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lys-0071 [83]
2 years ago
4

A bullet train travel at the speed of 365 km/h.In august 2001, singapore's national record for the men's 100 m sprint was set at

10.37 sec .How many times is a bullet train as fast as the fastest singaporean sprinter?
Mathematics
1 answer:
natali 33 [55]2 years ago
8 0

Answer:

Therefore bullet train is 10.5 times as fast as the fastest Singaporean sprinter.

Step-by-step explanation:

Given that,

A bullet train travels at the speed off 365 km/h.

365 km/h

=\frac{365\  km}{h}

=\frac{365\times 1000 \ m}{3600 \ s}    [ ∵1 km= 1000 m and 1 h = 3600 s]

=\frac {365 \times 5}{18} m/s

We know that,

Speed=\frac{Distance}{Time}

Singapore's national record for the men's 100 m sprint was set at 10.37 sec.

The speed of Singaporean sprinter is

=\frac{100 \ m}{10.37\ s}

Now,

\frac{\textrm{Sped of bullet train}}{\textrm{Sped of Singaporean sprinter}}

=\frac{\frac{365\times5}{18}}{\frac{100}{10.37}}

=\frac{365\times 5\times 10.37}{100\times 18}

=10.5

Therefore bullet train is 10.5 times as fast as the fastest Singaporean sprinter.

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Answer:

Option A

Option D

Option E

Step-by-step explanation:

we know that

If the height and base of triangle B are proportional to the height and base of triangle A

then

Triangle A and Triangle B are similar

Remember that

If two triangles are similar then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

\frac{h_A}{h_B} =\frac{b_A}{b_B}

where

h_A and h_B are the height of triangle A and triangle B

b_A and b_B are the base of triangle A and triangle B

In his problem we have

h_A=2.5\ cm\\b_A=1.6\ cm

substitute

\frac{2.5}{h_B} =\frac{1.6}{b_B}

Rewrite

\frac{2.5}{1.6} =\frac{h_B}{b_B}

\frac{h_B}{b_B}=1.5625

<u><em>Verify all the options</em></u>

A) we have

h_B=2.75\ cm\\b_B=1.76\ cm

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

\frac{2.75}{1.76}=1.5625

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

B) we have

h_B=9.25\ cm\\b_B=9.16\ cm

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

\frac{9.25}{9.16}=1.0098

The ratios are not equal

That means that are not proportional

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substitute the values in the proportion

\frac{3.2}{5}=0.64

The ratios are not the same

That means that are not proportional

therefore

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substitute the values in the proportion

\frac{1.25}{0.8}=1.5625

The ratios are the same

That means that are proportional

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substitute the values in the proportion

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