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2 years ago

14

A person standing 20 feet from a streetlight casts a shadow as shown. How many times taller is the streetlight than the person?

Assume the triangles are similar.

1 answer:

Xelga [282]2 years ago

6 0

Answer:

2 times taller.

Step-by-step explanation

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Answer:

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Step-by-step explanation:

The objective is to state whether or not the following limit exists

$\lim_{x \to -2} \frac{3(2x-1)^2 - 75}{x+2}$ .

First, we simplify the expression in the numerator of the fraction.

$3(2x-1)^2 -75 = 3(4x^2 - 4x +1) -75 = 12x^2 - 12x + 3 - 75 = 12x^2 - 12x -72$

Now, we obtain

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and the fraction is transformed into

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Therefore, the following limit is

$\lim_{x \to -2} \frac{3(2x-1)^2 - 75}{x+2} = \lim_{x \to -2} 12(x-3) = 12 \lim_{x \to -2} (x-3)$

You can plug in $-2$ in the equation, hence

$12 \lim_{x \to -2} (x-3) = 12 (-2-3) = -60$

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