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lakinbacon4

lakinbacon4

12.08.2020 •

Mathematics

A student who is 5 1/4 feet tall has a shadow that is 2 feet and 10 1/2 inches long. At the same time. a flag pole has a shadow that is 10 1/2 feel long. How tall, to the nearest inch, is the flag pole?

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Ответ:

fosofallout46521

31.01.2022

The height of the flag pole is approximately 19 feet and 2 inches.

Step-by-step explanation:

Let suppose that length of the shadow of the object is directly proportional to its height. Hence:

$l \propto h$

$l = k\cdot h$

Where:

- Height of the object, measured in inches.

- Shadow length of the object, measured in inches.

- Proportionality constant, dimensionless.

Now, let is find the value of the proportionality constant: ( $h = 5\,\frac{1}{4} \,ft$ and $l = 2\,ft\,\,10\,\frac{1}{2}\,in$ )

$h = \frac{21}{4}\,ft$

$h = \left(\frac{21}{4}\,ft \right)\cdot \left(12\,\frac{in}{ft} \right)$

$h = 63\,in$

$l = (2\,ft)\cdot \left(12\,\frac{in}{ft} \right) + \frac{21}{2}\,in$

$l = 24\,in + \frac{21}{2}\,in$

$l = \frac{48}{2}\,in+\frac{21}{2}\,in$

$l = \frac{69}{2}\,in$

Then,

$k = \frac{l}{h}$

$k = \frac{\frac{69}{2}\,in }{63\,in}$

$k = \frac{69}{126}$

$k = \frac{23}{42}$

The equation is represented by $l = \frac{23}{42}\cdot h$ . If $l = 10\,\frac{1}{2}\,ft$ , then:

$l = \frac{21}{2}\,ft$

$l = \left(\frac{21}{2}\,ft \right)\cdot \left(12\,\frac{in}{ft} \right)$

$l = 126\,in$

The height of the flag pole is: ( $l = 126\,in$ , $k = \frac{23}{42}$ )

$h = \frac{l}{k}$

$h = \frac{126\,in}{\frac{23}{42} }$

$h = \frac{5292}{23}\,in$

$h = 230\,\frac{2}{23}\,in$

$h = \frac{115}{6}\,ft\,\frac{2}{23}\,in$

$h = 19\,\frac{1}{6}\,ft \,\frac{2}{23}\,in$

$h = 19\,ft\,\,2\,\frac{2}{23}\,in$

$h = 19\,ft\,\,2\,in$

The height of the flag pole is approximately 19 feet and 2 inches.

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Ответ:

juliannabartra

21.11.2022

sans from undertale

Step-by-step explanation:

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