The general term formula of known sequence {an} is an = (n + 2) * (9 / 10) ^ n. when n takes what value, an takes the maximum value? Try to find the maximum value

The general term formula of known sequence {an} is an = (n + 2) * (9 / 10) ^ n. when n takes what value, an takes the maximum value? Try to find the maximum value

an=(n+2)*(9/10)^n
a(n+1)=(n+3)*(9/10)^(n+1)
a(n+1)/an=[(n+3)*(9/10)^(n+1)]/[(n+2)*(9/10)^n]
=9(n+3)/[10(n+2)]
When a (n + 1) / an ≥ 1, an is an increasing sequence
That is, 9 (n + 3) / [10 (n + 2)] ≥ 1
The solution is n ≤ 7, that is, an is increasing when n ≤ 7 and decreasing when n > 7
So when an is n = 7, the maximum of an is A7 = 9 * (9 / 10) ^ 7 = 9 ^ 8 / 10 ^ 7

45 of number a is number B, 23 of number B is number C, and number C is 30. What's the number a? (don't use equations)

The number of a is 56.25

If the length of the hypotenuse is 5.5cm, what is the length of the other right side of a right triangle whose length of a right side is 3cm

Let the side length of another right angle side be x.3 ^ 2 + x ^ 2 = 5.5 ^ 2 9 + x ^ 2 = 30.25 30.25-9 = x ^ 2 21.25 = x ^ 2 x = (radical 85) / 2 answer:

3 / 4 of a number is 30 more than 9 / 20 of 120

This number is (120 × 9 / 20 + 30) △ 3 / 4 = 112

Mr. Liu: let a be mxn matrix, B ≠ 0, and R (a) = n, then the system of linear equations AX = B () a has unique solution, B has infinite solutions, C has no solution, D may have no solution
Why do you choose D? I think I should choose a

R (a) = n does not guarantee R (a, b) = R (a), so (a) is wrong
R (a) = n can only guarantee the uniqueness of solutions when the equations have solutions

When processing a batch of parts, the work efficiency ratio of Party A and Party B is 5:4
1. If Party A and Party B complete half of each, it will take party a 12 hours to complete, and how many hours will Party B complete?
How many hours will it take if Party A and Party B complete the task together?
We need the formula!

1.
12 x 5 / 4 = 15 hours
two
A alone: 2 x 12 = 24 hours, every hour: 1 / 24
2 x 15 = 30 hours, 1 / 30 per hour
If Party A and Party B complete the task together, it will take 1 / (1 / 24 + 1 / 30) = 40 / 3 = 13 and 1 / 3 hours

(1) 2 (x + 15) - 21 = 3x-15 (2) 3 (x + 8) = 5x + 8 (3) 4 (x + 5 * 0.8) = 7x + 5 * 0.8 (4) x = 2 * [1.25 (X-10) - 10] equation,

(1)2(x+15)-21=3x-15
2x+30-21=3x-15
-x=-24
x=24
(2)3(x+8)=5x+8
3x+24=5x+8
2x=-16\x=8
(3)4(x+5*0.8)=7x+5*0.8
4x+16=7x+4
3x=-12
x=-4
（4）x=2*［1.25（x-10）-10］
x=2.5(x-10)-20
x=2.5x-45
-1.5x=-45
x=30

The weight ratio of grain in warehouse A and warehouse B is 7:5. If 20 tons are transported from warehouse A to warehouse B, the weight ratio of grain in warehouse A and warehouse B is 2:3
How much grain did the two warehouses have?

The total number remains unchanged
The proportion of a in the total: 7 △ 7 + 5 = 7 / 12
A now accounts for 2 / 5 of the total
Total: 20 ÷ (7 / 12-2 / 5) = 1200 / 11 tons
A: 1200 / 11 × 7 / 12 = 700 / 11 tons
B: 1200 / 11-700 / 11 = 500 / 11 tons

Solution equation: 2 / 5y-1 / 8 (2y-1) = 1

16y-5(2y-1)=40
16y-10y+5=40
6y=35
y=35/6

Simple algorithm of 2 divided by 2-3 divided by 2-3 divided by 2

2/（2/3）-（2/3）/2
=2*（3/2）-（2/3）/2
=3-1/3
=8/3
=Two and two thirds