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3 years ago

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The lighthouse on the beach casts a shadow that is 4848 feet long. Your friend is 5.55.5 feet tall and casts a shadow that is 2.

22.2 feet long. What is the height of the lighthouse?

2 answers:

astraxan [27]3 years ago

6 0

Check the picture below.

zhuklara [117]3 years ago

3 0

I think it's ...................
Let H = height of the lighthouse
5.5/2.2 = H/48
5/2 = H/48
H = 5*48/2 = 120 feet
Hope this helped ☺

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A: 300 B: Malorie

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1 year ago

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Eduardwww [97]

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$x^8 - \dfrac1{81} = \left(x^2\right)^4 - \left(\dfrac13\right)^4 \\\\ x^8 - \dfrac1{81} = \left(\left(x^2\right)^2 - \left(\dfrac13\right)^2\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)$

Depending on the precise definition of "completely" in this context, you can go a bit further and factorize $x^2-\frac13$ as yet another difference of squares:

$x^2 - \dfrac13 = x^2 - \left(\dfrac1{\sqrt3}\right)^2 = \left(x-\dfrac1{\sqrt3}\right)\left(x+\dfrac1{\sqrt3}\right)$

And if you're working over the field of complex numbers, you can go even further. For instance,

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But I think you'd be fine stopping at the first result,

$x^8 - \dfrac1{81} = \boxed{\left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)}$

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