Know the radius and chord length, find the arc length. Radius 1350, chord length 300, find the corresponding arc length?

Know the radius and chord length, find the arc length. Radius 1350, chord length 300, find the corresponding arc length?

Radius r = 1350, chord length L = 300, find the arc length C?
The central angle of the arc is a
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((300/2)/1350)
=759 degrees
=12.759*PI/180
=222682 radians
C=R*A=1350*0.222682=300.62

Sum 1 and 1 / 2, 3 and 1 / 4, 5 and 1 / 8, 7 and 1 / 16
1 and 1 / 2, 3 and 1 / 4, 5 and 1 / 8, 7 and 1 / 16
Find the sum of the first n terms of the above sequence!

a1=1+1/2
a2=3+1/4
a3=5+1/8
a4=7+1/16
.
an=(2n-1)+1/2^n
Sn=[1+3+5+7+...+(2n-1)]+(1/2+1/4+1/8+...+1/2^n)
=(2n-1+1)*n/2+1-1/2^n
=n^2＋1-1/2^n

A poem about berthing a boat in Guazhou!

Berthing in Guazhou
Song Dynasty - Wang Anshi
There is a water room in Guazhou, Jingkou,
Zhongshan is only a few mountains apart
The spring breeze is green on the South Bank of the river,
When will the moon shine on me?
Note: the poet passed by Guazhou by boat and missed the former residence of Jinling (Nanjing). There is only a Yangtze River between Jingkou and Guazhou. Zhongshan, where I live, is hidden behind several mountains. The warm spring wind blows green the fields in the south of the Yangtze River. When will the bright moon shine on me and return to my home at the foot of Zhongshan?

The equation x ^ 2 / M-Y ^ 2 / (m-1) = 1 represents an ellipse with focus on the Y axis, then the value range of M is

Ellipse
Then x ^ 2 / M + y ^ 2 / (1-m) = 1
m>0,1-m>0
Focus y-axis
Then 1-m > m > 0
So 0

The circumference of a rectangle is 48 cm, and its length is five seventh of its width. What's the area of a rectangle

The sum of length and width is 48 △ 2 = 24 (CM)
The width of rectangle is: 24 (1 + 5 / 7) = 14 (CM)
The length of the rectangle is: 24-14 = 10 (CM)
Rectangular area: 14 × 10 = 140 (cm2)

If cos (α + β) = 513 and sin (α - β) = - 45, then Cos2 α is the best=______ ．

∵ α, β ∈ (0, π 2), if cos (α + β) = 513, sin (α - β) = - 45, sin (α + β) = 1213, cos (α - β) = 35, so Cos2 α = cos [(α + β) + (α - β)] = cos (α + β) cos (α - β) - sin (α + β) sin (α - β) = 6365, so the answer is 6365

As shown in the figure, it is known that the two ends of the diameter AB passing through the circle O are the perpendicular lines am, BN and the perpendicular feet of the tangent line passing through the other point C on the circle O are m and N respectively
Verification: ab = am + BN

Certification:
Connect to OC
∵ Mn is tangent
∴OC⊥MN
∵AM⊥MN,BN⊥MN
∴AM//OC//BN
∵ o is the midpoint of ab
C is the midpoint of Mn
Mn is the median line of trapezoidal abnm
∴OC=（AM+BN）/2
That is am + BN = 2 * OC = ab

If point a (- 2, - 2) is on the image of inverse scale function y = KX (K ≠ 0), then when function value y ≥ - 2, the value range of independent variable x is______ ．

∵ point a (- 2, - 2) is on the image of the inverse scale function y = KX (K ≠ 0), the analytic expression of the inverse scale function is y = 4x, and its image is shown in the figure: from the function image, when the function value y ≥ - 2, x ≤ - 2 or x > 0. Therefore, the answer is: X ≤ - 2 or x > 0

(7.92-x) / (8-x) = 0.98

(7.92-X)/(8-X)=0.98
(7.92-X)=(8-X)0.98
7.92-x=7.84-0.98x
x-0.98x=7.92-7.84
0.02x=0.08
x=4

How to draw a function image like this and how to find it
y=f(x)=x 0≤x＜2
2 2≤x＜4
-x+6 4≤x＜6

This is a piecewise function
When 0 ≤ x ＜ 2, y = x is a segment of the linear function y = X,
When 2 ≤ x < 4, y = 2, it is a line segment parallel to X axis,
When 4 ≤ x ＜ 6, y = - x + 6 is a part of the linear function y = - x + 6
When drawing an image, pay special attention to the value range of the independent variable x
If you have any questions, please ask