and natural number is large


If integers include natural numbers, the range of integers is large



Find rules 7,5,14,4,21,3, (), ()
7,5,14,4,21,3,( ),( )


Halo 7, 5, 14, 4, 21, 3, (28), (2) odd items increase by 7 or multiple of 7 each time, even items decrease by 1 each time



If n is a natural number, try to prove that (n + 11) 2-N 2 can always be divided by 11


It is proved that: ∵ (n + 11) 2-n2 = N2 + 22n + 112-n2 = 22n + 112 = 11 (2n + 11); 11 can be divisible by 11 (2n + 11), and (n + 11) 2-n2 can always be divisible by 11



It is known that the function f (x) is an odd function defined on R with a period of 3,
And when 0


F (x) = ln (X & sup2; - x + 1) = 0
That is, X & sup2; - x + 1 = 1, that is, X (x-1) = 0
The solution is x = 0 or x = 1
∵0