Simple operation 14 + 15 + 16 +How much is 45 + 46?

Simple operation 14 + 15 + 16 +How much is 45 + 46?

=（14+46）+（15+45）+...
There are (46-14 + 1) items in total
=（14+46）*(46-14+1）/2
=60*23/2
=30*33
=990

It is known that the domain of definition and the range of value of the function f (x) = 2x2 + 4x + 1 are the range of real number a obtained by [- 1, a] (a > - 1)

f(x)=2x²+4x+1=2(x+1)²-1
When x = - 1, y = - 1
To make both the definition field and the value field be [- 1, a]
Then f (a) = a
2a²+4a+1=a
∴ 2a²+3a+1=0
(2a+1)(a+1)=0
A = - 1 or a = - 1 / 2
The value of real number a is - 1 / 2

If the width of the rectangle is increased by 3cm, the area of the rectangle will be increased by 24cm?

Suppose the width is x and the length is 2x
2x(x+3)-2x*x=24
6x=24
x=4
Original area = 4 * 8 = 32

What are the four operation symbols to be filled in the middle of 5? At last, they are equal to 24

5×5-5÷5=24

The sum of the first n terms of the sequence {an} is Sn, S1 = 1, S2 = 2 and Sn + 1-3sn + 2sn-1 = 0 to judge whether {an} is an equal ratio sequence

Sn+1-3Sn+2Sn-1=0
Sn+1-Sn-(2sn-2Sn-1)=0
an+1-2an=0
an+1=2an
Is an equal ratio sequence

The area of a rectangle and a square is 1225cm2, and that of a circle is 1256cm2? Which is the smallest? If the areas of these three figures are equal, can you find the size relationship between their girths?

The area of a rectangle and a square is 1225cm2, and that of a circle is 1256cm2. The maximum perimeter of the three figures is rectangle, and the minimum is circle. When the area of the three figures is equal, the relationship of their perimeter is reversed, that is, rectangle > square > circle

Calculation (write out the main process, in which the first and fourth questions are simplified) & nbsp; ① 3.6-2.8 + 7.4-7.2 ② (1-0.05) △ 1.9 + 0.1 ③ 429 × [1 - (34-38)] ④ 817 △ 23 + 123 × 917

①3.6-2.8+7.4-7.2=（3.6+7.4）-（2.8+7.2）=11-10=1；②（1-0.05）÷1.9+0.1=0.95÷1.9+0.1=0.5+0.1=0.6；③429×[1-（34-38）]=429×[1-38]=429×58=558；④817÷23+123×917=（817+917）×123=1×123=123．

If a set of data x1, X2 If the average of XN is 2 and the variance is 9, then the data are 2x1-3, 2x2-3 What are the average and variance of 2xn-3?

∵ a set of data x1, X2 X = 2, variance is S2 = 9, then another set of data 2x1-3, 2x2-3, 2x3-3 X ′ = 2 × 2-3 = 1, the variance is s ′ 2, ∵ S2 = 1n [(x1 -. X) 2 + (X2 -. X) 2 +] +（xn-.x）2]=9，∴S′2=1n[（2x1-1-2.x+1）2+（2x2-1-2.x+1）2+… +（2xn-1-2.x+1）2]=1n[4（x1-.x）2+4（x2-.x）2+… +4 (xn -. X) 2], = 4s2, = 4 × 9 = 36, a: the mean and variance are 1 and 36 respectively

Uncle Li's living room is 7 meters long and 4 meters wide. If you want to lay such tiles on the living room (5 decimeters long and 4 decimeters wide), how many pieces should you prepare at least?

7 m = 70 decimeters 4 M = 40 decimeters
70*40=2800
5*4=20
2800 / 20 = 140 pieces

Minimum value of 8-2 of X + X by mean value theorem

Title:
The minimum value of X + 8 / X - 2 can be obtained by mean value theorem
It is proved that:
X+8/X-2
≥2√(X*8/X)-2
=2√8-2
=4√2-2
Where x > 0, the equal sign holds when x = 8 / x, that is, X & sup2; = 8, x = 2 √ 2