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kobusy [5.1K]
2 years ago
15

Find the length of the longest line segment that can be drawn on a rectangular board 3.07m by 2.24m

Mathematics
1 answer:
nikklg [1K]2 years ago
3 0
For rectangle
l=3.07m
b=2.24m
so longest side that can be drawn is diagonal of rectangular board
=squareroot l^2+b^2
=squareroot3.07^2+2.24^2
=squareroot9.4249+5.0176
=squareroot14.4425
=3.80
So longest line that can be drawn in rectangular board is 3.80m
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Both copy machines reduce the dimensions of images that are run through the machines. Which
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<u>Answer:</u>

<u>As the number of copies increases The dimension of images continues to decrease until reaching 0. </u>

<u>Step-by-step explanation:</u>

Remember, that the term dimension refers not to an unlimited/unending length but to a specific measurable length.

Therefore, as both copy machines reduces the dimensions of images that are run through the machines over time the dimensions of images would decrease until reaching 0; Implying that the dimension is so small to be invisible, in a sense becoming 0.

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Answer:

(2.4, -1.2)

Step-by-step explanation:

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

D

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