Add 2.5cm to the side length of a square to get a new square. The area of the new square is increased by 40.75cm

Add 2.5cm to the side length of a square to get a new square. The area of the new square is increased by 40.75cm

Let the side length of the original square be x, then
(X+2.5)(X+2.5)-X*X=40.75
5X+6.25=40.75
X=6.9
The length of the original square is 6.9 cm and the area is 47.61 square cm
With the increase of side length, the side length is 9.4 cm and the area is 88.36 square cm

1.5 with four operations, it is equal to 24

（5-1/5）*5=24

If the first n terms of sequence {an} and Sn = n ^ 2An, and A1 is not equal to 0, then what is an / an + 1 equal to

Sn=n^2 *an
S(n+1)-Sn=(n+1)^2 *a(n+1)-n^2 *an=a(n+1)
(n+1)^2 -n^2 *an/a(n+1)=1
an/a(n+1)=[(n+1)^2 -1]/n^2=1+2/n +1/n^2

The floor of a classroom is 8 meters long, 6 meters wide, and paved with 4-decimeter-long square bricks. How many square bricks do you need? If each square brick costs 60 yuan, how much will it cost?

8m = 80m, 6m = 60m
Classroom area: 80 × 60 = 4800 (DM & # 178;) [DM = decimeter]
Square brick area: 4 × 4 = 16 (DM & # 178;)
Required square brick: 4800 △ 16 = 300 (pieces)
Cost: 300 × 60 = 18000 yuan

How to calculate 2 / 7 + (5 / 7-2 / 5) × 2 / 5?

Original form
=2/7+(5/7-2/5)×5/2
=2/7+5/7*5/2-2/5*5/2
=2/7+25/14-1
=4/14+25/14-14/14
=（4+25-14）/14
=15/14

Mathematical formula (x1 / Y1 + x2 / Y2 + X3 / Y3 +. + xn / yn) / n what is its simplified formula?

[ ∑（Xn/Yn）]/n

The perimeter of the rectangle is 20 cm and the area is 10 square meters. How long is the diagonal of the rectangle?

Rectangle length + width = 10 (1) a + B = 10,
Length × width = 10 (2) AB = 10, 2Ab = 20,
∴AC²=a²+b²
=（a+b）²-2ab
=100-20
=80.
So diagonal AC = √ 80 = 4 √ 5

Y = x / (x ^ + 2) maximum mean value theorem

If x = 0, y = 0
If x ≠ 0, y = 1 / (x + 2 / x)
According to the basic inequality, the denominator is greater than or equal to 2 radical 2 or less than or equal to - 2 radical 2
After taking the reciprocal, the range is - 2 / 4 root to 2 / 4 root (except 0)
In conclusion, y belongs to the closed interval between - 4 radical 2 and 4 radical 2
So the maximum value is 2 / 4

∫ how to find arcsinx * arccosxdx integral method

First, we simplify t = arcsin (x) x = sin (T) arccos (x) = π / 2 - t ∫ t (π / 2 - t) DSIn (T) = t (π / 2 - t) sin (T) -∫ sin D (t (π / 2 - t)) = t (π / 2 - t) sin (T) -∫ (π / 2-2t) sin DT = t (π / 2 - t) sin (T) + ∫ (π / 2-2t) DCOS (T) = t (π / 2 - t) sin (T) +

The perimeter of a rectangle is 42cm. It is divided twice (A and B in the figure). The area ratio of the four parts in figure a is a: B: C: D = 1:2:4:8, and the area ratio of the four parts in Figure B is m: n: s: P = 1:3:9:27. It is known that the difference between the width and the length of rectangle D and P is 1:3. How many square centimeters is the area of the original large rectangle?

Let the length of the original rectangle be x and the width be y, then x + y = 21. According to the proportional relation of area, the length of D is 45x and the width is 23y, the length of P is 910x and the width is 34y, (34y-23y): (910x-45x) = 1:3, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (34y-23y) × 3 = (910x-45x) × 1, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp;        94y-2y=110x，                      14y=110x，                     x：y=14：110，   &The & nbsp; & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp; & nbsp & & nbsp & nbsp & & nbsp; & & nbsp; & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & nbsp & nbsp; & & nbsp & nbsp & nbsp; & & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp y = 21: 5y2 + y = 21, & nbsp; 72y = 21, & nbsp; & nbsp; & nbsp; & nbsp; Y = 6, then x = 6 × 52, = 15; so the area of the original rectangle is: 15 × 6 = 90 (square centimeter). Answer: the area of the original large rectangle is 90 square centimeter