Prove

Question

Prove

mathmath333 · Answer

$\large \color{black}{\begin{align} & \normalsize \text{Prove the area of the region enclosed by the graph }\hspace{.33em}\~\ 
& y=-|x\pm k|+5,y=0\hspace{.33em}\~\
& \normalsize \text{ is constant for} \ \ k,\ k\in \mathbb{R}\ \hspace{.33em}\~\ 

\end{align}}$

ganeshie8 · Answer

I'm finding it hard to visualize... could you show the area in graph ?

mathmath333 · Answer

https://www.desmos.com/calculator/ylkcvfm5ss

ganeshie8 · Answer

Ahh that should be easy

ganeshie8 · Answer

First of all, we acknowledge that the the absolute value gives the distance between two points on number line:

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perl · Answer

You can prove it using calculus. The integral of that is constant.

ganeshie8 · Answer

In light that of above thing, $|x-k|$ represents the distance between $x$ and $k$.

ganeshie8 · Answer

Set the given function equal to $0$ and solve $x$ intercepts :
$$-|x-k|+5=0 \implies |x-k|=5$$

mathmath333 · Answer

x=5+k.-5+k

ganeshie8 · Answer

Yes, subtract them to get the base of triangle

mathmath333 · Answer

base->10

ganeshie8 · Answer

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