The area of a rectangle is 864 square meters, and its length is 12 meters more than its width

The area of a rectangle is 864 square meters, and its length is 12 meters more than its width

Let the length of a rectangle be a and the width be A-12
A (A-12) = 864 leads to a = 36
So the length and width of the rectangle are 36 and 24, respectively

A rectangle is 4 / 5 meters long and 4 / 3 times wide. How many square meters is the area of this rectangle?

Width = 4 / 5 △ 4 / 3 = 3 / 5m
Area = 4 / 5 × 3 / 5 = 12 / 25 m2

What is the problem-solving process of (- 2) ^ 50 + (- 2) ^ 49 + (- 2) ^ 48 + (- 2) ^ 47 +... + (- 2) + 1?
Let's use this conclusion: (x-1) [x ^ n + x ^ (n-1) + ·· + X + 1] = x ^ (n + 1) - 1
Don't give me a direct answer
Don't set s either

Let's use the conclusion you gave, let x = - 2, then
(-2-1)[(-2)^50+(-2)^49+…… +(-2)+1]=(-2)^51-1
So (- 2) ^ 50 + (- 2) ^ 49 + +(-2)+1=[(-2)^51-1]/[(-2)-1]=(-2^51-1)/(-3)=(2^51-1)/3

Find lim2 ^ n * sin (x / 2 ^ n) (n tends to infinity and X is not a constant of 0)

lim(n→∞) 2^n*sin(X/2^n)
=lim(n→∞) 2^n*(X/2^n)
=X
When x → 0, SiNx and X are infinitesimals of the same order, that is, LIM (x → 0) SiNx = x, denoted as SiNx ~ X

What is the remainder of 2009 437 times - 40 divided by 23?

A:
Because: 437 divided by 23 equals 19;
So: 2009 437 phase multiplication and division with 23 no remainder;
So: 2009 437 times - 23 divided by 23 has no remainder;
So: 2009 437 times minus 23 times divided by 23 has no remainder;
So: 2009 437 multiply - 40 and subtract 6 divided by 23, there is no remainder;
So: the remainder of 2009 437 multiplied by - 40 divided by 23 is 6

17.8 / (1.78 * 4)

17.8/(1.78*4)
=17.8÷1.78÷4
=10÷4
=2.5

High school mathematics, solving the second definition of conic

Ellipse is a kind of conic (some people call it conic section). Now there are two definitions in high school textbooks
1. The sum of the distances from two points on the plane is the set of fixed points (the fixed value is greater than the distance between two points) (these two fixed points are also called the focus of the ellipse, and the distance between the focus is called the focal length);
2. The set of points on the plane whose ratio of the distance to the fixed point and the distance to the fixed line is constant (the fixed point is not on the fixed line, the constant is a positive number less than 1) (the fixed point is the focus of the ellipse, and the line is called the directrix of the ellipse). These two definitions are equivalent
The function and significance of the Quasilinear and focus are the same. They are used to determine the shape and position of ellipse, hyperbola and parabola. X = A / C
The unified definition of eccentricity is the ratio of the distance from the moving point to the focus and the distance from the moving point to the guide line
Eccentricity is defined as the ratio of the distance between two focal points of an ellipse to the length of its major axis
Eccentricity = (RA RP) / (RA + RP), RA is the distance from the far point, RP is the distance from the near point
Eccentricity of circle = 0
Eccentricity of ellipse: e = ∈ C / a (0,1) (C, half focal length; a, long half axis (ellipse) / real half axis (hyperbola))
Eccentricity of parabola: e = 1
Eccentricity of hyperbola: e = ∈ C / a (1, + ∞) (C, half focal length; a, long half axis (ellipse) / real half axis (hyperbola))

Known inequality system x + 2 > m + N and X-1

From x + 2 > m + N and x-1m + n-2; X

Take one fourth from one third of a kilogram of wheat, how many parts are left? How many kilograms are left?

What's left
=1-1 / 4
=3 / 4
There is still weight left
=1 / 3 × 3 / 4
=1 / 4 (kg)

In the sequence {an}, A3 = 1, a1 + A2 + +an=an+1（n=1，2，3…） (I) find A1, A2; (II) find the first n terms and Sn of sequence {an};

(I) ∵ A1 = A2, a1 + A2 = A3, ∵ 2A1 = A3 = 1, ∵ A1 = 12, A2 = 12. (II) ∵ Sn = an + 1 = Sn + 1-sn, ∵ 2Sn = Sn + 1, Sn + 1sn = 2, ∵ Sn} is an equal ratio sequence with S1 = A1 = 12 and common ratio of 2