Given that the perimeter ratio of two circles is 4:5, what is the area ratio of the two circles? We need both the train of thought and the formula

Given that the perimeter ratio of two circles is 4:5, what is the area ratio of the two circles? We need both the train of thought and the formula

The girth ratio is 4:5
The radius ratio is 4:5
The area ratio is the square of the radius ratio, which is 16:25

In the oblique triangular prism abc-a ′ B ′ C ', the length of each edge is a. a ′ B = a ′ C = A. It is proved that the BCC ′ B ′ on the side is a rectangle. The height of the prism is obtained

It is proved that taking the midpoint D, d 'of BC, b'c' respectively to connect a'B, a'c, a'd, DD ', ad
It is shown that BC is perpendicular to plane a'dd '
It is obvious that BC is perpendicular to ad, (1) the reason is that the length of each edge of triangle ABC is a, and D is the midpoint
Because a ′ B = a ′ C = a, the triangle a ′ BC is an isosceles triangle, and D is the middle point of the bottom edge, so a ′ D is perpendicular to BC (2)
And because ad, a'd intersects at point D
From (1) (2)
BC perpendicular to plane AA'd'd
And because DD 'is in plane AA'd'd,
So DD 'is perpendicular to BC
And because DD 'is parallel to BB'
So BC is perpendicular to BB ', because the side BCC' B 'is a parallelogram
So the side bcc'b'is rectangular
It is proved that the height of a prism is the height on a'd 'of the triangle add' side
Obviously, a'd = a'd '= 2 / 2 root 3a, so the triangle add' is an isosceles triangle
All three sides know that it's good to ask for the height of the waist,
It turns out that the root of three is 3a
Ask again if you don't ask!

Know the chord length, arc length and the height from chord length to the top of arc length to calculate the sector area
The chord length is 1.1m, the arc length is 2.09m and the height is 0.5m

Let R be the radius, then
(R-0.5)²+(1.1/2)²=R²
The radius is calculated by sector area = 1 / 2 × arc length × radius
Center angle n = 360-4arctan [(1.1 / 2) 0.5]
The sector area is (n / 360) * π R & # 178

Ask a question of [summation of series]
Un=n^(n+1/n)/(n+1/n)^n
How to find the limit of quotient of (n + 1 / N) power and (n + 1 / N) power with general term n
There seems to be a limit like (1 + 1 / N2) ^ n after flowering. It's different from the special limit. How to find it
Again, it's the problem of finding the sum of series to judge whether it converges. Then the limit of the general term is 1, not 0, so it doesn't converge. But I'm not sure how to find it

This can be calculated, the limit is really 1, I've sent it to you

Notes on the ancient poems of berthing boats in Guazhou

"Yishuijian" is a positive phrase with the same internal structure as "zhizhijian", "jibujian", "yixianjian" and "yinianjian". The central word is "Jian", and the limited component is "Yishui". The whole sentence means that Jingkou and Guazhou are within the distance of a (horizontal) River, Wang Anshi wanted to talk about the proximity of Jiangnan and Jiangbei, not their isolation

The line y = KX + 1 and the ellipse x ^ 2 / 5 + y ^ 2 / M = 1 always have a common point, the range of M?
There is a problem with the teacher's solution, as follows
Our teacher's solution is as follows: if y = KX + 1 passes through the point (0,1), it requires that the line intersects the ellipse, that is, if the point is inside or on the ellipse, substitute (0,1) into the elliptic equation less than or equal to 1, and M is not 5
Why should (0,1) be substituted into the elliptic equation less than or equal to 1? What is the result?
Then I found that all such problems only need to substitute the fixed point into the ellipse and less than or equal to 1, and then go on
We can solve the range. Why? What is greater than or equal to one?
What is the meaning of less than or equal to 1? Why can we solve a preliminary range of M?

Substituting in and finding less than or equal to 1 ensures that the point is in the interior of the ellipse or on the ellipse, which is similar to judging the position relationship between a point and a circle
That is to say, the point whose sum of distances to two focal points is less than or equal to 2a is on or in the ellipse
We get that X & sup2 / A & sup2; + Y & sup2 / B & sup2; ≤ 1 represents the upper or inner part of the ellipse

The circumference of a rectangle is 72cm, and its length is twice of its width. How many square centimeters is its area?

Let the width be X
2*(x+2x)=72
6x=72
x=12
Length: 12x2 = 24 (CM)
Area: 24x12 = 288

Given cos θ = - 3 / 5, θ∈ (Pie / 2, pie), find sin (θ + Pie / 3)
right off!
Given Tan α = 2, find the value of Tan (α - π / 4)
Given cos θ = - 5 / 13, θ∈ (pie, 3 Pie / 2), find cos (θ + π / 6)

cosθ=-3/5,θ∈（π/2,π）,
So sin θ > 0
Because (sin θ) ^ 2 + (COS θ) ^ 2 = 1
So sin θ = 4 / 5
sin(θ+π/3)=sinθcosπ/3+cosθsinπ/3=(4/5)*(1/2)+(-3/5)*(√3/2)
=(4-3√3)/10

Given that there is only one circle passing through points a (0, 1), B (4, a) and tangent to X axis, the value of a and the equation of the corresponding circle are obtained

Consider two cases: (I) let the center coordinate of the circle be (x, y), when point B is the tangent point, B is on the x-axis, so a = 0. Then B (4, 0), so the midpoint coordinate of AB is (2, 12), and the slope of the straight line AB is 1 − 00 − 4 = - 14, then the slope of the vertical line AB is 4, so the equation of the vertical line AB is Y-12 = 4 (X-2) and x = 4, so the equation of the circle is: (x-4) 2 + (Y − 172) 2 = (172) 2; (II) when a = 1, AB is parallel to X axis, then the vertical equation of AB is x = 2, let the center coordinate of the circle be (2, y), according to Pythagorean theorem: y2 = 22 + (Y-1) 2, the solution is y = 52, so the equation of the circle is: (X-2) 2 + (Y − 52) 2 = (52) 2 The range is: (X-2) 2 + (Y − 52) 2 = (52) 2

2. In the function, when the independent variable satisfies (), the image is in the first quadrant
2. In the function - 2x + 3, when the independent variable x satisfies (), the image is in the first quadrant
Forget to read it!

Calculate the intersection point with X, Y axis. Or draw the image directly, and the result is 0 to 1.5