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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°

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Answer:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

Step-by-step explanation:

The sum of x and y is 28. In other words, x plus y equals 28 and can be written as equation A:

x + y = 28

The difference between x and y is 6. In other words, x minus y equals 6 and can be written as equation B:

x - y = 6

Now solve equation B for x to get the revised equation B:

x - y = 6

x = 6 + y

Then substitute x in equation A from the revised equation B and then solve for y:

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y = 11

Now we know y is 11. Which means that we can substitute y for 11 in equation A and solve for x:

x + y = 28

x + 11 = 28

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Summary: The sum of two numbers is 28 and their difference is 6. What are the two numbers? Answer: 17 and 11 as proven here:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

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2 years ago
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Step-by-step explanation:

As it is given that

cosФ= 3/2

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Now in quadrant 4 we know that by the rules of trigonometry that

cos Ф is positive in 4th quadrant also in 4th quadrant

and sinФ is negative in 4th quadrant

also we know that by simple rules of trigonometry in a right angled triangle

cos Ф=\frac{Base}{Hypotenuse} =\frac{3}{2}

now from the law of trigonometry

cos²Ф+sin²Ф=1

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solving the equation

sin²Ф=1-cos²Ф

Putting in the values of cos Ф

sin²Ф=1-(\frac{3}{2})^{2}

sin²Ф=1-(\frac{9}{4})

solving the fraction

sin²Ф=(\frac{4-9}{4})

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so taking square root of both sides

\sqrt{sin^{2}\alpha}=\sqrt{\frac{-5}{4} }

here

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as we know that in imaginary numbers

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And in the given values we can see that it is none of the values

Also seeing the question we can see that the question is absurd because

cos Ф= base / hypotenuse

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but in real geometry this is the rule that hypotenuse can never be smaller then base either it is equal to base or greater then base

the formula for finding value of finding hypotenuse is

hypotenuse ² = base ² + perp ²

so this formula shows that if perp is 0 then hypotenuse will be equal to base

in other cases it would be greater then base





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