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# HEEEEELP

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Suppose $$f(x),g(x),h(x)$$ are all linear functions, and $$j(x)$$ and $$k(x)$$ are defined by

$$j(x) = \max\{f(x),g(x),h(x)\},$$

$$k(x) = \min\{f(x),g(x),h(x)\}.$$

This means that, for each $$x$$, we define $$j(x)$$ to be equal to either $$f(x), g(x)$$  or $$h(x)$$ whichever is greatest; similarly, $$k(x)$$ is the least of these three values.

Shown below is the graph of $$y=j(x)$$ for $$-3.5\le x\le 3.5$$.

Let $$\ell$$ be the length of the graph of $$y=k(x)$$ for $$-3.5\le x\le 3.5$$. What is the value of $$\ell^2$$?

It is not 49.

Graph:

Jul 8, 2020
edited by BillyBobJoeJr  Jul 8, 2020

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Where is the graph?

Jul 8, 2020
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oops sorry

BillyBobJoeJr  Jul 8, 2020
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$$\overline{FG}=\sqrt{3.5^2+7^2}\\ \overline{FGE}=2\sqrt{3.5^2+7^2}\\ [\overline{FGE}]^2=4(3.5^2+7^2)\\ [\overline{FGE}]^2=245\\ l^2=245$$

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Jul 9, 2020
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It was correct, thank you so much

BillyBobJoeJr  Jul 10, 2020