<u>Answer-</u>
<em>After 76 swings</em><em> the angle through which it swings less than 1°</em>
<u>Solution-</u>
From the question,
Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.
So the angle of the second swing = 
Then the angle of third swing = 
So, this follows a Geometric Progression.

a = The initial term = 30
r = Common ratio = 
As we have to find the number swings when the angle swept by the pendulum is less than 1°.
So we have the nth number is the series as 1, applying the formula

Putting the values,


Taking logarithm of both sides,







Therefore, after 76 swings the angle through which it swings less than 1°
Answer:
The fraction is 1/4
Step-by-step explanation:
we know that
The area of an equilateral triangle, using the law of sines is equal to



where
x is the length side of the triangle
In this problem
Let
b ----> the length side of the regular hexagon
2b ---> the length side of the equilateral triangle
step 1
Find the area of the six triangles
Multiply the area of one triangle by 6
![A=6[x^{2}\frac{\sqrt{3}}{4}]](https://tex.z-dn.net/?f=A%3D6%5Bx%5E%7B2%7D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D%5D)

we have

substitute

step 2
Find the area of the regular hexagon
Remember that, a regular hexagon can be divided into 6 equilateral triangles
so
The area of the regular hexagon is the same that the area of 6 equilateral triangles

we have

substitute

step 3
To find out what fraction of the total area of the six triangles is the area of the hexagon, divide the area of the hexagon by the total area of the six triangles

Answer:
<h3>Domain [
-3 , ∞ ]</h3>
Step-by-step explanation:
Domain is the set of all inputs for which the given function is defined.
graphically it represents the shadow of the graph taken on the x axis from above and below the x axis
Here is the shadow will be formed from -3 till +∞, hence we have our domain as [-3 , ∞ ]
Answer:
13
Step-by-step explanation:
Answer:

Step-by-step explanation: