1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aleksandr82 [10.1K]
3 years ago
12

A pendulum is set swinging. its first oscillation is through 30 and each succeeding oscillation is through 95% of the angle of t

he one before it. After how many swings is the angle through which it swings less than 1 degree?
Mathematics
1 answer:
Marat540 [252]3 years ago
8 0

<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 = (30\times \frac{95}{100})^{\circ}

Then the angle of third swing = (30\times (\frac{95}{100})^2)^{\circ}

So, this follows a Geometric Progression.

(30,\ 30\cdot \frac{95}{100},\ 30\cdot (\frac{95}{100})^2............,0)

a = The initial term = 30

r = Common ratio = \frac{95}{100}

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

T_n=ar^{n-1}

Putting the values,

\Rightarrow 1=30(\frac{95}{100})^{n-1}

\Rightarrow \frac{1}{30} =(\frac{95}{100})^{n-1}

Taking logarithm of both sides,

\Rightarrow \log \frac{1}{30} =\log (\frac{95}{100})^{n-1}

\Rightarrow \log \frac{1}{30} =(n-1)\log (\frac{95}{100})

\Rightarrow -1.5=(n-1)(-0.02)

\Rightarrow 1.5=(n-1)(0.02)

\Rightarrow n-1=\dfrac{1.5}{0.02}

\Rightarrow n-1=75

\Rightarrow n=76

Therefore, after 76 swings the angle through which it swings less than 1°

You might be interested in
Brainliest + Points!
LenaWriter [7]
Hey refer to attachment!!!

Draw straight line from 220 (in thousands ) to the plotted line. Draw line parallel to x-axis from point where it touches the plotted line to the y -axis.

It'll automatically meet at 500 which is the answer..

All you need to do is to see the graph carefully.

Hope it helps *_*

3 0
3 years ago
The area of a rectangle whose base measures 4 cm is greater than 24 cm. Which graph represents all possible values for the heigh
Bond [772]

Answer:

Whichever one shows >24

Step-by-step explanation:

Which ever one that is greater than 6

7 0
3 years ago
Read 2 more answers
1/7 + 6/7 equals1/7 + 6/7 equals
Ivanshal [37]

Answer:

7/7 = 1

Step-by-step explanation:

1/7 is one out of seven part plus 6/7 which is 6 out of seven parts. The denominator does not need to change because it is a common denominator. Just simply add the numerators, 1 and 6 and you get 7. The numerator is divided by the denominator (7/7) which equals to 1.

4 0
3 years ago
Read 2 more answers
On Sunday, a local hamburger shop sold a combined total of 378 hamburgers and cheeseburgers. The number of cheeseburgers was sol
ipn [44]

Answer:

The number of hamburgers sold was 126.

Step-by-step explanation:

Let h = number of hamburgers sold

let c = cheeseburgers sold

c+h = 378

c = 2h

Substitute c =2h into c+h =278

c+h =378

2h+h = 378

Combine like terms

3h = 378

Divide by 3

3h/3 =378/3

h =126

The number of hamburgers sold was 126.

5 0
3 years ago
Help i need the answer 7x-64=83+14x
dusya [7]

If you're trying to get x your answer would be -21.

3 0
3 years ago
Other questions:
  • Multiply.<br> 3/4 x -5 1/6
    10·1 answer
  • Sion 3x-2y for X = 7 and y = 3
    10·1 answer
  • The term that describes how long it takes a function to repeat its behavior is the
    15·2 answers
  • P − 4.8 less than or = to 6.
    11·2 answers
  • How do you find a slope
    6·1 answer
  • Danica is arranging flowers for a party. On each table, t, there will be a vase of 9 flowers and 3 bowls of flowers with f flowe
    14·1 answer
  • Look at the graph below. What is the slope of the line?
    15·1 answer
  • Tan 45°. tan² 30° tan 60° <br>slove it​
    8·1 answer
  • A vector U has initial point (-3,-2) and terminal point (-6,1) .<br> Write U in component form.
    13·1 answer
  • Interpreting Points on Graphs of Proportional Relationships
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!