When a rectangular iron block with a bottom area of 4 square centimeter is put into a glass container with a bottom area of 20 square centimeter, the water in the container rises by 1 centimeter Ask for the height of the iron

Height of iron block = 20 × 1 △ 4 = 5cm

A rectangular iron block with a bottom area of 3 square centimeters is sunk into a glass container with a bottom area of 52.2 square centimeters

A rectangular iron block with a bottom area of 3 square centimeters is sunk into a glass container with a bottom area of 52.2 square centimeters. The water surface of the container is 1 cm higher than the original one. How many centimeters is the iron block high?
This iron block is (52.2-3) × 1 / 3 = 16.4 (CM)

A sealed rectangular glass jar is 50 cm long, 30 cm wide, 20 cm high and 10 cm deep. If the glass jar is erected, the water depth will be 10 cm?

A: at this time, the water depth is 25 cm

Let f (x) = 1 / 1 + X. the sequence {an} with all positive numbers satisfies A1 = 1, an + 2 = f (an). If A2010 = A2012, then the value of A20 + a11 is?
When n is an odd number, the recurrence relation shows that:
a3=1/2,a5=2/3,a7=3/5,a9=5/8,a11=8/13
And A2010 = A2012 = 1 / (1 + A2010)
When n is even,
a2=a2010=a2012
Its value is equation X1 / (1 + x)
That is, x ^ 2 + X-1 = 0
Ψ x = (- 1 ± root 5) / 2
And the number sequence is a positive number sequence,
Ψ A20 = (- 1 + radical 5) / 2
Ψ A20 + a11 = (13 with 5 + 3) / 26
I would like to ask: why A2010 = A2012 = 1 / (1 + A2010), we can get even number terms are equal. Thank you for your advice

It's too simple. Maybe you think too much
a2012= 1/(1+a2010) (1)
a2010 = 1/(1+a2008) (2)
from (2)
a2012 = 1/(1+a2008) (3)
from (1) and (3)
a2012 = a2008
Inductively
a2=a4=a6=.a2n

Let the function y = f (x) be a solution of the differential equation y "- 2Y '+ 4Y = 0. If f (x0) > 0, f' (x0) = 0, then the function f (x) increases monotonically in a certain field of point x0?

f'(x0)=0,y'=0
f(x0)>0,y>0
When y '' = 2Y '- 4yx0, f' (x)

What's the rule of 0,1,4,15,56209

The rules are as follows
1*4-0=4
4*4-1=15
15*4-4=56
56*4-15=209
If my answer is helpful to you, please select it as a satisfactory answer in time. Thank you~~

Can other non-zero natural numbers be transformed into pseudo fractions of denominators 1, 2, 3?

Certainly, according to the relationship between fraction and division, any integer can be transformed into a pseudo fraction of the specified denominator

On the problems of positive, negative, integer and natural numbers
Positive numbers contain decimals,
Negative numbers contain negative decimals,
Integers contain positive and negative numbers,
Natural numbers contain decimals, fractions,

Positive numbers contain decimals and fractions;
Negative numbers contain negative decimals and negative fractions;
Integers contain positive and negative numbers, but not 0;
Natural numbers are integers greater than or equal to 0

What are the following two numbers? 3, 7, 19, 55 (), ()

163 487

What is the maximum natural number that can be divided by 30 and has exactly 30 positive divisors

Let P1 ^ A1 * P2 ^ A2 *... * PN ^ an be the prime factor of positive integer decomposition,
Then the number of divisors is (a1 + 1) (A2 + 1) (A3 + 3)... (an + 1)
Because the number required in the question can be divided by 30, there must be prime factors 2,3,5,
Let this number be 2 ^ A1 * 3 ^ A2 * 5 ^ A3
Then its divisor number is (a1 + 1) (A2 + 1) (A3 + 1),
Because 30 = 2 * 3 * 5, this number has no prime factor except 2,3,5, so a1 + 1, A2 + 1, A3 + 1 can only be 2,3,5 or 3,2,5 or 5,2,3 or 5,3,2 or 2,5,3 or 3,5,2, there are 6
Then A1, A2, A3 can only take 1,2,4 or 2,1,4 or 4,1,2 or 4,2,1 or 1,4,2 or 2,4,1
That is, the six natural numbers are
2^1*3^2*5^4=11250
2^2*3^1*5^4=7500
2^4*3^1*5^2=1200
2^4*3^2*5^1=720
2^1*3^4*5^2=4050
2^2*3^4*5^1=1620
So to sum up, the maximum natural number is 11250

When a rectangular iron block with a bottom area of 4 square centimeter is put into a glass container with a bottom area of 20 square centimeter, the water in the container rises by 1 centimeter Ask for the height of the iron